task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-rlve-pan-solar-panels-l6-s6 | construct | rlve_pan_solar_panels | poi_solar_panels_max_gcd | number_theory | competition | 6 | RLVE-Gym/pan_solar_panels | MIT | [
"agentic_trivial"
] | Find integers X and Y with 11707983753 <= X <= 63094150893 and 5203277709 <= Y <= 8897864003 such that gcd(X, Y) >= 8897864003.
(The maximum possible value of gcd(X, Y) over these ranges is exactly 8897864003.)
Answer format: {"X": <integer>, "Y": <integer>}
Write your final answer as JSON to `/workdir/answer.json`.... | {"A": 11707983753, "B": 63094150893, "C": 5203277709, "D": 8897864003, "target": 8897864003, "family": "rlve_pan_solar_panels", "subset": "construct"} | null | null | null | {"X": 62285048021, "Y": 8897864003} | 1 |
construct-rlve-pan-solar-panels-l6-s7 | construct | rlve_pan_solar_panels | poi_solar_panels_max_gcd | number_theory | competition | 6 | RLVE-Gym/pan_solar_panels | MIT | [
"agentic_trivial"
] | Find integers X and Y with 18558601965 <= X <= 34495217625 and 72377195950 <= Y <= 76079473950 such that gcd(X, Y) >= 25359824650.
(The maximum possible value of gcd(X, Y) over these ranges is exactly 25359824650.)
Answer format: {"X": <integer>, "Y": <integer>}
Write your final answer as JSON to `/workdir/answer.js... | {"A": 18558601965, "B": 34495217625, "C": 72377195950, "D": 76079473950, "target": 25359824650, "family": "rlve_pan_solar_panels", "subset": "construct"} | null | null | null | {"X": 25359824650, "Y": 76079473950} | 1 |
construct-rlve-pan-solar-panels-l6-s8 | construct | rlve_pan_solar_panels | poi_solar_panels_max_gcd | number_theory | competition | 6 | RLVE-Gym/pan_solar_panels | MIT | [
"agentic_trivial"
] | Find integers X and Y with 54697587910 <= X <= 64922233593 and 7490625801 <= Y <= 54198831201 such that gcd(X, Y) >= 32461116796.
(The maximum possible value of gcd(X, Y) over these ranges is exactly 32461116796.)
Answer format: {"X": <integer>, "Y": <integer>}
Write your final answer as JSON to `/workdir/answer.jso... | {"A": 54697587910, "B": 64922233593, "C": 7490625801, "D": 54198831201, "target": 32461116796, "family": "rlve_pan_solar_panels", "subset": "construct"} | null | null | null | {"X": 64922233592, "Y": 32461116796} | 1 |
construct-rlve-pan-solar-panels-l6-s9 | construct | rlve_pan_solar_panels | poi_solar_panels_max_gcd | number_theory | competition | 6 | RLVE-Gym/pan_solar_panels | MIT | [
"agentic_trivial"
] | Find integers X and Y with 26958113992 <= X <= 30778571821 and 34764604900 <= Y <= 96352711891 such that gcd(X, Y) >= 30778571821.
(The maximum possible value of gcd(X, Y) over these ranges is exactly 30778571821.)
Answer format: {"X": <integer>, "Y": <integer>}
Write your final answer as JSON to `/workdir/answer.js... | {"A": 26958113992, "B": 30778571821, "C": 34764604900, "D": 96352711891, "target": 30778571821, "family": "rlve_pan_solar_panels", "subset": "construct"} | null | null | null | {"X": 30778571821, "Y": 92335715463} | 1 |
construct-rlve-polynomial-global-minimum-l1-s0 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2)*x^0 + (4)*x^1 + (2)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSON... | {"coeffs": [2, 4, 2], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -1.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s1 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1)*x^0 + (2)*x^1 + (1)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSON... | {"coeffs": [1, 2, 1], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -1.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s2 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSON to `/workdir/answer... | {"coeffs": [0, 0, 1], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s3 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1)*x^0 + (-2)*x^1 + (1)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSO... | {"coeffs": [1, -2, 1], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s4 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (8)*x^0 + (8)*x^1 + (2)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSON... | {"coeffs": [8, 8, 2], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -2.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s5 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (8)*x^0 + (-8)*x^1 + (2)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSO... | {"coeffs": [8, -8, 2], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 2.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s6 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (4)*x^0 + (4)*x^1 + (1)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSON... | {"coeffs": [4, 4, 1], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -2.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s7 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2)*x^0 + (-4)*x^1 + (2)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSO... | {"coeffs": [2, -4, 2], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s8 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (4)*x^0 + (-4)*x^1 + (1)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSO... | {"coeffs": [4, -4, 1], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 2.0} | 1 |
construct-rlve-polynomial-global-minimum-l1-s9 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 1 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2)*x^2.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answer as JSON to `/workdir/answer... | {"coeffs": [0, 0, 2], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.0} | 1 |
