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It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.0742797864368185e-05, "probability_ratio_vs_uniform": 1.2222839359310456, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. 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Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.0742797864368185e-05, "probability_ratio_vs_uniform": 1.2222839359310456, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.0742797864368185e-05, "probability_ratio_vs_uniform": 1.2222839359310456, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 235, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 9, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourist", "answer_preview": "62", "source": "math", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.086150147486478e-05, "probability_ratio_vs_uniform": 1.2258450442459434, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 240, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 9, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourist", "answer_preview": "62", "source": "math", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.09875538025517e-05, "probability_ratio_vs_uniform": 1.229626614076551, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 245, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 9, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourist", "answer_preview": "62", "source": "math", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1116443753708154e-05, "probability_ratio_vs_uniform": 1.2334933126112446, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 250, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 9, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourist", "answer_preview": "62", "source": "math", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1234929085476324e-05, "probability_ratio_vs_uniform": 1.2370478725642897, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 255, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 9, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourist", "answer_preview": "62", "source": "math", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1368650272488594e-05, "probability_ratio_vs_uniform": 1.2410595081746578, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 260, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 9, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "Two tour guides are leading six tourists. The guides decide to split up. Each tourist must choose one of the guides, but with the stipulation that each guide must take at least one tourist. How many different groupings of guides and tourist", "answer_preview": "62", "source": "math", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1488809074508026e-05, "probability_ratio_vs_uniform": 1.2446642722352408, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 265, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.161437027505599e-05, "probability_ratio_vs_uniform": 1.2484311082516797, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}]}
{"global_step": 270, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.173977504251525e-05, "probability_ratio_vs_uniform": 1.2521932512754574, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}]}
{"global_step": 275, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 18, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "Apollo pulls the sun across the sky every night. Once a month, his fiery chariot\u2019s wheels need to be replaced. He trades golden apples to three different blacksmiths to get them to make him new wheels.   Hephaestus charged three golden appl", "answer_preview": "265", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.1862167563522235e-05, "probability_ratio_vs_uniform": 1.255865026905667, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}]}
{"global_step": 280, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 25, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2001141991931945e-05, "probability_ratio_vs_uniform": 1.2600342597579584, "seen": 0, "prompt_preview": "Danny collects bottle caps. He threw away 60 of the old ones at the park and found 58 new ones. He also traded 15 of his bottle caps with his friends, receiving 25 bottle caps in return. Now he has 67 bottle caps in his collection. How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}]}
{"global_step": 285, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 25, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.211923442198895e-05, "probability_ratio_vs_uniform": 1.2635770326596685, "seen": 0, "prompt_preview": "Danny collects bottle caps. He threw away 60 of the old ones at the park and found 58 new ones. He also traded 15 of his bottle caps with his friends, receiving 25 bottle caps in return. Now he has 67 bottle caps in his collection. How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}]}
{"global_step": 290, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 25, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2242641939083114e-05, "probability_ratio_vs_uniform": 1.2672792581724934, "seen": 0, "prompt_preview": "Danny collects bottle caps. He threw away 60 of the old ones at the park and found 58 new ones. He also traded 15 of his bottle caps with his friends, receiving 25 bottle caps in return. Now he has 67 bottle caps in his collection. How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}]}
{"global_step": 295, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 25, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.235606320435181e-05, "probability_ratio_vs_uniform": 1.2706818961305544, "seen": 0, "prompt_preview": "Danny collects bottle caps. He threw away 60 of the old ones at the park and found 58 new ones. He also traded 15 of his bottle caps with his friends, receiving 25 bottle caps in return. Now he has 67 bottle caps in his collection. How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}]}
{"global_step": 300, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 16, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "Jackson had 20 kilograms of meat. He used 1/4 of the meat to make meatballs, 15% of the remaining meat to make spring rolls, and 2 pounds of meat to prepare a stew. After that, he used 10% of the leftover meat to make kebabs. How many kilog", "answer_preview": "10.66", "source": "orca_math", "last_feedback": null}, {"sample_id": 19, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "Determine the smallest possible value of the expression  $$ \\frac{a b+1}{a+b}+\\frac{b c+1}{b+c}+\\frac{c a+1}{c+a} $$  where \\(a, b, c \\in \\mathbb{R}\\) satisfy \\(a+b+c=-1\\) and \\(a b c \\leq -3\\).", "answer_preview": "3", "source": "olympiads", "last_feedback": null}, {"sample_id": 21, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "Peter has 18 oranges, 27 pears, and some bananas. He wants to make fruit baskets with the same number of each fruit in each basket. The greatest number of fruit baskets he can make is 3. How many bananas does Peter have?", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 25, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.248783443472348e-05, "probability_ratio_vs_uniform": 1.2746350330417044, "seen": 0, "prompt_preview": "Danny collects bottle caps. He threw away 60 of the old ones at the park and found 58 new ones. He also traded 15 of his bottle caps with his friends, receiving 25 bottle caps in return. Now he has 67 bottle caps in his collection. How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}]}
{"global_step": 305, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2613988625817e-05, "probability_ratio_vs_uniform": 1.27841965877451, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2613988625817e-05, "probability_ratio_vs_uniform": 1.27841965877451, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2613988625817e-05, "probability_ratio_vs_uniform": 1.27841965877451, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2613988625817e-05, "probability_ratio_vs_uniform": 1.27841965877451, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2613988625817e-05, "probability_ratio_vs_uniform": 1.27841965877451, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. 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How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2613988625817e-05, "probability_ratio_vs_uniform": 1.27841965877451, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}]}
