id stringclasses 10
values | question stringclasses 10
values | answer stringclasses 10
values | topic stringclasses 5
values | parent_seed_ids stringclasses 9
values | target_molecule stringclasses 2
values | candidate_molecule stringclasses 1
value | cohort_vector stringclasses 1
value | cohort_target stringclasses 1
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values | audit_json stringclasses 10
values | clean_accept int64 1 1 | refinement_rounds int64 1 1 | accepted_at float64 1.78B 1.78B |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5e44e247af3783c5 | Evaluate the sum S = sum_{k=1}^{2019} k/(k+1)!. | 1 - 1/2020! | counting__probability | ["3717b13fffb488aa", "27cdd2dd93f24515"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.7432240545749664, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.4803718030452728, "verifier_agreements": 2, "verifier_answers": ["1 - 1/2020!", "1 - \\frac{1}{2020!}"], "target_fingerprint": ""} | 1 | 1 | 1,777,227,609.393657 |
19545b420e0873d2 | In triangle ABC the side lengths are AB = 13, BC = 14, and CA = 15. Find the inradius of triangle ABC. | 4 | algebra | ["648c41407ca96533", "a0176f34dbf9162a"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.7930878847837448, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.4572722613811493, "verifier_agreements": 2, "verifier_answers": ["4", "4"], "target_fingerprint": ""} | 1 | 1 | 1,777,228,485.863014 |
4e92e52d33e0d2ab | Triangle ABC has side lengths AB = 13, BC = 14, and CA = 15. Find the radius of its circumcircle. | 65/8 | number_theory | ["7e32d801337f5145", "bf9acf0f4cfcadf6", "3902a5bed649d3f8", "47c5862d507cb2ab"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | FULL | {"synthesis_mode": "FULL", "spot_check_correctness": 1.0, "anti_distance": 0.7352128624916077, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.863884687423706, "verifier_agreements": 2, "verifier_answers": ["65/8", "65/8"], "target_fingerprint": ""} | 1 | 1 | 1,777,228,594.861666 |
5b4dad425a9bc6be | Let real numbers x, y, z satisfy x + y + z = 6, xy + yz + zx = 11, and x^3 + y^3 + z^3 = 36. Find the value of xyz. | 6 | algebra | ["648c41407ca96533", "a0176f34dbf9162a", "489856633c9bc7c8", "cf0b8c3bf6ab521f"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | FULL | {"synthesis_mode": "FULL", "spot_check_correctness": 1.0, "anti_distance": 0.7148540616035461, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.5426169633865356, "verifier_agreements": 2, "verifier_answers": ["6", "6"], "target_fingerprint": ""} | 1 | 1 | 1,777,228,981.076611 |
cd2d65ee136448a1 | Compute gcd(2^100 + 1, 2^200 + 1). | 1 | prealgebra | ["49807124e921340f", "0e2a833a7180fd41"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.8179263472557068, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.48887085914611816, "verifier_agreements": 2, "verifier_answers": ["1", "1"], "target_fingerprint": ""} | 1 | 1 | 1,777,229,429.705149 |
3585eb5de70f961f | Let x and y be positive real numbers with x + y = 12. Find the minimum value of (x^2 + y^2) / (xy). | 2 | number_theory | ["26fe7509e6503068", "c60aae1fba9eb8a9"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.6748673915863037, "novelty_max_minhash": 0.140625, "novelty_max_cosine": 0.6914433836936951, "verifier_agreements": 2, "verifier_answers": ["2", "2"], "target_fingerprint": ""} | 1 | 1 | 1,777,229,853.740752 |
a18ec353a69f4111 | Compute the sum S = \sum_{k=1}^{99} \frac{k}{(k+1)!}. | 1 - 1/100! | precalculus | ["701e1b0bd5df468f", "d3a53f7b96ee8637"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.7318255305290222, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.7644564509391785, "verifier_agreements": 2, "verifier_answers": ["1 - 1/100!", "1 - \\frac{1}{100!}"], "target_fingerprint": ""} | 1 | 1 | 1,777,230,030.091663 |
aeea4a71bf2fddad | Evaluate the infinite series S = sum_{n=1}^\infty \frac{1}{n^2(n+1)}. | \frac{\pi^2}{6} - 1 | number_theory | ["7e32d801337f5145", "bf9acf0f4cfcadf6"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.7642606943845749, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.58076012134552, "verifier_agreements": 2, "verifier_answers": ["\\pi^2/6 - 1", "1"], "target_fingerprint": ""} | 1 | 1 | 1,777,230,139.423321 |
5eecb9f2821db57a | A tiling is made from congruent equilateral triangle tiles. Two regular polygons are formed by arranging these tiles: one is a regular octagon and the other is a regular dodecagon. Each side of each polygon coincides with one side of a single triangle tile, so all polygon side lengths are equal. If the perimeter of the... | 144 cm | prealgebra | ["49807124e921340f"] | {"fingerprint": "- Recognize the decomposition: observe that both the given figure and the target polygon are built from the same congruent equilateral pieces, so each piece\u2019s side equals a side of the polygons.\n\n- Introduce the common side length conceptually: treat the shared edge length as a single unknown le... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | LIGHT | {"synthesis_mode": "LIGHT", "spot_check_correctness": 1.0, "anti_distance": 0.4829775094985962, "novelty_max_minhash": 0.078125, "novelty_max_cosine": 0.5413011908531189, "verifier_agreements": 2, "verifier_answers": ["144 cm", "144 cm"], "target_fingerprint": "- Recognize the decomposition: observe that both the given... | 1 | 1 | 1,777,230,340.707362 |
4b474ed02c360d4a | Find the area of a triangle with side lengths 13, 14, and 15. | 84 | number_theory | ["7e32d801337f5145", "bf9acf0f4cfcadf6", "3902a5bed649d3f8", "47c5862d507cb2ab"] | {"fingerprint": ""} | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | FULL | {"synthesis_mode": "FULL", "spot_check_correctness": 1.0, "anti_distance": 0.7031303942203522, "novelty_max_minhash": 0.2890625, "novelty_max_cosine": 0.6819842457771301, "verifier_agreements": 2, "verifier_answers": ["84", "84"], "target_fingerprint": ""} | 1 | 1 | 1,777,231,134.197759 |
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