construct-rlve-polynomial-global-minimum-l2-s0 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1)*x^0 + (2)*x^1 + (1)*x^2 + (2)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answ... | {"coeffs": [1, 2, 1, 0, 2], "fmin": "0.375000000000000000000000000000000000000000000", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.5} | 1 |
construct-rlve-polynomial-global-minimum-l2-s1 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2)*x^0 + (-2)*x^1 + (7)*x^2 + (-4)*x^3 + (1)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write you... | {"coeffs": [2, -2, 7, -4, 1], "fmin": "1.84334762302241694290479002810725397107414358", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.16487765151863348} | 1 |
construct-rlve-polynomial-global-minimum-l2-s2 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (36)*x^0 + (68)*x^1 + (49)*x^2 + (16)*x^3 + (2)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write y... | {"coeffs": [36, 68, 49, 16, 2], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -2.0} | 1 |
construct-rlve-polynomial-global-minimum-l2-s3 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (17)*x^0 + (30)*x^1 + (25)*x^2 + (8)*x^3 + (1)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write yo... | {"coeffs": [17, 30, 25, 8, 1], "fmin": "5.00000000000000000000000000000000000000000000", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -1.0} | 1 |
construct-rlve-polynomial-global-minimum-l2-s4 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (3)*x^0 + (10)*x^1 + (13)*x^2 + (8)*x^3 + (2)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write you... | {"coeffs": [3, 10, 13, 8, 2], "fmin": "0", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -1.0} | 1 |
construct-rlve-polynomial-global-minimum-l2-s5 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1)*x^0 + (-2)*x^1 + (1)*x^2 + (1)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final ans... | {"coeffs": [1, -2, 1, 0, 1], "fmin": "0.289273423937777937935889154385276791977392087", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.5897545123014584} | 1 |
construct-rlve-polynomial-global-minimum-l2-s6 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (4)*x^0 + (4)*x^1 + (14)*x^2 + (8)*x^3 + (2)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your... | {"coeffs": [4, 4, 14, 8, 2], "fmin": "3.68669524604483388580958005621450794214828716", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.16487765151863348} | 1 |
construct-rlve-polynomial-global-minimum-l2-s7 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (40)*x^0 + (-56)*x^1 + (50)*x^2 + (-16)*x^3 + (2)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write... | {"coeffs": [40, -56, 50, -16, 2], "fmin": "19.7346895646033218508698818641353958279729113", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.8718261016382063} | 1 |
construct-rlve-polynomial-global-minimum-l2-s8 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (5)*x^0 + (7)*x^2 + (4)*x^3 + (1)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write your final answ... | {"coeffs": [5, 0, 7, 4, 1], "fmin": "5.00000000000000000000000000000000000000000000", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.0} | 1 |
construct-rlve-polynomial-global-minimum-l2-s9 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 2 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (18)*x^0 + (28)*x^1 + (26)*x^2 + (8)*x^3 + (1)*x^4.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
Write yo... | {"coeffs": [18, 28, 26, 8, 1], "fmin": "8.55166289846733219174765454317744194832562008", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.7865883372377703} | 1 |
construct-rlve-polynomial-global-minimum-l3-s0 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (5)*x^0 + (-2)*x^1 + (43)*x^2 + (-32)*x^3 + (32)*x^4 + (-12)*x^5 + (2)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"... | {"coeffs": [5, -2, 43, -32, 32, -12, 2], "fmin": "4.97633548420288359252975785584755474318034134", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.023871924416206353} | 1 |
construct-rlve-polynomial-global-minimum-l3-s1 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (5)*x^0 + (-8)*x^1 + (7)*x^2 + (-4)*x^3 + (1)*x^4 + (1)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0": <number>}
... | {"coeffs": [5, -8, 7, -4, 1, 0, 1], "fmin": "1.69667515419507119226579346765472617101625085", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.8297724319303421} | 1 |
construct-rlve-polynomial-global-minimum-l3-s2 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (4)*x^0 + (16)*x^1 + (32)*x^2 + (40)*x^3 + (32)*x^4 + (12)*x^5 + (2)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0... | {"coeffs": [4, 16, 32, 40, 32, 12, 2], "fmin": "0.587391075289587500801061587752950893718624289", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.5996387644174705} | 1 |
construct-rlve-polynomial-global-minimum-l3-s3 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (131)*x^0 + (374)*x^1 + (493)*x^2 + (312)*x^3 + (122)*x^4 + (24)*x^5 + (2)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format... | {"coeffs": [131, 374, 493, 312, 122, 24, 2], "fmin": "29.2407259074097020484122474827769352880083035", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.7076803039181355} | 1 |
construct-rlve-polynomial-global-minimum-l3-s4 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (3)*x^0 + (14)*x^1 + (31)*x^2 + (40)*x^3 + (31)*x^4 + (12)*x^5 + (2)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0... | {"coeffs": [3, 14, 31, 40, 31, 12, 2], "fmin": "0.297571300705168110536450164339969018404943177", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.607497107756472} | 1 |