{"global_step": 310, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.27349514211528e-05, "probability_ratio_vs_uniform": 1.282048542634584, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.27349514211528e-05, "probability_ratio_vs_uniform": 1.282048542634584, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.27349514211528e-05, "probability_ratio_vs_uniform": 1.282048542634584, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. 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{"global_step": 315, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.286081821192056e-05, "probability_ratio_vs_uniform": 1.2858245463576168, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.286081821192056e-05, "probability_ratio_vs_uniform": 1.2858245463576168, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. 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{"global_step": 320, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2977069824701175e-05, "probability_ratio_vs_uniform": 1.2893120947410353, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.2977069824701175e-05, "probability_ratio_vs_uniform": 1.2893120947410353, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. 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{"global_step": 325, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 25, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "Danny collects bottle caps. He threw away 60 of the old ones at the park and found 58 new ones. He also traded 15 of his bottle caps with his friends, receiving 25 bottle caps in return. Now he has 67 bottle caps in his collection. How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.309951691539027e-05, "probability_ratio_vs_uniform": 1.292985507461708, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}]}
{"global_step": 330, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.322077802498825e-05, "probability_ratio_vs_uniform": 1.2966233407496475, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.322077802498825e-05, "probability_ratio_vs_uniform": 1.2966233407496475, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. 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The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.322077802498825e-05, "probability_ratio_vs_uniform": 1.2966233407496475, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. 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Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.322077802498825e-05, "probability_ratio_vs_uniform": 1.2966233407496475, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}]}
{"global_step": 335, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.334066034061834e-05, "probability_ratio_vs_uniform": 1.3002198102185503, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.334066034061834e-05, "probability_ratio_vs_uniform": 1.3002198102185503, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. 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Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.334066034061834e-05, "probability_ratio_vs_uniform": 1.3002198102185503, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}]}
{"global_step": 340, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.3468811782076955e-05, "probability_ratio_vs_uniform": 1.3040643534623086, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.3468811782076955e-05, "probability_ratio_vs_uniform": 1.3040643534623086, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. 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If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.3468811782076955e-05, "probability_ratio_vs_uniform": 1.3040643534623086, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. 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Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.3468811782076955e-05, "probability_ratio_vs_uniform": 1.3040643534623086, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}]}
{"global_step": 345, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.359294325695373e-05, "probability_ratio_vs_uniform": 1.307788297708612, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.359294325695373e-05, "probability_ratio_vs_uniform": 1.307788297708612, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.359294325695373e-05, "probability_ratio_vs_uniform": 1.307788297708612, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.359294325695373e-05, "probability_ratio_vs_uniform": 1.307788297708612, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.359294325695373e-05, "probability_ratio_vs_uniform": 1.307788297708612, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. 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Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.359294325695373e-05, "probability_ratio_vs_uniform": 1.307788297708612, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}]}
{"global_step": 350, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.371965042082593e-05, "probability_ratio_vs_uniform": 1.3115895126247779, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.371965042082593e-05, "probability_ratio_vs_uniform": 1.3115895126247779, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.371965042082593e-05, "probability_ratio_vs_uniform": 1.3115895126247779, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.371965042082593e-05, "probability_ratio_vs_uniform": 1.3115895126247779, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. 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{"global_step": 355, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.385359716252424e-05, "probability_ratio_vs_uniform": 1.3156079148757271, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.385359716252424e-05, "probability_ratio_vs_uniform": 1.3156079148757271, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. 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If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.399094177642837e-05, "probability_ratio_vs_uniform": 1.3197282532928512, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. 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What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 25, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.399094177642837e-05, "probability_ratio_vs_uniform": 1.3197282532928512, "seen": 0, "prompt_preview": "Danny collects bottle caps. He threw away 60 of the old ones at the park and found 58 new ones. He also traded 15 of his bottle caps with his friends, receiving 25 bottle caps in return. Now he has 67 bottle caps in his collection. How many", "answer_preview": "59", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.399094177642837e-05, "probability_ratio_vs_uniform": 1.3197282532928512, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.399094177642837e-05, "probability_ratio_vs_uniform": 1.3197282532928512, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.399094177642837e-05, "probability_ratio_vs_uniform": 1.3197282532928512, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}]}
{"global_step": 365, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.413157876115292e-05, "probability_ratio_vs_uniform": 1.3239473628345877, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.413157876115292e-05, "probability_ratio_vs_uniform": 1.3239473628345877, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.413157876115292e-05, "probability_ratio_vs_uniform": 1.3239473628345877, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.413157876115292e-05, "probability_ratio_vs_uniform": 1.3239473628345877, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.413157876115292e-05, "probability_ratio_vs_uniform": 1.3239473628345877, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.413157876115292e-05, "probability_ratio_vs_uniform": 1.3239473628345877, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. 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Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.413157876115292e-05, "probability_ratio_vs_uniform": 1.3239473628345877, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}]}
