family stringclasses 1 value | question_id int64 0 2 | signal_type stringclasses 2 values | amplitude_scale float64 0.5 2.5 | frequency_cycles float64 1 16 | phase_deg float64 0 240 ⌀ | time_step int64 0 255 | p_value float64 3.5 4.5 | prompt stringlengths 59 76 | ground_truth float64 0.52 2.33 | symbolic_baseline_answer float64 0.52 2.33 |
|---|---|---|---|---|---|---|---|---|---|---|
linear_system | 2 | sinusoid | 1 | 2 | 120 | 16 | 3.826795 | Solve this system for x:
3.8267949192431123x + 1y = 10
2x + 4y = 12
FINAL: | 2.104127 | 2.104127 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 17 | 3.849632 | Solve this system for x:
3.8496320385042044x + 1y = 10
2x + 4y = 12
FINAL: | 2.089782 | 2.089782 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 18 | 3.878248 | Solve this system for x:
3.8782477141982556x + 1y = 10
2x + 4y = 12
FINAL: | 2.07208 | 2.07208 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 19 | 3.911542 | Solve this system for x:
3.9115422619561997x + 1y = 10
2x + 4y = 12
FINAL: | 2.051858 | 2.051858 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 20 | 3.948236 | Solve this system for x:
3.948236190979496x + 1y = 10
2x + 4y = 12
FINAL: | 2.030023 | 2.030023 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 21 | 3.986919 | Solve this system for x:
3.9869193741539712x + 1y = 10
2x + 4y = 12
FINAL: | 2.007503 | 2.007503 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 22 | 4.026105 | Solve this system for x:
4.02610523844401x + 1y = 10
2x + 4y = 12
FINAL: | 1.985193 | 1.985193 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 23 | 4.064288 | Solve this system for x:
4.064287893060632x + 1y = 10
2x + 4y = 12
FINAL: | 1.963927 | 1.963927 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 24 | 4.1 | Solve this system for x:
4.1x + 1y = 10
2x + 4y = 12
FINAL: | 1.944444 | 1.944444 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 25 | 4.131869 | Solve this system for x:
4.1318691630200135x + 1y = 10
2x + 4y = 12
FINAL: | 1.927382 | 1.927382 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 26 | 4.158671 | Solve this system for x:
4.158670668058247x + 1y = 10
2x + 4y = 12
FINAL: | 1.913263 | 1.913263 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 27 | 4.179375 | Solve this system for x:
4.179374548306537x + 1y = 10
2x + 4y = 12
FINAL: | 1.902497 | 1.902497 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 28 | 4.193185 | Solve this system for x:
4.193185165257813x + 1y = 10
2x + 4y = 12
FINAL: | 1.895383 | 1.895383 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 29 | 4.199572 | Solve this system for x:
4.199571784647721x + 1y = 10
2x + 4y = 12
FINAL: | 1.892111 | 1.892111 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 30 | 4.198289 | Solve this system for x:
4.198288972274762x + 1y = 10
2x + 4y = 12
FINAL: | 1.892767 | 1.892767 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 31 | 4.189386 | Solve this system for x:
4.189386025899021x + 1y = 10
2x + 4y = 12
FINAL: | 1.897335 | 1.897335 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 32 | 4.173205 | Solve this system for x:
4.173205080756888x + 1y = 10
2x + 4y = 12
FINAL: | 1.905693 | 1.905693 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 33 | 4.150368 | Solve this system for x:
4.150367961495795x + 1y = 10
2x + 4y = 12
FINAL: | 1.917615 | 1.917615 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 34 | 4.121752 | Solve this system for x:
4.121752285801744x + 1y = 10
2x + 4y = 12
FINAL: | 1.932766 | 1.932766 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 35 | 4.088458 | Solve this system for x:
4.0884577380438x + 1y = 10
2x + 4y = 12
FINAL: | 1.950699 | 1.950699 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 36 | 4.051764 | Solve this system for x:
4.051763809020504x + 1y = 10
2x + 4y = 12
FINAL: | 1.970852 | 1.970852 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 37 | 4.013081 | Solve this system for x:
4.013080625846029x + 1y = 10
2x + 4y = 12
FINAL: | 1.992553 | 1.992553 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 38 | 3.973895 | Solve this system for x:
3.97389476155599x + 1y = 10
2x + 4y = 12
FINAL: | 2.015029 | 2.015029 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 39 | 3.935712 | Solve this system for x:
3.9357121069393677x + 1y = 10
2x + 4y = 12
FINAL: | 2.037423 | 2.037423 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 40 | 3.9 | Solve this system for x:
3.9000000000000004x + 1y = 10
2x + 4y = 12
FINAL: | 2.058824 | 2.058824 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 41 | 3.868131 | Solve this system for x:
3.8681308369799865x + 1y = 10
2x + 4y = 12
FINAL: | 2.078304 | 2.078304 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 42 | 3.841329 | Solve this system for x:
3.841329331941753x + 1y = 10
2x + 4y = 12
FINAL: | 2.094975 | 2.094975 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 43 | 3.820625 | Solve this system for x:
3.8206254516934623x + 1y = 10
2x + 4y = 12
FINAL: | 2.108037 | 2.108037 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 44 | 3.806815 | Solve this system for x:
3.8068148347421866x + 1y = 10
2x + 4y = 12
FINAL: | 2.116841 | 2.116841 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 45 | 3.800428 | Solve this system for x:
3.8004282153522793x + 1y = 10
2x + 4y = 12
FINAL: | 2.120937 | 2.120937 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 46 | 3.801711 | Solve this system for x:
3.8017110277252377x + 1y = 10
2x + 4y = 12
FINAL: | 2.120113 | 2.120113 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 47 | 3.810614 | Solve this system for x:
3.810613974100979x + 1y = 10
2x + 4y = 12
FINAL: | 2.114411 | 2.114411 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 48 | 3.826795 | Solve this system for x:
3.8267949192431123x + 1y = 10
2x + 4y = 12
FINAL: | 2.104127 | 2.104127 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 49 | 3.849632 | Solve this system for x:
3.8496320385042044x + 1y = 10
2x + 4y = 12
FINAL: | 2.089782 | 2.089782 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 50 | 3.878248 | Solve this system for x:
3.8782477141982556x + 1y = 10
2x + 4y = 12
FINAL: | 2.07208 | 2.07208 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 51 | 3.911542 | Solve this system for x:
3.9115422619561997x + 1y = 10
2x + 4y = 12
FINAL: | 2.051858 | 2.051858 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 52 | 3.948236 | Solve this system for x:
3.948236190979496x + 1y = 10
2x + 4y = 12
FINAL: | 2.030023 | 2.030023 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 53 | 3.986919 | Solve this system for x:
3.9869193741539712x + 1y = 10
2x + 4y = 12
FINAL: | 2.007503 | 2.007503 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 54 | 4.026105 | Solve this system for x:
4.02610523844401x + 1y = 10
2x + 4y = 12
FINAL: | 1.985193 | 1.985193 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 55 | 4.064288 | Solve this system for x:
4.064287893060632x + 1y = 10
2x + 4y = 12
FINAL: | 1.963927 | 1.963927 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 56 | 4.1 | Solve this system for x:
4.1x + 1y = 10
2x + 4y = 12
FINAL: | 1.944444 | 1.944444 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 57 | 4.131869 | Solve this system for x:
4.1318691630200135x + 1y = 10
2x + 4y = 12
FINAL: | 1.927382 | 1.927382 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 58 | 4.158671 | Solve this system for x:
4.158670668058247x + 1y = 10
2x + 4y = 12
FINAL: | 1.913263 | 1.913263 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 59 | 4.179375 | Solve this system for x:
4.179374548306537x + 1y = 10
2x + 4y = 12
FINAL: | 1.902497 | 1.902497 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 60 | 4.193185 | Solve this system for x:
4.193185165257813x + 1y = 10
2x + 4y = 12
FINAL: | 1.895383 | 1.895383 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 61 | 4.199572 | Solve this system for x:
4.199571784647721x + 1y = 10
2x + 4y = 12
FINAL: | 1.892111 | 1.892111 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 62 | 4.198289 | Solve this system for x:
4.198288972274762x + 1y = 10
2x + 4y = 12
FINAL: | 1.892767 | 1.892767 |
linear_system | 2 | sinusoid | 1 | 2 | 120 | 63 | 4.189386 | Solve this system for x:
4.189386025899021x + 1y = 10
2x + 4y = 12
FINAL: | 1.897335 | 1.897335 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 0 | 4.173205 | Solve this system for x:
4.173205080756888x + 1y = 10
2x + 4y = 12