construct-rlve-polynomial-global-minimum-l3-s5 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (133)*x^0 + (376)*x^1 + (487)*x^2 + (316)*x^3 + (121)*x^4 + (24)*x^5 + (2)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format... | {"coeffs": [133, 376, 487, 316, 121, 24, 2], "fmin": "24.3069302671124772112525806487936335179249847", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.8056733792055042} | 1 |
construct-rlve-polynomial-global-minimum-l3-s6 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (25)*x^0 + (46)*x^1 + (41)*x^2 + (28)*x^3 + (16)*x^4 + (6)*x^5 + (1)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {"x0... | {"coeffs": [25, 46, 41, 28, 16, 6, 1], "fmin": "0.302176497910558206534386684258452194888657946", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -1.723584662053382} | 1 |
construct-rlve-polynomial-global-minimum-l3-s7 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (146)*x^0 + (356)*x^1 + (506)*x^2 + (312)*x^3 + (121)*x^4 + (24)*x^5 + (2)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format... | {"coeffs": [146, 356, 506, 312, 121, 24, 2], "fmin": "61.0494148059365849200539747958503145605441076", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.5869653520946588} | 1 |
construct-rlve-polynomial-global-minimum-l3-s8 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (17)*x^0 + (-38)*x^1 + (40)*x^2 + (-28)*x^3 + (16)*x^4 + (-6)*x^5 + (1)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: {... | {"coeffs": [17, -38, 40, -28, 16, -6, 1], "fmin": "1.84336768688194447748236972497826351284182613", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.164807302064863} | 1 |
construct-rlve-polynomial-global-minimum-l3-s9 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 3 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (65)*x^0 + (190)*x^1 + (241)*x^2 + (160)*x^3 + (62)*x^4 + (12)*x^5 + (1)*x^6.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer format: ... | {"coeffs": [65, 190, 241, 160, 62, 12, 1], "fmin": "6.69375361817812410334478160913312142495056204", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.900475393694498} | 1 |
construct-rlve-polynomial-global-minimum-l4-s0 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (86)*x^0 + (-236)*x^1 + (321)*x^2 + (-280)*x^3 + (201)*x^4 + (-124)*x^5 + (57)*x^6 + (-16)*x^7 + (2)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value y... | {"coeffs": [86, -236, 321, -280, 201, -124, 57, -16, 2], "fmin": "10.7964631124392756531309803147488454831222998", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.1083662058643997} | 1 |
construct-rlve-polynomial-global-minimum-l4-s1 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (657)*x^0 + (2462)*x^1 + (4089)*x^2 + (3912)*x^3 + (2361)*x^4 + (920)*x^5 + (226)*x^6 + (32)*x^7 + (2)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value... | {"coeffs": [657, 2462, 4089, 3912, 2361, 920, 226, 32, 2], "fmin": "5.88053310896852224985989205193571226904359967", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -1.3030307136310035} | 1 |
construct-rlve-polynomial-global-minimum-l4-s2 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (17)*x^0 + (-38)*x^1 + (41)*x^2 + (-28)*x^3 + (16)*x^4 + (-6)*x^5 + (1)*x^6 + (1)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
Answer... | {"coeffs": [17, -38, 41, -28, 16, -6, 1, 0, 1], "fmin": "3.46633500593890112836775579236407510292207695", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.8528978226813155} | 1 |
construct-rlve-polynomial-global-minimum-l4-s3 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (12)*x^0 + (-32)*x^1 + (66)*x^2 + (-100)*x^3 + (101)*x^4 + (-68)*x^5 + (30)*x^6 + (-8)*x^7 + (1)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you s... | {"coeffs": [12, -32, 66, -100, 101, -68, 30, -8, 1], "fmin": "0.554784401684218622146398324128100732256163468", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.576147969509968} | 1 |
construct-rlve-polynomial-global-minimum-l4-s4 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (148)*x^0 + (-420)*x^1 + (505)*x^2 + (-328)*x^3 + (121)*x^4 + (-24)*x^5 + (2)*x^6 + (2)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
... | {"coeffs": [148, -420, 505, -328, 121, -24, 2, 0, 2], "fmin": "5.98933258447042258665584624933238310752601671", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.010624440939622} | 1 |
construct-rlve-polynomial-global-minimum-l4-s5 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (131)*x^0 + (-374)*x^1 + (493)*x^2 + (-312)*x^3 + (122)*x^4 + (-24)*x^5 + (2)*x^6 + (1)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
... | {"coeffs": [131, -374, 493, -312, 122, -24, 2, 0, 1], "fmin": "29.3026078113689615574615525109518708194956206", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.7048002815465262} | 1 |
construct-rlve-polynomial-global-minimum-l4-s6 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (67)*x^0 + (186)*x^1 + (275)*x^2 + (108)*x^3 + (131)*x^4 + (-44)*x^5 + (29)*x^6 + (-8)*x^7 + (1)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you s... | {"coeffs": [67, 186, 275, 108, 131, -44, 29, -8, 1], "fmin": "33.1767934036231713604135473530712469505576924", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.36115263909669215} | 1 |
construct-rlve-polynomial-global-minimum-l4-s7 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (387)*x^0 + (1402)*x^1 + (2285)*x^2 + (2104)*x^3 + (1242)*x^4 + (472)*x^5 + (114)*x^6 + (16)*x^7 + (1)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value... | {"coeffs": [387, 1402, 2285, 2104, 1242, 472, 114, 16, 1], "fmin": "31.0969928359091970896203059480734214435088796", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.8348559318962129} | 1 |