{"global_step": 370, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.4270502257859334e-05, "probability_ratio_vs_uniform": 1.32811506773578, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.4270502257859334e-05, "probability_ratio_vs_uniform": 1.32811506773578, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. The schoolchild who gathered the most mushrooms collected \\( \\frac{1}{5} \\) of the total amount of mushrooms, while the one who gathered the least collected \\( \\frac{1}{7} \\) of the total amount", "answer_preview": "6", "source": "olympiads", "last_feedback": null}, {"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.4270502257859334e-05, "probability_ratio_vs_uniform": 1.32811506773578, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.4270502257859334e-05, "probability_ratio_vs_uniform": 1.32811506773578, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. 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Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 33, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.4270502257859334e-05, "probability_ratio_vs_uniform": 1.32811506773578, "seen": 0, "prompt_preview": "Calculate the sum of the squares of the numbers 17, 19, 23, and 29. Express your answer as a single integer.", "answer_preview": "2020", "source": "big_math", "last_feedback": null}, {"sample_id": 35, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.4270502257859334e-05, "probability_ratio_vs_uniform": 1.32811506773578, "seen": 0, "prompt_preview": "Samantha bought 8 packages of cat food, 5 packages of dog food, and 3 packages of bird food. Each package of cat food contained 12 cans, each package of dog food contained 7 cans, and each package of bird food contained 4 cans. If she gave ", "answer_preview": "9", "source": "orca_math", "last_feedback": null}]}
{"global_step": 375, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 4, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.439345866558142e-05, "probability_ratio_vs_uniform": 1.3318037599674426, "seen": 0, "prompt_preview": "Given $$\\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \\_\\_\\_\\_\\_.", "answer_preview": "1", "source": "cn_k12", "last_feedback": null}, {"sample_id": 5, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.439345866558142e-05, "probability_ratio_vs_uniform": 1.3318037599674426, "seen": 0, "prompt_preview": "Several schoolchildren went mushroom picking. 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{"global_step": 445, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.637029269360937e-05, "probability_ratio_vs_uniform": 1.3911087808082812, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. 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{"global_step": 450, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.6517594455508515e-05, "probability_ratio_vs_uniform": 1.3955278336652555, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. 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{"global_step": 460, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.679012272390537e-05, "probability_ratio_vs_uniform": 1.403703681717161, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. 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What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8320216592401266e-05, "probability_ratio_vs_uniform": 1.449606497772038, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 515, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 6, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "At a university banquet, there are 2017 mathematicians, each with a menu that includes two different main courses, and no two mathematicians have the same pair of main courses. The price of each main course is equal to the number of mathema", "answer_preview": "127010", "source": "olympiads", "last_feedback": null}, {"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 37, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Find the length of their common chord. Express your answer as a single number.", "answer_preview": "10", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.850132972933352e-05, "probability_ratio_vs_uniform": 1.4550398918800056, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 520, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 37, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Find the length of their common chord. Express your answer as a single number.", "answer_preview": "10", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.868447285844013e-05, "probability_ratio_vs_uniform": 1.460534185753204, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}]}
{"global_step": 525, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 37, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Find the length of their common chord. Express your answer as a single number.", "answer_preview": "10", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.8856618377612904e-05, "probability_ratio_vs_uniform": 1.4656985513283871, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}]}
{"global_step": 530, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 37, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Find the length of their common chord. Express your answer as a single number.", "answer_preview": "10", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.903660374111496e-05, "probability_ratio_vs_uniform": 1.4710981122334488, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}]}
{"global_step": 535, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 37, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "Two circles with radii 13 and 5 intersect, and the distance between their centers is 12. Find the length of their common chord. Express your answer as a single number.", "answer_preview": "10", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.922086009173654e-05, "probability_ratio_vs_uniform": 1.4766258027520962, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}]}
{"global_step": 540, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.936906771035865e-05, "probability_ratio_vs_uniform": 1.4810720313107595, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}]}
{"global_step": 545, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.954369433107786e-05, "probability_ratio_vs_uniform": 1.4863108299323358, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}]}
{"global_step": 550, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 23, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "a is the average (arithmetic mean) of the first 7 positive multiples of 8 and b is the median of the first 3 positive multiples of a certain positive integer. The value of a^2 - b^2 is zero. What is the value of that positive integer?", "answer_preview": "16", "source": "orca_math", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9689580919221044e-05, "probability_ratio_vs_uniform": 1.4906874275766313, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}]}
{"global_step": 555, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 4.9849681090563536e-05, "probability_ratio_vs_uniform": 1.495490432716906, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}]}
{"global_step": 560, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.003464320907369e-05, "probability_ratio_vs_uniform": 1.5010392962722108, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}]}
{"global_step": 565, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.022006735089235e-05, "probability_ratio_vs_uniform": 1.5066020205267705, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}]}
{"global_step": 570, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0403941713739187e-05, "probability_ratio_vs_uniform": 1.5121182514121756, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}]}
{"global_step": 575, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.056562804384157e-05, "probability_ratio_vs_uniform": 1.5169688413152471, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}]}
{"global_step": 580, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 31, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "Given that \\( x \\) and \\( y \\) are real numbers such that \\( |x| + x + y = 10 \\) and \\( |y| + x - y = 10 \\), if \\( P = x + y \\), find the value of \\( P \\).", "answer_preview": "4", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.07057920913212e-05, "probability_ratio_vs_uniform": 1.521173762739636, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}]}
{"global_step": 585, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 59, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.0886530516436324e-05, "probability_ratio_vs_uniform": 1.5265959154930897, "seen": 0, "prompt_preview": "There are 12 students playing a card game where each game involves 4 players, and any two students play together at most once. What is the maximum number of games they can play?", "answer_preview": "9", "source": "olympiads", "last_feedback": null}]}