FINAL: | 1.905693 | 1.905693 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 1 | 4.121752 | Solve this system for x:
4.121752285801744x + 1y = 10
2x + 4y = 12
FINAL: | 1.932766 | 1.932766 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 2 | 4.051764 | Solve this system for x:
4.051763809020504x + 1y = 10
2x + 4y = 12
FINAL: | 1.970852 | 1.970852 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 3 | 3.973895 | Solve this system for x:
3.97389476155599x + 1y = 10
2x + 4y = 12
FINAL: | 2.015029 | 2.015029 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 4 | 3.9 | Solve this system for x:
3.9x + 1y = 10
2x + 4y = 12
FINAL: | 2.058824 | 2.058824 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 5 | 3.841329 | Solve this system for x:
3.841329331941753x + 1y = 10
2x + 4y = 12
FINAL: | 2.094975 | 2.094975 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 6 | 3.806815 | Solve this system for x:
3.806814834742186x + 1y = 10
2x + 4y = 12
FINAL: | 2.116841 | 2.116841 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 7 | 3.801711 | Solve this system for x:
3.8017110277252377x + 1y = 10
2x + 4y = 12
FINAL: | 2.120113 | 2.120113 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 8 | 3.826795 | Solve this system for x:
3.8267949192431123x + 1y = 10
2x + 4y = 12
FINAL: | 2.104127 | 2.104127 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 9 | 3.878248 | Solve this system for x:
3.8782477141982556x + 1y = 10
2x + 4y = 12
FINAL: | 2.07208 | 2.07208 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 10 | 3.948236 | Solve this system for x:
3.948236190979496x + 1y = 10
2x + 4y = 12
FINAL: | 2.030023 | 2.030023 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 11 | 4.026105 | Solve this system for x:
4.02610523844401x + 1y = 10
2x + 4y = 12
FINAL: | 1.985193 | 1.985193 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 12 | 4.1 | Solve this system for x:
4.1x + 1y = 10
2x + 4y = 12
FINAL: | 1.944444 | 1.944444 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 13 | 4.158671 | Solve this system for x:
4.158670668058247x + 1y = 10
2x + 4y = 12
FINAL: | 1.913263 | 1.913263 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 14 | 4.193185 | Solve this system for x:
4.193185165257813x + 1y = 10
2x + 4y = 12
FINAL: | 1.895383 | 1.895383 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 15 | 4.198289 | Solve this system for x:
4.198288972274762x + 1y = 10
2x + 4y = 12
FINAL: | 1.892767 | 1.892767 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 16 | 4.173205 | Solve this system for x:
4.173205080756888x + 1y = 10
2x + 4y = 12
FINAL: | 1.905693 | 1.905693 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 17 | 4.121752 | Solve this system for x:
4.121752285801744x + 1y = 10
2x + 4y = 12
FINAL: | 1.932766 | 1.932766 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 18 | 4.051764 | Solve this system for x:
4.051763809020504x + 1y = 10
2x + 4y = 12
FINAL: | 1.970852 | 1.970852 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 19 | 3.973895 | Solve this system for x:
3.97389476155599x + 1y = 10
2x + 4y = 12
FINAL: | 2.015029 | 2.015029 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 20 | 3.9 | Solve this system for x:
3.9000000000000004x + 1y = 10
2x + 4y = 12
FINAL: | 2.058824 | 2.058824 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 21 | 3.841329 | Solve this system for x:
3.841329331941753x + 1y = 10
2x + 4y = 12
FINAL: | 2.094975 | 2.094975 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 22 | 3.806815 | Solve this system for x:
3.8068148347421866x + 1y = 10
2x + 4y = 12
FINAL: | 2.116841 | 2.116841 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 23 | 3.801711 | Solve this system for x:
3.8017110277252377x + 1y = 10
2x + 4y = 12
FINAL: | 2.120113 | 2.120113 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 24 | 3.826795 | Solve this system for x:
3.8267949192431123x + 1y = 10
2x + 4y = 12
FINAL: | 2.104127 | 2.104127 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 25 | 3.878248 | Solve this system for x:
3.8782477141982556x + 1y = 10
2x + 4y = 12
FINAL: | 2.07208 | 2.07208 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 26 | 3.948236 | Solve this system for x:
3.948236190979496x + 1y = 10
2x + 4y = 12
FINAL: | 2.030023 | 2.030023 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 27 | 4.026105 | Solve this system for x:
4.02610523844401x + 1y = 10
2x + 4y = 12
FINAL: | 1.985193 | 1.985193 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 28 | 4.1 | Solve this system for x:
4.1x + 1y = 10
2x + 4y = 12
FINAL: | 1.944444 | 1.944444 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 29 | 4.158671 | Solve this system for x:
4.158670668058247x + 1y = 10
2x + 4y = 12
FINAL: | 1.913263 | 1.913263 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 30 | 4.193185 | Solve this system for x:
4.193185165257813x + 1y = 10
2x + 4y = 12
FINAL: | 1.895383 | 1.895383 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 31 | 4.198289 | Solve this system for x:
4.198288972274762x + 1y = 10
2x + 4y = 12
FINAL: | 1.892767 | 1.892767 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 32 | 4.173205 | Solve this system for x:
4.173205080756888x + 1y = 10
2x + 4y = 12
FINAL: | 1.905693 | 1.905693 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 33 | 4.121752 | Solve this system for x:
4.121752285801744x + 1y = 10
2x + 4y = 12
FINAL: | 1.932766 | 1.932766 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 34 | 4.051764 | Solve this system for x:
4.051763809020504x + 1y = 10
2x + 4y = 12
FINAL: | 1.970852 | 1.970852 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 35 | 3.973895 | Solve this system for x:
3.97389476155599x + 1y = 10
2x + 4y = 12
FINAL: | 2.015029 | 2.015029 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 36 | 3.9 | Solve this system for x:
3.9000000000000004x + 1y = 10
2x + 4y = 12
FINAL: | 2.058824 | 2.058824 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 37 | 3.841329 | Solve this system for x:
3.8413293319417527x + 1y = 10
2x + 4y = 12
FINAL: | 2.094975 | 2.094975 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 38 | 3.806815 | Solve this system for x:
3.806814834742186x + 1y = 10
2x + 4y = 12
FINAL: | 2.116841 | 2.116841 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 39 | 3.801711 | Solve this system for x:
3.8017110277252377x + 1y = 10
2x + 4y = 12
FINAL: | 2.120113 | 2.120113 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 40 | 3.826795 | Solve this system for x:
3.8267949192431123x + 1y = 10
2x + 4y = 12
FINAL: | 2.104127 | 2.104127 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 41 | 3.878248 | Solve this system for x:
3.8782477141982556x + 1y = 10
2x + 4y = 12
FINAL: | 2.07208 | 2.07208 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 42 | 3.948236 | Solve this system for x:
3.9482361909794963x + 1y = 10
2x + 4y = 12
FINAL: | 2.030023 | 2.030023 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 43 | 4.026105 | Solve this system for x:
4.026105238444011x + 1y = 10
2x + 4y = 12
FINAL: | 1.985193 | 1.985193 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 44 | 4.1 | Solve this system for x:
4.1x + 1y = 10
2x + 4y = 12
FINAL: | 1.944444 | 1.944444 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 45 | 4.158671 | Solve this system for x:
4.158670668058247x + 1y = 10
2x + 4y = 12
FINAL: | 1.913263 | 1.913263 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 46 | 4.193185 | Solve this system for x:
4.193185165257813x + 1y = 10
2x + 4y = 12
FINAL: | 1.895383 | 1.895383 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 47 | 4.198289 | Solve this system for x:
4.198288972274762x + 1y = 10
2x + 4y = 12
FINAL: | 1.892767 | 1.892767 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 48 | 4.173205 | Solve this system for x:
4.173205080756888x + 1y = 10
2x + 4y = 12
FINAL: | 1.905693 | 1.905693 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 49 | 4.121752 | Solve this system for x:
4.121752285801744x + 1y = 10
2x + 4y = 12
FINAL: | 1.932766 | 1.932766 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 50 | 4.051764 | Solve this system for x:
4.051763809020504x + 1y = 10
2x + 4y = 12
FINAL: | 1.970852 | 1.970852 |
linear_system | 2 | sinusoid | 1 | 4 | 120 | 51 | 3.973895 | Solve this system for x:
3.97389476155599x + 1y = 10
2x + 4y = 12
FINAL: | 2.015029 | 2.015029 |
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