construct-rlve-polynomial-global-minimum-l4-s8 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (259)*x^0 + (1026)*x^1 + (1809)*x^2 + (1812)*x^3 + (1136)*x^4 + (454)*x^5 + (113)*x^6 + (16)*x^7 + (1)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value... | {"coeffs": [259, 1026, 1809, 1812, 1136, 454, 113, 16, 1], "fmin": "9.89695755968471494080979536809714275866512981", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.9503040205448318} | 1 |
construct-rlve-polynomial-global-minimum-l4-s9 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 4 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2)*x^0 + (6)*x^1 + (29)*x^2 + (56)*x^3 + (71)*x^4 + (56)*x^5 + (30)*x^6 + (8)*x^7 + (1)*x^8.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
... | {"coeffs": [2, 6, 29, 56, 71, 56, 30, 8, 1], "fmin": "1.59415268296088023471190880488608201624969055", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.16105159721585188} | 1 |
construct-rlve-polynomial-global-minimum-l5-s0 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1172)*x^0 + (-5548)*x^1 + (12082)*x^2 + (-15800)*x^3 + (13701)*x^4 + (-8200)*x^5 + (3418)*x^6 + (-976)*x^7 + (182)*x^8 + (-20)*x^9 + (1)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated e... | {"coeffs": [1172, -5548, 12082, -15800, 13701, -8200, 3418, -976, 182, -20, 1], "fmin": "10.7010847634060040633710150034620738750663521", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.1733649898933909} | 1 |
construct-rlve-polynomial-global-minimum-l5-s1 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1029)*x^0 + (-5118)*x^1 + (11549)*x^2 + (-15348)*x^3 + (13457)*x^4 + (-8058)*x^5 + (3361)*x^6 + (-960)*x^7 + (182)*x^8 + (-20)*x^9 + (1)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated e... | {"coeffs": [1029, -5118, 11549, -15348, 13457, -8058, 3361, -960, 182, -20, 1], "fmin": "43.7499870326427411535594836745528629069513310", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.7132231041589705} | 1 |
construct-rlve-polynomial-global-minimum-l5-s2 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (554)*x^0 + (-2140)*x^1 + (3724)*x^2 + (-3840)*x^3 + (2662)*x^4 + (-1400)*x^5 + (645)*x^6 + (-272)*x^7 + (92)*x^8 + (-20)*x^9 + (2)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly... | {"coeffs": [554, -2140, 3724, -3840, 2662, -1400, 645, -272, 92, -20, 2], "fmin": "5.33887754200651065522228570908354424239371767", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 1.1619308491873104} | 1 |
construct-rlve-polynomial-global-minimum-l5-s3 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2115)*x^0 + (10048)*x^1 + (23321)*x^2 + (30512)*x^3 + (27012)*x^4 + (16060)*x^5 + (6749)*x^6 + (1912)*x^7 + (361)*x^8 + (40)*x^9 + (2)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exa... | {"coeffs": [2115, 10048, 23321, 30512, 27012, 16060, 6749, 1912, 361, 40, 2], "fmin": "385.307096773224604010444346575792992643649679", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.5072723875200363} | 1 |
construct-rlve-polynomial-global-minimum-l5-s4 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (9)*x^0 + (-4)*x^1 + (162)*x^2 + (-248)*x^3 + (522)*x^4 + (-548)*x^5 + (450)*x^6 + (-248)*x^7 + (91)*x^8 + (-20)*x^9 + (2)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the... | {"coeffs": [9, -4, 162, -248, 522, -548, 450, -248, 91, -20, 2], "fmin": "8.97483437977983751981436996655876362984717222", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.012703244588695565} | 1 |
construct-rlve-polynomial-global-minimum-l5-s5 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (18)*x^0 + (34)*x^1 + (68)*x^2 + (44)*x^3 + (86)*x^4 + (50)*x^5 + (29)*x^6 + (8)*x^7 + (1)*x^8 + (2)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value ... | {"coeffs": [18, 34, 68, 44, 86, 50, 29, 8, 1, 0, 2], "fmin": "13.3008018487483972034558674677888941773653793", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.2798425351160118} | 1 |
construct-rlve-polynomial-global-minimum-l5-s6 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2056)*x^0 + (-10220)*x^1 + (23105)*x^2 + (-30620)*x^3 + (26981)*x^4 + (-16060)*x^5 + (6750)*x^6 + (-1912)*x^7 + (361)*x^8 + (-40)*x^9 + (2)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluate... | {"coeffs": [2056, -10220, 23105, -30620, 26981, -16060, 6750, -1912, 361, -40, 2], "fmin": "142.429407109776784749641321076634589399466232", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.6149685846840874} | 1 |
construct-rlve-polynomial-global-minimum-l5-s7 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (12)*x^0 + (38)*x^1 + (113)*x^2 + (264)*x^3 + (436)*x^4 + (510)*x^5 + (421)*x^6 + (240)*x^7 + (91)*x^8 + (20)*x^9 + (2)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the de... | {"coeffs": [12, 38, 113, 264, 436, 510, 421, 240, 91, 20, 2], "fmin": "2.84579795605538056483683107621277921429385342", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.9162604681692862} | 1 |
construct-rlve-polynomial-global-minimum-l5-s8 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (67)*x^0 + (186)*x^1 + (287)*x^2 + (40)*x^3 + (272)*x^4 + (-240)*x^5 + (211)*x^6 + (-120)*x^7 + (47)*x^8 + (-10)*x^9 + (1)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the... | {"coeffs": [67, 186, 287, 40, 272, -240, 211, -120, 47, -10, 1], "fmin": "38.7470475930799924039816348559858550567925699", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.2808606259243819} | 1 |