{"global_step": 590, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 47, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "Find the smallest positive angle $x$ that satisfies $\\sin 2x \\sin 3x = \\cos 2x \\cos 3x,$ in degrees.", "answer_preview": "18", "source": "openmath", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 59, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1067596359644085e-05, "probability_ratio_vs_uniform": 1.5320278907893226, "seen": 0, "prompt_preview": "There are 12 students playing a card game where each game involves 4 players, and any two students play together at most once. What is the maximum number of games they can play?", "answer_preview": "9", "source": "olympiads", "last_feedback": null}]}
{"global_step": 595, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 59, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "There are 12 students playing a card game where each game involves 4 players, and any two students play together at most once. What is the maximum number of games they can play?", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1254166464786977e-05, "probability_ratio_vs_uniform": 1.5376249939436093, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}]}
{"global_step": 600, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 59, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "There are 12 students playing a card game where each game involves 4 players, and any two students play together at most once. What is the maximum number of games they can play?", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.145749310031533e-05, "probability_ratio_vs_uniform": 1.54372479300946, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}]}
{"global_step": 605, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 13, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "At a dog show, each dog was assigned an ordinal number from 1 to 24 by lot. Due to health issues, one of the dogs could not participate in the competition. It turned out that among the remaining 23 dogs, one had a number equal to the arithm", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1660710596479475e-05, "probability_ratio_vs_uniform": 1.5498213178943843, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}]}
{"global_step": 610, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.1878105296054855e-05, "probability_ratio_vs_uniform": 1.5563431588816456, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}]}
{"global_step": 615, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 32, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "Given the function f(x) = x(2017 + ln(x))e, where e is the base of the natural logarithm, find the value of x_0 such that f'(x_0) = 2018. Express your answer as a single numerical value.", "answer_preview": "1", "source": "big_math", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.204887565923855e-05, "probability_ratio_vs_uniform": 1.5614662697771564, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}]}
{"global_step": 620, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 39, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "Consider all prisms whose base is a convex 2015-gon.  What is the maximum number of edges of such a prism that can be intersected by a plane not passing through its vertices?", "answer_preview": "2017", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.222478648647666e-05, "probability_ratio_vs_uniform": 1.5667435945942998, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}]}
{"global_step": 625, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.2429601055337116e-05, "probability_ratio_vs_uniform": 1.5728880316601135, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 630, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.263385173748247e-05, "probability_ratio_vs_uniform": 1.5790155521244742, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 635, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.284638245939277e-05, "probability_ratio_vs_uniform": 1.5853914737817831, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 640, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.3049134294269606e-05, "probability_ratio_vs_uniform": 1.5914740288280882, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 645, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.324714948073961e-05, "probability_ratio_vs_uniform": 1.5974144844221883, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 650, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.344855890143663e-05, "probability_ratio_vs_uniform": 1.6034567670430988, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 655, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.369803329813294e-05, "probability_ratio_vs_uniform": 1.6109409989439882, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 660, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.390363367041573e-05, "probability_ratio_vs_uniform": 1.6171090101124719, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 665, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 61, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "A number, when divided by 44, gives 432 as quotient and a certain remainder. When dividing the same number by 31, the remainder is 5. What is the remainder when the number is divided by 44?", "answer_preview": "2", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.40915279998444e-05, "probability_ratio_vs_uniform": 1.622745839995332, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}]}
{"global_step": 670, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.430935198091902e-05, "probability_ratio_vs_uniform": 1.6292805594275706, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}]}
{"global_step": 675, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 73, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "Three cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, the black car is traveling at a varying speed of Y miles per hour, and the green car is traveling at a consta", "answer_preview": "53.33", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.448601223179139e-05, "probability_ratio_vs_uniform": 1.6345803669537418, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}]}
{"global_step": 680, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.469435200211592e-05, "probability_ratio_vs_uniform": 1.6408305600634776, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}]}
{"global_step": 685, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.488053648150526e-05, "probability_ratio_vs_uniform": 1.6464160944451578, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}]}
{"global_step": 690, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 44, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "We successively write all the numbers from 1 to one million. Then, we replace each number with the sum of its digits. We repeat this process until only single-digit numbers remain. Which single-digit number appears most frequently?", "answer_preview": "1", "source": "olympiads", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.508599861059338e-05, "probability_ratio_vs_uniform": 1.6525799583178014, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}]}
{"global_step": 695, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 123, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.531894203159027e-05, "probability_ratio_vs_uniform": 1.659568260947708, "seen": 0, "prompt_preview": "Given real numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 = 20 \\). Find the maximum value of \\( xy + 8x + y \\).", "answer_preview": "42", "source": "olympiads", "last_feedback": null}]}
{"global_step": 700, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 68, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "How many monomials of degree 7 contain the letters a, b, and c, and have a coefficient of 1? Express your answer as a whole number.", "answer_preview": "15", "source": "big_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 123, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.552502261707559e-05, "probability_ratio_vs_uniform": 1.6657506785122678, "seen": 0, "prompt_preview": "Given real numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 = 20 \\). Find the maximum value of \\( xy + 8x + y \\).", "answer_preview": "42", "source": "olympiads", "last_feedback": null}]}
