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 | 1 | sinusoid | 1 | 2 | 240 | 56 | 4.1 | Solve this system for x:
4.1x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 57 | 4.064288 | Solve this system for x:
4.064287893060633x + 2y = 8
1x + 3y = 9
FINAL: | 0.588647 | 0.588647 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 58 | 4.026105 | Solve this system for x:
4.026105238444011x + 2y = 8
1x + 3y = 9
FINAL: | 0.595338 | 0.595338 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 59 | 3.986919 | Solve this system for x:
3.9869193741539717x + 2y = 8
1x + 3y = 9
FINAL: | 0.602364 | 0.602364 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 60 | 3.948236 | Solve this system for x:
3.9482361909794963x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 61 | 3.911542 | Solve this system for x:
3.9115422619561997x + 2y = 8
1x + 3y = 9
FINAL: | 0.616356 | 0.616356 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 62 | 3.878248 | Solve this system for x:
3.878247714198256x + 2y = 8
1x + 3y = 9
FINAL: | 0.622746 | 0.622746 |
linear_system | 1 | sinusoid | 1 | 2 | 240 | 63 | 3.849632 | Solve this system for x:
3.849632038504205x + 2y = 8
1x + 3y = 9
FINAL: | 0.628345 | 0.628345 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 0 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 1 | 3.801711 | Solve this system for x:
3.801711027725238x + 2y = 8
1x + 3y = 9
FINAL: | 0.63795 | 0.63795 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 2 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 3 | 3.841329 | Solve this system for x:
3.841329331941753x + 2y = 8
1x + 3y = 9
FINAL: | 0.629988 | 0.629988 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 4 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 5 | 3.973895 | Solve this system for x:
3.9738947615559894x + 2y = 8
1x + 3y = 9
FINAL: | 0.604736 | 0.604736 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 6 | 4.051764 | Solve this system for x:
4.051763809020504x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 7 | 4.121752 | Solve this system for x:
4.121752285801744x + 2y = 8
1x + 3y = 9
FINAL: | 0.578857 | 0.578857 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 8 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 9 | 4.198289 | Solve this system for x:
4.198288972274762x + 2y = 8
1x + 3y = 9
FINAL: | 0.566312 | 0.566312 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 10 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 11 | 4.158671 | Solve this system for x:
4.158670668058248x + 2y = 8
1x + 3y = 9
FINAL: | 0.572737 | 0.572737 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 12 | 4.1 | Solve this system for x:
4.1x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 13 | 4.026105 | Solve this system for x:
4.026105238444011x + 2y = 8
1x + 3y = 9
FINAL: | 0.595338 | 0.595338 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 14 | 3.948236 | Solve this system for x:
3.948236190979496x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 15 | 3.878248 | Solve this system for x:
3.878247714198256x + 2y = 8
1x + 3y = 9
FINAL: | 0.622746 | 0.622746 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 16 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 17 | 3.801711 | Solve this system for x:
3.8017110277252377x + 2y = 8
1x + 3y = 9
FINAL: | 0.63795 | 0.63795 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 18 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 19 | 3.841329 | Solve this system for x:
3.8413293319417527x + 2y = 8
1x + 3y = 9
FINAL: | 0.629988 | 0.629988 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 20 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 21 | 3.973895 | Solve this system for x:
3.9738947615559894x + 2y = 8
1x + 3y = 9
FINAL: | 0.604736 | 0.604736 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 22 | 4.051764 | Solve this system for x:
4.051763809020503x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 23 | 4.121752 | Solve this system for x:
4.121752285801744x + 2y = 8
1x + 3y = 9
FINAL: | 0.578857 | 0.578857 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 24 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 25 | 4.198289 | Solve this system for x:
4.198288972274762x + 2y = 8
1x + 3y = 9
FINAL: | 0.566312 | 0.566312 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 26 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 27 | 4.158671 | Solve this system for x:
4.158670668058248x + 2y = 8
1x + 3y = 9
FINAL: | 0.572737 | 0.572737 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 28 | 4.1 | Solve this system for x:
4.1x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 29 | 4.026105 | Solve this system for x:
4.026105238444011x + 2y = 8
1x + 3y = 9
FINAL: | 0.595338 | 0.595338 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 30 | 3.948236 | Solve this system for x:
3.9482361909794963x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 31 | 3.878248 | Solve this system for x:
3.878247714198256x + 2y = 8
1x + 3y = 9
FINAL: | 0.622746 | 0.622746 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 32 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 33 | 3.801711 | Solve this system for x:
3.8017110277252377x + 2y = 8
1x + 3y = 9
FINAL: | 0.63795 | 0.63795 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 34 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 35 | 3.841329 | Solve this system for x:
3.8413293319417527x + 2y = 8
1x + 3y = 9
FINAL: | 0.629988 | 0.629988 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 36 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 37 | 3.973895 | Solve this system for x:
3.9738947615559894x + 2y = 8
1x + 3y = 9
FINAL: | 0.604736 | 0.604736 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 38 | 4.051764 | Solve this system for x:
4.051763809020503x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 39 | 4.121752 | Solve this system for x:
4.121752285801744x + 2y = 8
1x + 3y = 9
FINAL: | 0.578857 | 0.578857 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 40 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 41 | 4.198289 | Solve this system for x:
4.198288972274762x + 2y = 8
1x + 3y = 9
FINAL: | 0.566312 | 0.566312 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 42 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 43 | 4.158671 | Solve this system for x:
4.158670668058248x + 2y = 8
1x + 3y = 9
FINAL: | 0.572737 | 0.572737 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 44 | 4.1 | Solve this system for x:
4.1000000000000005x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 45 | 4.026105 | Solve this system for x:
4.026105238444011x + 2y = 8
1x + 3y = 9
FINAL: | 0.595338 | 0.595338 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 46 | 3.948236 | Solve this system for x:
3.9482361909794963x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 47 | 3.878248 | Solve this system for x:
3.878247714198256x + 2y = 8
1x + 3y = 9
FINAL: | 0.622746 | 0.622746 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 48 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 49 | 3.801711 | Solve this system for x:
3.801711027725238x + 2y = 8
1x + 3y = 9
FINAL: | 0.63795 | 0.63795 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 50 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 51 | 3.841329 | Solve this system for x:
3.8413293319417527x + 2y = 8
1x + 3y = 9
FINAL: | 0.629988 | 0.629988 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 52 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 53 | 3.973895 | Solve this system for x:
3.9738947615559894x + 2y = 8
1x + 3y = 9
FINAL: | 0.604736 | 0.604736 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 54 | 4.051764 | Solve this system for x:
4.051763809020503x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 55 | 4.121752 | Solve this system for x:
4.121752285801744x + 2y = 8
1x + 3y = 9
FINAL: | 0.578857 | 0.578857 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 56 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 57 | 4.198289 | Solve this system for x:
4.198288972274762x + 2y = 8
1x + 3y = 9
FINAL: | 0.566312 | 0.566312 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 58 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 59 | 4.158671 | Solve this system for x:
4.158670668058248x + 2y = 8
1x + 3y = 9
FINAL: | 0.572737 | 0.572737 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 60 | 4.1 | Solve this system for x:
4.1000000000000005x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 61 | 4.026105 | Solve this system for x:
4.026105238444011x + 2y = 8
1x + 3y = 9
FINAL: | 0.595338 | 0.595338 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 62 | 3.948236 | Solve this system for x:
3.9482361909794963x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 4 | 240 | 63 | 3.878248 | Solve this system for x:
3.878247714198256x + 2y = 8
1x + 3y = 9
FINAL: | 0.622746 | 0.622746 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 0 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 1 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 2 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 3 | 4.051764 | Solve this system for x:
4.051763809020504x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 4 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 5 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 6 | 4.1 | Solve this system for x:
4.1x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 7 | 3.948236 | Solve this system for x:
3.948236190979496x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 8 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 9 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 10 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 11 | 4.051764 | Solve this system for x:
4.051763809020503x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 12 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 13 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 14 | 4.1 | Solve this system for x:
4.1x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 15 | 3.948236 | Solve this system for x:
3.9482361909794963x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 16 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 17 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 18 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 19 | 4.051764 | Solve this system for x:
4.051763809020503x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 20 | 4.173205 | Solve this system for x:
4.173205080756888x + 2y = 8
1x + 3y = 9
FINAL: | 0.570363 | 0.570363 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 21 | 4.193185 | Solve this system for x:
4.193185165257813x + 2y = 8
1x + 3y = 9
FINAL: | 0.567132 | 0.567132 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 22 | 4.1 | Solve this system for x:
4.1000000000000005x + 2y = 8
1x + 3y = 9
FINAL: | 0.582524 | 0.582524 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 23 | 3.948236 | Solve this system for x:
3.9482361909794963x + 2y = 8
1x + 3y = 9
FINAL: | 0.609464 | 0.609464 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 24 | 3.826795 | Solve this system for x:
3.8267949192431123x + 2y = 8
1x + 3y = 9
FINAL: | 0.632886 | 0.632886 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 25 | 3.806815 | Solve this system for x:
3.806814834742186x + 2y = 8
1x + 3y = 9
FINAL: | 0.636913 | 0.636913 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 26 | 3.9 | Solve this system for x:
3.9x + 2y = 8
1x + 3y = 9
FINAL: | 0.618557 | 0.618557 |
linear_system | 1 | sinusoid | 1 | 8 | 240 | 27 | 4.051764 | Solve this system for x:
4.051763809020503x + 2y = 8
1x + 3y = 9
FINAL: | 0.590825 | 0.590825 |
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