construct-rlve-polynomial-global-minimum-l5-s9 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 5 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (1316)*x^0 + (-6084)*x^1 + (13361)*x^2 + (-17136)*x^3 + (14562)*x^4 + (-8512)*x^5 + (3474)*x^6 + (-976)*x^7 + (181)*x^8 + (-20)*x^9 + (1)*x^10.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated e... | {"coeffs": [1316, -6084, 13361, -17136, 14562, -8512, 3474, -976, 181, -20, 1], "fmin": "130.156484856561391265759423015482628774058567", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.6994679439729765} | 1 |
construct-rlve-polynomial-global-minimum-l6-s0 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (8203)*x^0 + (-49144)*x^1 + (135397)*x^2 + (-224960)*x^3 + (254822)*x^4 + (-200902)*x^5 + (121543)*x^6 + (-47360)*x^7 + (18890)*x^8 + (-1528)*x^9 + (1530)*x^10 + (316)*x^11 + (93)*x^12 + (14)*x^13 + (1)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted... | {"coeffs": [8203, -49144, 135397, -224960, 254822, -200902, 121543, -47360, 18890, -1528, 1530, 316, 93, 14, 1], "fmin": "599.026655896942263909784693534688976681448453", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.47623916069975464} | 1 |
construct-rlve-polynomial-global-minimum-l6-s1 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (4101)*x^0 + (-24576)*x^1 + (67698)*x^2 + (-112980)*x^3 + (127737)*x^4 + (-103372)*x^5 + (62140)*x^6 + (-28776)*x^7 + (10925)*x^8 + (-3762)*x^9 + (1266)*x^10 + (-388)*x^11 + (92)*x^12 + (-14)*x^13 + (1)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted... | {"coeffs": [4101, -24576, 67698, -112980, 127737, -103372, 62140, -28776, 10925, -3762, 1266, -388, 92, -14, 1], "fmin": "59.0039109627281987932410883940007931597765564", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.756373857798139} | 1 |
construct-rlve-polynomial-global-minimum-l6-s2 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (5190)*x^0 + (-29512)*x^1 + (79379)*x^2 + (-127900)*x^3 + (140291)*x^4 + (-109484)*x^5 + (62525)*x^6 + (-26312)*x^7 + (8101)*x^8 + (-1780)*x^9 + (265)*x^10 + (-24)*x^11 + (1)*x^12 + (1)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min ... | {"coeffs": [5190, -29512, 79379, -127900, 140291, -109484, 62525, -26312, 8101, -1780, 265, -24, 1, 0, 1], "fmin": "401.273538184172151469942883704208305601216270", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.5961621062336377} | 1 |
construct-rlve-polynomial-global-minimum-l6-s3 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (2069)*x^0 + (10246)*x^1 + (23227)*x^2 + (31192)*x^3 + (27901)*x^4 + (17724)*x^5 + (8570)*x^6 + (3504)*x^7 + (1352)*x^8 + (480)*x^9 + (134)*x^10 + (24)*x^11 + (2)*x^12 + (2)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * m... | {"coeffs": [2069, 10246, 23227, 31192, 27901, 17724, 8570, 3504, 1352, 480, 134, 24, 2, 0, 2], "fmin": "74.2472391815217440684469375737734650173534310", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.812132799110263} | 1 |
construct-rlve-polynomial-global-minimum-l6-s4 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (4180)*x^0 + (-24774)*x^1 + (68105)*x^2 + (-112144)*x^3 + (129063)*x^4 + (-97580)*x^5 + (65381)*x^6 + (-18592)*x^7 + (13972)*x^8 + (2234)*x^9 + (2267)*x^10 + (704)*x^11 + (183)*x^12 + (28)*x^13 + (2)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if... | {"coeffs": [4180, -24774, 68105, -112144, 129063, -97580, 65381, -18592, 13972, 2234, 2267, 704, 183, 28, 2], "fmin": "541.935335217995011933947316009356626897218595", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.39669493608220563} | 1 |
construct-rlve-polynomial-global-minimum-l6-s5 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (91)*x^0 + (-228)*x^1 + (384)*x^2 + (-352)*x^3 + (551)*x^4 + (-460)*x^5 + (449)*x^6 + (-232)*x^7 + (91)*x^8 + (-20)*x^9 + (2)*x^10 + (2)*x^12 + (2)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is e... | {"coeffs": [91, -228, 384, -352, 551, -460, 449, -232, 91, -20, 2, 0, 2, 0, 2], "fmin": "49.4599143834983871155681427159046516509382922", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.37754846104387085} | 1 |
construct-rlve-polynomial-global-minimum-l6-s6 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (9)*x^0 + (4)*x^1 + (400)*x^2 + (-344)*x^3 + (3274)*x^4 + (-2616)*x^5 + (8093)*x^6 + (-5392)*x^7 + (7042)*x^8 + (-3574)*x^9 + (2135)*x^10 + (-704)*x^11 + (184)*x^12 + (-28)*x^13 + (2)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f ... | {"coeffs": [9, 4, 400, -344, 3274, -2616, 8093, -5392, 7042, -3574, 2135, -704, 184, -28, 2], "fmin": "8.99004459031947540668898065482177119741379617", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.004966169808665889} | 1 |
construct-rlve-polynomial-global-minimum-l6-s7 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (290)*x^0 + (972)*x^1 + (1886)*x^2 + (1896)*x^3 + (1332)*x^4 + (700)*x^5 + (324)*x^6 + (136)*x^7 + (46)*x^8 + (10)*x^9 + (1)*x^10 + (1)*x^12 + (2)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is ev... | {"coeffs": [290, 972, 1886, 1896, 1332, 700, 324, 136, 46, 10, 1, 0, 1, 0, 2], "fmin": "103.939371385237371080334822769150151061705516", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.5158905311965551} | 1 |
construct-rlve-polynomial-global-minimum-l6-s8 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (33413)*x^0 + (231790)*x^1 + (749715)*x^2 + (1494528)*x^3 + (2053610)*x^4 + (2049636)*x^5 + (1539820)*x^6 + (877160)*x^7 + (385421)*x^8 + (127698)*x^9 + (32165)*x^10 + (5800)*x^11 + (730)*x^12 + (56)*x^13 + (2)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is ... | {"coeffs": [33413, 231790, 749715, 1494528, 2053610, 2049636, 1539820, 877160, 385421, 127698, 32165, 5800, 730, 56, 2], "fmin": "804.264456026734478923457362303020999634080037", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": -0.565365562277958} | 1 |