{"global_step": 705, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. Calculate the number of possible distributions of these spots among the three classes.", "answer_preview": "36", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 123, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "Given real numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 = 20 \\). Find the maximum value of \\( xy + 8x + y \\).", "answer_preview": "42", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.5796663218643516e-05, "probability_ratio_vs_uniform": 1.6738998965593055, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}]}
{"global_step": 710, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. 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Find the maximum value of \\( xy + 8x + y \\).", "answer_preview": "42", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6054013839457184e-05, "probability_ratio_vs_uniform": 1.6816204151837155, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}]}
{"global_step": 715, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 79, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "There are 10 \"Triple-A Student\" quota spots to be divided among three classes A, B, and C, with each class getting at least one spot. 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Find the maximum value of \\( xy + 8x + y \\).", "answer_preview": "42", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.623503966489807e-05, "probability_ratio_vs_uniform": 1.687051189946942, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}]}
{"global_step": 720, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 123, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "Given real numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 = 20 \\). Find the maximum value of \\( xy + 8x + y \\).", "answer_preview": "42", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6461438362021e-05, "probability_ratio_vs_uniform": 1.69384315086063, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}]}
{"global_step": 725, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 123, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "Given real numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 = 20 \\). Find the maximum value of \\( xy + 8x + y \\).", "answer_preview": "42", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.6693410442676395e-05, "probability_ratio_vs_uniform": 1.7008023132802919, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}]}
{"global_step": 730, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.692130798706785e-05, "probability_ratio_vs_uniform": 1.7076392396120355, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 735, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.712141137337312e-05, "probability_ratio_vs_uniform": 1.7136423412011936, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 740, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.735268860007636e-05, "probability_ratio_vs_uniform": 1.7205806580022909, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 745, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7631685194792226e-05, "probability_ratio_vs_uniform": 1.7289505558437668, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 750, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.7904770073946565e-05, "probability_ratio_vs_uniform": 1.737143102218397, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 755, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.812929157400504e-05, "probability_ratio_vs_uniform": 1.7438787472201511, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 760, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.839727236889303e-05, "probability_ratio_vs_uniform": 1.7519181710667908, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 765, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.8672096201917157e-05, "probability_ratio_vs_uniform": 1.7601628860575147, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 770, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.891824184800498e-05, "probability_ratio_vs_uniform": 1.7675472554401495, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 775, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.916185546084307e-05, "probability_ratio_vs_uniform": 1.7748556638252921, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 780, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9379144659033045e-05, "probability_ratio_vs_uniform": 1.7813743397709914, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 785, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 131, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "How many airplanes? (From the 11th grade, 8 points)  The Absent-minded Scientist's work involves long business trips, and therefore he often flies with the same airline. This airline has many identical airplanes, and they all have names. Si", "answer_preview": "134", "source": "olympiads", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.966535536572337e-05, "probability_ratio_vs_uniform": 1.7899606609717011, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}]}
{"global_step": 790, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 12, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "The foci of the ellipse $\\frac{x^{2}}{5^{2}}+\\frac{y^{2}}{3^{2}}=1$ are $F_{1}$ and $F_{2}$. If a point $P$ on the ellipse makes $P F_{1} \\perp P F_{2}$, find the area of the triangle $\\triangle P F_{1} F_{2}$.", "answer_preview": "9", "source": "olympiads", "last_feedback": null}, {"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 5.9956924815196544e-05, "probability_ratio_vs_uniform": 1.7987077444558963, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}]}
{"global_step": 795, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. 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If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 76, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "The highest common factors of all the pairs chosen from the positive integers Q, R, and S are three different primes. What is the smallest possible value of Q + R + S? Express your answer as a single integer.", "answer_preview": "31", "source": "big_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 170, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.0228179791010916e-05, "probability_ratio_vs_uniform": 1.8068453937303275, "seen": 0, "prompt_preview": "\\(\\frac{\\sin 6 \\alpha}{\\sin 2 \\alpha} + \\frac{\\cos (6 \\alpha - \\pi)}{\\cos 2 \\alpha}\\).", "answer_preview": "2", "source": "olympiads", "last_feedback": null}]}
{"global_step": 800, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.049884177627973e-05, "probability_ratio_vs_uniform": 1.814965253288392, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}]}
{"global_step": 805, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.071883035474457e-05, "probability_ratio_vs_uniform": 1.821564910642337, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}]}
{"global_step": 810, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.098623634898104e-05, "probability_ratio_vs_uniform": 1.8295870904694311, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}]}
{"global_step": 815, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. What is the smallest possible value of $N$?", "answer_preview": "80", "source": "olympiads", "last_feedback": null}, {"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 56, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.124365609139204e-05, "probability_ratio_vs_uniform": 1.8373096827417612, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}]}
{"global_step": 820, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. 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If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 97, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "Find the ratio \\(\\frac{S_1}{S_2}\\), where  \\[ S_1 = \\frac{1}{2^{18}} + \\frac{1}{2^{17}} - \\frac{1}{2^{16}} + \\ldots + \\frac{1}{2^3} + \\frac{1}{2^2} - \\frac{1}{2}, \\]  \\[ S_2 = \\frac{1}{2} + \\frac{1}{2^2} - \\frac{1}{2^3} + \\ldots + \\frac{1}{", "answer_preview": "0.2", "source": "olympiads", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.148147804196924e-05, "probability_ratio_vs_uniform": 1.8444443412590772, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}]}
{"global_step": 825, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.177358591230586e-05, "probability_ratio_vs_uniform": 1.8532075773691759, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. 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David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.177358591230586e-05, "probability_ratio_vs_uniform": 1.8532075773691759, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.177358591230586e-05, "probability_ratio_vs_uniform": 1.8532075773691759, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.177358591230586e-05, "probability_ratio_vs_uniform": 1.8532075773691759, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? 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{"global_step": 830, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.207612750586122e-05, "probability_ratio_vs_uniform": 1.8622838251758367, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. 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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.207612750586122e-05, "probability_ratio_vs_uniform": 1.8622838251758367, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.207612750586122e-05, "probability_ratio_vs_uniform": 1.8622838251758367, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? 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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.229318387340754e-05, "probability_ratio_vs_uniform": 1.8687955162022263, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.229318387340754e-05, "probability_ratio_vs_uniform": 1.8687955162022263, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? 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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.301216490101069e-05, "probability_ratio_vs_uniform": 1.8903649470303208, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 151, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.301216490101069e-05, "probability_ratio_vs_uniform": 1.8903649470303208, "seen": 0, "prompt_preview": "What is the largest integer \\( n \\) such that the quantity \\[ \\frac{50!}{(5!)^{n}} \\] is an integer? Note: Here \\( k! = 1 \\times 2 \\times 3 \\times \\cdots \\times k \\) is the product of all integers from 1 to \\( k \\). For example, \\( 4! = 1 \\", "answer_preview": "12", "source": "olympiads", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.301216490101069e-05, "probability_ratio_vs_uniform": 1.8903649470303208, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.301216490101069e-05, "probability_ratio_vs_uniform": 1.8903649470303208, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.301216490101069e-05, "probability_ratio_vs_uniform": 1.8903649470303208, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}]}
{"global_step": 855, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. 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If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?", "answer_preview": "12", "source": "orca_math", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 191, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.322973786154762e-05, "probability_ratio_vs_uniform": 1.8968921358464286, "seen": 0, "prompt_preview": "Calculate the value of \\\\(\\\\tan 15^{\\\\circ} + \\\\cot 15^{\\\\circ}\\\\). Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}]}
{"global_step": 860, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 40, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.348383612930775e-05, "probability_ratio_vs_uniform": 1.9045150838792324, "seen": 0, "prompt_preview": "Grandma baked 21 batches of pies with $N$ pies in each batch, where $N > 70$. Then she distributed all the pies onto several trays, with 70 pies on each tray. 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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.348383612930775e-05, "probability_ratio_vs_uniform": 1.9045150838792324, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.348383612930775e-05, "probability_ratio_vs_uniform": 1.9045150838792324, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). 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Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}]}
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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.37723715044558e-05, "probability_ratio_vs_uniform": 1.9131711451336741, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.37723715044558e-05, "probability_ratio_vs_uniform": 1.9131711451336741, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). 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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.518572627101094e-05, "probability_ratio_vs_uniform": 1.955571788130328, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.518572627101094e-05, "probability_ratio_vs_uniform": 1.955571788130328, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). 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Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.565239164046943e-05, "probability_ratio_vs_uniform": 1.969571749214083, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}]}
{"global_step": 900, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.602607754757628e-05, "probability_ratio_vs_uniform": 1.9807823264272884, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.602607754757628e-05, "probability_ratio_vs_uniform": 1.9807823264272884, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. 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Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}]}
{"global_step": 905, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.634302553720772e-05, "probability_ratio_vs_uniform": 1.9902907661162317, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.634302553720772e-05, "probability_ratio_vs_uniform": 1.9902907661162317, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. 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Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.634302553720772e-05, "probability_ratio_vs_uniform": 1.9902907661162317, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.634302553720772e-05, "probability_ratio_vs_uniform": 1.9902907661162317, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}]}
{"global_step": 910, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 191, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "Calculate the value of \\\\(\\\\tan 15^{\\\\circ} + \\\\cot 15^{\\\\circ}\\\\). Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.661032239207998e-05, "probability_ratio_vs_uniform": 1.9983096717623994, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}]}
{"global_step": 915, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 191, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "Calculate the value of \\\\(\\\\tan 15^{\\\\circ} + \\\\cot 15^{\\\\circ}\\\\). Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.694539479212835e-05, "probability_ratio_vs_uniform": 2.0083618437638506, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}]}
{"global_step": 920, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 191, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "Calculate the value of \\\\(\\\\tan 15^{\\\\circ} + \\\\cot 15^{\\\\circ}\\\\). Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.727879372192547e-05, "probability_ratio_vs_uniform": 2.018363811657764, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}]}
{"global_step": 925, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 124, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "Suppose that  $x$  is measured in radians. Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 173, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).", "answer_preview": "15", "source": "olympiads", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 191, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "Calculate the value of \\\\(\\\\tan 15^{\\\\circ} + \\\\cot 15^{\\\\circ}\\\\). Express your answer as a single number.", "answer_preview": "4", "source": "big_math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.755127833457664e-05, "probability_ratio_vs_uniform": 2.026538350037299, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}]}