construct-rlve-polynomial-global-minimum-l6-s9 | construct | rlve_polynomial_global_minimum | polynomial_global_minimum | analysis | competition | 6 | RLVE-Gym/polynomial_minimum | MIT | [
"agentic_trivial"
] | Let f(x) = (10252)*x^0 + (-38914)*x^1 + (158359)*x^2 + (-194940)*x^3 + (281423)*x^4 + (-188670)*x^5 + (128025)*x^6 + (-52208)*x^7 + (19204)*x^8 + (-5482)*x^9 + (1531)*x^10 + (-412)*x^11 + (93)*x^12 + (-14)*x^13 + (1)*x^14.
Find a real number x0 at which f attains its global minimum over the reals. Your answer is accep... | {"coeffs": [10252, -38914, 158359, -194940, 281423, -188670, 128025, -52208, 19204, -5482, 1531, -412, 93, -14, 1], "fmin": "7446.13613902279440821340804238562201956792358", "family": "rlve_polynomial_global_minimum", "subset": "construct"} | null | null | null | {"x0": 0.15579061483539391} | 1 |
construct-rlve-polynomial-integer-roots-l1-s0 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (27)*x^0 + (-9)*x^1 + (-3)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/an... | {"coeffs": [27, -9, -3, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, 3, 3]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s1 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (2)*x^1 + (-3)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/answer.json`. ... | {"coeffs": [0, 2, -3, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [0, 1, 2]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s2 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (-3)*x^1 + (-2)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/answer.json`.... | {"coeffs": [0, -3, -2, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-1, 0, 3]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s3 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (2)*x^0 + (-1)*x^1 + (-2)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/ans... | {"coeffs": [2, -1, -2, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-1, 1, 2]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s4 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (-18)*x^0 + (-3)*x^1 + (4)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/an... | {"coeffs": [-18, -3, 4, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, -3, 2]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s5 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (-18)*x^0 + (21)*x^1 + (-8)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/a... | {"coeffs": [-18, 21, -8, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [2, 3, 3]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s6 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (-27)*x^0 + (-9)*x^1 + (3)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/an... | {"coeffs": [-27, -9, 3, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, -3, 3]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s7 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (8)*x^0 + (12)*x^1 + (6)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/answ... | {"coeffs": [8, 12, 6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-2, -2, -2]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s8 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (3)*x^0 + (7)*x^1 + (5)*x^2 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/answe... | {"coeffs": [3, 7, 5, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, -1, -1]} | 1 |
construct-rlve-polynomial-integer-roots-l1-s9 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 1 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-3 polynomial
P(x) = (6)*x^0 + (-7)*x^1 + (1)*x^3
can be written as (x - a_1)(x - a_2)...(x - a_3) with integers a_1, ..., a_3 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_3]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/answer.json`. ... | {"coeffs": [6, -7, 0, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, 1, 2]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s0 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (-2)*x^2 + (-1)*x^3 + (2)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answer as JSON to `/workdir/ans... | {"coeffs": [0, 0, -2, -1, 2, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-2, -1, 0, 0, 1]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s1 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (15)*x^0 + (-43)*x^1 + (38)*x^2 + (-6)*x^3 + (-5)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answer ... | {"coeffs": [15, -43, 38, -6, -5, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, 1, 1, 1, 5]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s2 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (360)*x^0 + (-402)*x^1 + (121)*x^2 + (9)*x^3 + (-9)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answe... | {"coeffs": [360, -402, 121, 9, -9, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-4, 2, 3, 3, 5]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s3 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (-288)*x^0 + (48)*x^1 + (82)*x^2 + (-19)*x^3 + (-4)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answe... | {"coeffs": [-288, 48, 82, -19, -4, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-4, -2, 3, 3, 4]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s4 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (12)*x^1 + (31)*x^2 + (27)*x^3 + (9)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answer as JSON to `/... | {"coeffs": [0, 12, 31, 27, 9, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-4, -3, -1, -1, 0]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s5 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (32)*x^1 + (16)*x^2 + (-18)*x^3 + (-1)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answer as JSON to ... | {"coeffs": [0, 32, 