{"global_step": 930, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. 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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.791192572563887e-05, "probability_ratio_vs_uniform": 2.037357771769166, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}]}
{"global_step": 935, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. 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Find the maximum value of \\[\\frac{\\sin2x+\\sin4x+\\sin6x}{\\cos2x+\\cos4x+\\cos6x}\\] for  $0\\le x\\le \\frac{\\pi}{16}$", "answer_preview": "1", "source": "aops_forum", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. 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What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.825724267400801e-05, "probability_ratio_vs_uniform": 2.0477172802202404, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}]}
{"global_step": 940, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.873367965454236e-05, "probability_ratio_vs_uniform": 2.0620103896362707, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.873367965454236e-05, "probability_ratio_vs_uniform": 2.0620103896362707, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. 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Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.873367965454236e-05, "probability_ratio_vs_uniform": 2.0620103896362707, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. 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If g(2) = 6, then g(-2) = _____.", "answer_preview": "-2", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 945, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.914533150848001e-05, "probability_ratio_vs_uniform": 2.0743599452544004, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.914533150848001e-05, "probability_ratio_vs_uniform": 2.0743599452544004, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. 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What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.914533150848001e-05, "probability_ratio_vs_uniform": 2.0743599452544004, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 382, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.914533150848001e-05, "probability_ratio_vs_uniform": 2.0743599452544004, "seen": 0, "prompt_preview": "Given that function f(x) is an odd function defined on R, g(x) = f(x) + ax^3 + 2. If g(2) = 6, then g(-2) = _____.", "answer_preview": "-2", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 950, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 223, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "Let $f(x)=x^{3}+x+1$. Suppose $g$ is a cubic polynomial such that $g(0)=-1$, and the roots of $g$ are the squares of the roots of $f$. Find $g(9)$.", "answer_preview": "899", "source": "omnimath", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 382, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.955327989999205e-05, "probability_ratio_vs_uniform": 2.0865983969997615, "seen": 0, "prompt_preview": "Given that function f(x) is an odd function defined on R, g(x) = f(x) + ax^3 + 2. If g(2) = 6, then g(-2) = _____.", "answer_preview": "-2", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 955, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 382, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "Given that function f(x) is an odd function defined on R, g(x) = f(x) + ax^3 + 2. If g(2) = 6, then g(-2) = _____.", "answer_preview": "-2", "source": "cn_k12", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 6.988216773606837e-05, "probability_ratio_vs_uniform": 2.096465032082051, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}]}
{"global_step": 960, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.022962381597608e-05, "probability_ratio_vs_uniform": 2.1068887144792825, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}]}
{"global_step": 965, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.049734995234758e-05, "probability_ratio_vs_uniform": 2.1149204985704273, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}]}
{"global_step": 970, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. He fell for an additional multiple of that depth before hitting the ground, and the platforms are evenly spaced out in height. David was on", "answer_preview": "3", "source": "orca_math", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.089637801982462e-05, "probability_ratio_vs_uniform": 2.1268913405947387, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}]}
{"global_step": 975, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.122507668100297e-05, "probability_ratio_vs_uniform": 2.1367523004300892, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 66, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.122507668100297e-05, "probability_ratio_vs_uniform": 2.1367523004300892, "seen": 0, "prompt_preview": "Walter fell from the eighth platform of some scaffolding and fell past David after falling 4 meters. 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What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.122507668100297e-05, "probability_ratio_vs_uniform": 2.1367523004300892, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.122507668100297e-05, "probability_ratio_vs_uniform": 2.1367523004300892, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.122507668100297e-05, "probability_ratio_vs_uniform": 2.1367523004300892, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}]}
{"global_step": 980, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 294, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "The numbers from 1 to 8 are arranged at the vertices of a cube so that the sum of the numbers at any three vertices lying on one face is at least 10. What is the minimal possible sum of the numbers on one face of the cube?", "answer_preview": "16", "source": "olympiads", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.160247332649305e-05, "probability_ratio_vs_uniform": 2.1480741997947916, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 985, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 487, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.196728984126821e-05, "probability_ratio_vs_uniform": 2.1590186952380463, "seen": 0, "prompt_preview": "A line passing through $(2,1)$ intersects the coordinate axes at points $A$ and $B$. The area of $\\triangle BO$ (where $O$ is the origin) is exactly $4$. Find the number of lines $l$ that satisfy the given conditions.", "answer_preview": "3", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 990, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 487, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.239009573822841e-05, "probability_ratio_vs_uniform": 2.1717028721468523, "seen": 0, "prompt_preview": "A line passing through $(2,1)$ intersects the coordinate axes at points $A$ and $B$. The area of $\\triangle BO$ (where $O$ is the origin) is exactly $4$. Find the number of lines $l$ that satisfy the given conditions.", "answer_preview": "3", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 995, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 487, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.27690348867327e-05, "probability_ratio_vs_uniform": 2.183071046601981, "seen": 0, "prompt_preview": "A line passing through $(2,1)$ intersects the coordinate axes at points $A$ and $B$. The area of $\\triangle BO$ (where $O$ is the origin) is exactly $4$. Find the number of lines $l$ that satisfy the given conditions.", "answer_preview": "3", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 1000, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 192, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "If three piles of toys added together make 240 toys in total, with the larger pile being twice the size of the smaller pile and the third pile being three times the size of the smaller pile, how many toys are in the largest pile?", "answer_preview": "120", "source": "orca_math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 487, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.312003435799852e-05, "probability_ratio_vs_uniform": 2.1936010307399556, "seen": 0, "prompt_preview": "A line passing through $(2,1)$ intersects the coordinate axes at points $A$ and $B$. The area of $\\triangle BO$ (where $O$ is the origin) is exactly $4$. Find the number of lines $l$ that satisfy the given conditions.", "answer_preview": "3", "source": "cn_k12", "last_feedback": null}]}
{"global_step": 1005, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 487, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "A line passing through $(2,1)$ intersects the coordinate axes at points $A$ and $B$. The area of $\\triangle BO$ (where $O$ is the origin) is exactly $4$. Find the number of lines $l$ that satisfy the given conditions.", "answer_preview": "3", "source": "cn_k12", "last_feedback": null}, {"sample_id": 493, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.355146954068914e-05, "probability_ratio_vs_uniform": 2.206544086220674, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math", "last_feedback": null}]}
{"global_step": 1010, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 136, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$  Find the minimum value of \\[\\frac{1}{a} + \\frac{2}{b}.\\]", "answer_preview": "9", "source": "math", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 493, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math", "last_feedback": null}, {"sample_id": 586, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.406055374303833e-05, "probability_ratio_vs_uniform": 2.22181661229115, "seen": 0, "prompt_preview": "A rectangular prism has a volume of $12 \\mathrm{~cm}^{3}$. A new prism is formed by doubling the length, doubling the width, and tripling the height of the original prism. What is the volume of this new prism?", "answer_preview": "144", "source": "omnimath", "last_feedback": null}]}
{"global_step": 1015, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 493, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math", "last_feedback": null}, {"sample_id": 586, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "A rectangular prism has a volume of $12 \\mathrm{~cm}^{3}$. A new prism is formed by doubling the length, doubling the width, and tripling the height of the original prism. What is the volume of this new prism?", "answer_preview": "144", "source": "omnimath", "last_feedback": null}, {"sample_id": 617, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.452178397215903e-05, "probability_ratio_vs_uniform": 2.235653519164771, "seen": 0, "prompt_preview": "In a class, there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row, the number of desks is determined by the formula: d_n = d_(n-1) + n, where d_n represents the ", "answer_preview": "141", "source": "orca_math", "last_feedback": null}]}
{"global_step": 1020, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 493, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math", "last_feedback": null}, {"sample_id": 617, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "In a class, there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row, the number of desks is determined by the formula: d_n = d_(n-1) + n, where d_n represents the ", "answer_preview": "141", "source": "orca_math", "last_feedback": null}, {"sample_id": 632, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.491892029065639e-05, "probability_ratio_vs_uniform": 2.2475676087196916, "seen": 0, "prompt_preview": "The greatest number that divides 178340 and 253785 leaving remainders 20 and 35 respectively, and also divides 375690 leaving a remainder of 50 is:", "answer_preview": "10", "source": "orca_math", "last_feedback": null}]}
{"global_step": 1025, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 493, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math", "last_feedback": null}, {"sample_id": 617, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "In a class, there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row, the number of desks is determined by the formula: d_n = d_(n-1) + n, where d_n represents the ", "answer_preview": "141", "source": "orca_math", "last_feedback": null}, {"sample_id": 632, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.52665800973773e-05, "probability_ratio_vs_uniform": 2.257997402921319, "seen": 0, "prompt_preview": "The greatest number that divides 178340 and 253785 leaving remainders 20 and 35 respectively, and also divides 375690 leaving a remainder of 50 is:", "answer_preview": "10", "source": "orca_math", "last_feedback": null}]}
{"global_step": 1030, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 493, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math", "last_feedback": null}, {"sample_id": 617, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "In a class, there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row, the number of desks is determined by the formula: d_n = d_(n-1) + n, where d_n represents the ", "answer_preview": "141", "source": "orca_math", "last_feedback": null}, {"sample_id": 632, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.56031004129909e-05, "probability_ratio_vs_uniform": 2.268093012389727, "seen": 0, "prompt_preview": "The greatest number that divides 178340 and 253785 leaving remainders 20 and 35 respectively, and also divides 375690 leaving a remainder of 50 is:", "answer_preview": "10", "source": "orca_math", "last_feedback": null}]}
{"global_step": 1035, "feedback_mode": "best_reward", "top_k": 10, "rows": [{"sample_id": 42, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "Given $f(x) = x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1$, calculate $v_2$ using the Horner's method when $x = 2$.", "answer_preview": "24", "source": "cn_k12", "last_feedback": null}, {"sample_id": 177, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "sum of 49 odd numbers is ?", "answer_preview": "2401", "source": "orca_math", "last_feedback": null}, {"sample_id": 185, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "On the first day, Barry Sotter used his magic wand to make an object's length increase by $\\frac{1}{2}$, meaning that if the length of the object was originally $x,$ then it is now $x + \\frac{1}{2} x.$  On the second day he increased the ob", "answer_preview": "198", "source": "math", "last_feedback": null}, {"sample_id": 298, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "Given vectors $\\overrightarrow{v} = \\left(a_{n+1} - \\frac{a_n}{2}, \\frac{a_{n+1}^2}{2a_n}\\right)$ and $\\overrightarrow{\\mu} = (3, 3)$, and $\\overrightarrow{v}$ is parallel to $\\overrightarrow{\\mu}$, if $a_1 = 5$, find the sum of the first 1", "answer_preview": "50", "source": "big_math", "last_feedback": null}, {"sample_id": 405, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "Let \\(d\\) and \\(f\\) be positive integers and \\(a_{1} = 0.9\\). If \\(a_{i+1} = a_{i}^{2}\\) and \\(\\prod_{i=1}^{4} a_{i} = \\frac{3^{d}}{f}\\), determine the smallest possible value of \\(d\\).", "answer_preview": "30", "source": "olympiads", "last_feedback": null}, {"sample_id": 453, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. Some fraction of the female attendees arrived on time, and 0.115 fraction of the attendees did not arrive on time. What fraction of the fem", "answer_preview": "0.9", "source": "orca_math", "last_feedback": null}, {"sample_id": 463, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "During the holiday, a school organizes a trip for 360 teachers and students. A bus rental company offers two types of buses for hire: Type A buses have 40 seats each and a rental fee of 400 yuan; Type B buses have 50 seats each and a rental", "answer_preview": "3520", "source": "cn_k12", "last_feedback": null}, {"sample_id": 493, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "What is the value of y in the expression ( ( 2 ^ 5 ) * ( y ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) if the result is 0.16666666666666666?", "answer_preview": "81", "source": "orca_math", "last_feedback": null}, {"sample_id": 617, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "In a class, there are a total of 8 rows of desks and each desk can seat one student. There are 10 desks in the first row. In each subsequent row, the number of desks is determined by the formula: d_n = d_(n-1) + n, where d_n represents the ", "answer_preview": "141", "source": "orca_math", "last_feedback": null}, {"sample_id": 632, "sample_count": 0, "error_ema": 0.0, "novelty_component": 2.0, "risk_component": 0.0, "count_shrinkage_multiplier": 0.0, "priority_score": 2.0, "sampling_probability": 7.606646977365017e-05, "probability_ratio_vs_uniform": 2.281994093209505, "seen": 0, "prompt_preview": "The greatest number that divides 178340 and 253785 leaving remainders 20 and 35 respectively, and also divides 375690 leaving a remainder of 50 is:", "answer_preview": "10", "source": "orca_math", "last_feedback": null}]}