16, -18, -1, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-4, -1, 0, 2, 4]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s6 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (-3)*x^1 + (-4)*x^2 + (2)*x^3 + (4)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answer as JSON to `/w... | {"coeffs": [0, -3, -4, 2, 4, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, -1, -1, 0, 1]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s7 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (900)*x^0 + (135)*x^1 + (-154)*x^2 + (-24)*x^3 + (6)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answ... | {"coeffs": [900, 135, -154, -24, 6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-5, -5, -3, 3, 4]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s8 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (-64)*x^1 + (32)*x^2 + (12)*x^3 + (-8)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answer as JSON to ... | {"coeffs": [0, -64, 32, 12, -8, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-2, 0, 2, 4, 4]} | 1 |
construct-rlve-polynomial-integer-roots-l2-s9 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 2 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-5 polynomial
P(x) = (40)*x^1 + (78)*x^2 + (49)*x^3 + (12)*x^4 + (1)*x^5
can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_5]} (any order, with multiplicity)
Write your final answer as JSON to `... | {"coeffs": [0, 40, 78, 49, 12, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-5, -4, -2, -1, 0]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s0 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (147456)*x^0 + (18432)*x^1 + (-40960)*x^2 + (-512)*x^3 + (3328)*x^4 + (-72)*x^5 + (-100)*x^6 + (2)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (any or... | {"coeffs": [147456, 18432, -40960, -512, 3328, -72, -100, 2, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-8, -6, -4, -2, 4, 4, 4, 6]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s1 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (-29400)*x^0 + (81410)*x^1 + (-80211)*x^2 + (33956)*x^3 + (-5777)*x^4 + (-142)*x^5 + (187)*x^6 + (-24)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (an... | {"coeffs": [-29400, 81410, -80211, 33956, -5777, -142, 187, -24, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-6, 1, 1, 4, 5, 5, 7, 7]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s2 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (-79380)*x^0 + (165564)*x^1 + (-118737)*x^2 + (36180)*x^3 + (-2873)*x^4 + (-1012)*x^5 + (285)*x^6 + (-28)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} ... | {"coeffs": [-79380, 165564, -118737, 36180, -2873, -1012, 285, -28, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-5, 1, 3, 3, 6, 6, 7, 7]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s3 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (1474560)*x^0 + (-1216512)*x^1 + (304640)*x^2 + (4416)*x^3 + (-13056)*x^4 + (1572)*x^5 + (60)*x^6 + (-21)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} ... | {"coeffs": [1474560, -1216512, 304640, 4416, -13056, 1572, 60, -21, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-8, -6, 4, 4, 5, 6, 8, 8]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s4 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (12800)*x^0 + (-9920)*x^1 + (-10768)*x^2 + (10188)*x^3 + (-2193)*x^4 + (-246)*x^5 + (160)*x^6 + (-22)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (any... | {"coeffs": [12800, -9920, -10768, 10188, -2193, -246, 160, -22, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-4, -1, 1, 4, 4, 5, 5, 8]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s5 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (-105840)*x^0 + (21798)*x^1 + (69009)*x^2 + (18128)*x^3 + (-2001)*x^4 + (-1058)*x^5 + (-49)*x^6 + (12)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (an... | {"coeffs": [-105840, 21798, 69009, 18128, -2001, -1058, -49, 12, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-7, -7, -6, -3, -3, 1, 5, 8]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s6 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (-1152)*x^0 + (-3024)*x^1 + (-2356)*x^2 + (-96)*x^3 + (519)*x^4 + (102)*x^5 + (-36)*x^6 + (-6)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (any order,... | {"coeffs": [-1152, -3024, -2356, -96, 519, 102, -36, -6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-3, -2, -2, -1, -1, 3, 4, 8]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s7 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (-60480)*x^0 + (-41256)*x^1 + (10908)*x^2 + (12298)*x^3 + (1365)*x^4 + (-520)*x^5 + (-82)*x^6 + (6)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (any o... | {"coeffs": [-60480, -41256, 10908, 12298, 1365, -520, -82, 6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-8, -5, -3, -3, -2, 2, 6, 7]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s8 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (126000)*x^1 + (74700)*x^2 + (5860)*x^3 + (-4163)*x^4 + (-836)*x^5 + (22)*x^6 + (16)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (any order, with mult... | {"coeffs": [0, 126000, 74700, 5860, -4163, -836, 22, 16, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-7, -6, -5, -5, -4, 0, 5, 6]} | 1 |
construct-rlve-polynomial-integer-roots-l3-s9 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 3 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-8 polynomial
P(x) = (-288)*x^1 + (444)*x^2 + (133)*x^3 + (-455)*x^4 + (166)*x^5 + (10)*x^6 + (-11)*x^7 + (1)*x^8
can be written as (x - a_1)(x - a_2)...(x - a_8) with integers a_1, ..., a_8 (not necessarily distinct). Find such integers.
Answer format: {"roots": [a_1, ..., a_8]} (any order, with multiplici... | {"coeffs": [0, -288, 444, 133, -455, 166, 10, -11, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-4, -1, 0, 1, 1, 3, 3, 8]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s0 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-2365440000)*x^0 + (-753664000)*x^1 + (731731200)*x^2 + (257007040)*x^3 + (-33282368)*x^4 + (-18656304)*x^5 + (-561184)*x^6 + (389716)*x^7 + (28332)*x^8 + (-3181)*x^9 + (-301)*x^10 + (9)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (not ... | {"coeffs": [-2365440000, -753664000, 731731200, 257007040, -33282368, -18656304, -561184, 389716, 28332, -3181, -301, 9, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-10, -8, -8, -7, -6, -5, -2, 2, 4, 10, 10, 11]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s1 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-434649600)*x^0 + (322176960)*x^1 + (209263936)*x^2 + (-55765748)*x^3 + (-40332612)*x^4 + (-2461927)*x^5 + (1555355)*x^6 + (231549)*x^7 + (-13609)*x^8 + (-4213)*x^9 + (-111)*x^10 + (19)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (not n... | {"coeffs": [-434649600, 322176960, 209263936, -55765748, -40332612, -2461927, 1555355, 231549, -13609, -4213, -111, 19, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-11, -8, -7, -7, -5, -5, -4, 1, 2, 6, 7, 12]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s2 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-101039400)*x^1 + (-98597250)*x^2 + (19947951)*x^3 + (16543665)*x^4 + (-1930980)*x^5 + (-911816)*x^6 + (79714)*x^7 + (21638)*x^8 + (-1292)*x^9 + (-238)*x^10 + (7)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (not necessarily distinct). F... | {"coeffs": [0, -101039400, -98597250, 19947951, 16543665, -1930980, -911816, 79714, 21638, -1292, -238, 7, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-11, -9, -9, -5, -3, -1, 0, 4, 5, 6, 7, 9]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s3 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-3345408000)*x^0 + (2286028800)*x^1 + (198635520)*x^2 + (-571101952)*x^3 + (174921632)*x^4 + (-8925368)*x^5 + (-5508876)*x^6 + (1237022)*x^7 + (-85943)*x^8 + (-3252)*x^9 + (866)*x^10 + (-50)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (... | {"coeffs": [-3345408000, 2286028800, 198635520, -571101952, 174921632, -8925368, -5508876, 1237022, -85943, -3252, 866, -50, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-11, -5, -2, 4, 4, 4, 5, 6, 10, 11, 12, 12]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s4 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-167270400)*x^0 + (97574400)*x^1 + (166922016)*x^2 + (-105574976)*x^3 + (1165402)*x^4 + (8206805)*x^5 + (-845311)*x^6 + (-208047)*x^7 + (28593)*x^8 + (1823)*x^9 + (-301)*x^10 + (-5)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (not neces... | {"coeffs": [-167270400, 97574400, 166922016, -105574976, 1165402, 8206805, -845311, -208047, 28593, 1823, -301, -5, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-12, -11, -6, -5, -1, 1, 3, 4, 5, 8, 8, 11]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s5 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-1428840000)*x^0 + (-642978000)*x^1 + (929505600)*x^2 + (31855680)*x^3 + (-105826072)*x^4 + (9363241)*x^5 + (3011639)*x^6 + (-420075)*x^7 + (-24549)*x^8 + (5739)*x^9 + (-59)*x^10 + (-25)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (not ... | {"coeffs": [-1428840000, -642978000, 929505600, 31855680, -105826072, 9363241, 3011639, -420075, -24549, 5739, -59, -25, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-10, -9, -7, -3, -1, 2, 5, 7, 9, 10, 10, 12]} | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.