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 | 2.5 | 2 | 0 | 16 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 17 | 3.902455 | Solve this system for x:
3.902454838991936x + 2y = 8
1x + 3y = 9
FINAL: | 0.618087 | 0.618087 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 18 | 3.808658 | Solve this system for x:
3.808658283817455x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 19 | 3.722215 | Solve this system for x:
3.722214883490199x + 2y = 8
1x + 3y = 9
FINAL: | 0.654547 | 0.654547 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 20 | 3.646447 | Solve this system for x:
3.646446609406726x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 21 | 3.584265 | Solve this system for x:
3.5842651938487275x + 2y = 8
1x + 3y = 9
FINAL: | 0.685495 | 0.685495 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 22 | 3.53806 | Solve this system for x:
3.538060233744357x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 23 | 3.509607 | Solve this system for x:
3.509607359798385x + 2y = 8
1x + 3y = 9
FINAL: | 0.703497 | 0.703497 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 24 | 3.5 | Solve this system for x:
3.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.705882 | 0.705882 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 25 | 3.509607 | Solve this system for x:
3.509607359798385x + 2y = 8
1x + 3y = 9
FINAL: | 0.703497 | 0.703497 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 26 | 3.53806 | Solve this system for x:
3.5380602337443565x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 27 | 3.584265 | Solve this system for x:
3.584265193848727x + 2y = 8
1x + 3y = 9
FINAL: | 0.685495 | 0.685495 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 28 | 3.646447 | Solve this system for x:
3.646446609406726x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 29 | 3.722215 | Solve this system for x:
3.722214883490199x + 2y = 8
1x + 3y = 9
FINAL: | 0.654547 | 0.654547 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 30 | 3.808658 | Solve this system for x:
3.8086582838174547x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 31 | 3.902455 | Solve this system for x:
3.9024548389919356x + 2y = 8
1x + 3y = 9
FINAL: | 0.618087 | 0.618087 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 32 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 33 | 4.097545 | Solve this system for x:
4.097545161008064x + 2y = 8
1x + 3y = 9
FINAL: | 0.582941 | 0.582941 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 34 | 4.191342 | Solve this system for x:
4.191341716182545x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 35 | 4.277785 | Solve this system for x:
4.277785116509801x + 2y = 8
1x + 3y = 9
FINAL: | 0.553845 | 0.553845 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 36 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 37 | 4.415735 | Solve this system for x:
4.4157348061512725x + 2y = 8
1x + 3y = 9
FINAL: | 0.533466 | 0.533466 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 38 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 39 | 4.490393 | Solve this system for x:
4.490392640201615x + 2y = 8
1x + 3y = 9
FINAL: | 0.52305 | 0.52305 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 40 | 4.5 | Solve this system for x:
4.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.521739 | 0.521739 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 41 | 4.490393 | Solve this system for x:
4.490392640201615x + 2y = 8
1x + 3y = 9
FINAL: | 0.52305 | 0.52305 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 42 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 43 | 4.415735 | Solve this system for x:
4.4157348061512725x + 2y = 8
1x + 3y = 9
FINAL: | 0.533466 | 0.533466 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 44 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 45 | 4.277785 | Solve this system for x:
4.2777851165098015x + 2y = 8
1x + 3y = 9
FINAL: | 0.553845 | 0.553845 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 46 | 4.191342 | Solve this system for x:
4.191341716182546x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 47 | 4.097545 | Solve this system for x:
4.097545161008064x + 2y = 8
1x + 3y = 9
FINAL: | 0.582941 | 0.582941 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 48 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 49 | 3.902455 | Solve this system for x:
3.9024548389919365x + 2y = 8
1x + 3y = 9
FINAL: | 0.618087 | 0.618087 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 50 | 3.808658 | Solve this system for x:
3.808658283817455x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 51 | 3.722215 | Solve this system for x:
3.7222148834901994x + 2y = 8
1x + 3y = 9
FINAL: | 0.654547 | 0.654547 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 52 | 3.646447 | Solve this system for x:
3.646446609406726x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 53 | 3.584265 | Solve this system for x:
3.5842651938487275x + 2y = 8
1x + 3y = 9
FINAL: | 0.685495 | 0.685495 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 54 | 3.53806 | Solve this system for x:
3.538060233744357x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 55 | 3.509607 | Solve this system for x:
3.509607359798385x + 2y = 8
1x + 3y = 9
FINAL: | 0.703497 | 0.703497 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 56 | 3.5 | Solve this system for x:
3.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.705882 | 0.705882 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 57 | 3.509607 | Solve this system for x:
3.509607359798385x + 2y = 8
1x + 3y = 9
FINAL: | 0.703497 | 0.703497 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 58 | 3.53806 | Solve this system for x:
3.5380602337443565x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 59 | 3.584265 | Solve this system for x:
3.584265193848727x + 2y = 8
1x + 3y = 9
FINAL: | 0.685495 | 0.685495 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 60 | 3.646447 | Solve this system for x:
3.6464466094067256x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 61 | 3.722215 | Solve this system for x:
3.722214883490199x + 2y = 8
1x + 3y = 9
FINAL: | 0.654547 | 0.654547 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 62 | 3.808658 | Solve this system for x:
3.8086582838174547x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 2 | 0 | 63 | 3.902455 | Solve this system for x:
3.902454838991936x + 2y = 8
1x + 3y = 9
FINAL: | 0.618087 | 0.618087 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 0 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 1 | 4.191342 | Solve this system for x:
4.191341716182545x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 2 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 3 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 4 | 4.5 | Solve this system for x:
4.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.521739 | 0.521739 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 5 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 6 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 7 | 4.191342 | Solve this system for x:
4.191341716182545x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 8 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 9 | 3.808658 | Solve this system for x:
3.808658283817455x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 10 | 3.646447 | Solve this system for x:
3.646446609406726x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 11 | 3.53806 | Solve this system for x:
3.538060233744357x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 12 | 3.5 | Solve this system for x:
3.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.705882 | 0.705882 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 13 | 3.53806 | Solve this system for x:
3.5380602337443565x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 14 | 3.646447 | Solve this system for x:
3.646446609406726x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 15 | 3.808658 | Solve this system for x:
3.8086582838174547x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 16 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 17 | 4.191342 | Solve this system for x:
4.191341716182545x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 18 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 19 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 20 | 4.5 | Solve this system for x:
4.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.521739 | 0.521739 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 21 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 22 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 23 | 4.191342 | Solve this system for x:
4.191341716182546x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 24 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 25 | 3.808658 | Solve this system for x:
3.808658283817455x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 26 | 3.646447 | Solve this system for x:
3.646446609406726x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 27 | 3.53806 | Solve this system for x:
3.538060233744357x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 28 | 3.5 | Solve this system for x:
3.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.705882 | 0.705882 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 29 | 3.53806 | Solve this system for x:
3.5380602337443565x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 30 | 3.646447 | Solve this system for x:
3.6464466094067256x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 31 | 3.808658 | Solve this system for x:
3.8086582838174547x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 32 | 4 | Solve this system for x:
3.9999999999999996x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 33 | 4.191342 | Solve this system for x:
4.191341716182545x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 34 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 35 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 36 | 4.5 | Solve this system for x:
4.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.521739 | 0.521739 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 37 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 38 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 39 | 4.191342 | Solve this system for x:
4.191341716182546x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 40 | 4 | Solve this system for x:
4.0x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 41 | 3.808658 | Solve this system for x:
3.808658283817456x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 42 | 3.646447 | Solve this system for x:
3.646446609406726x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 43 | 3.53806 | Solve this system for x:
3.538060233744357x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 44 | 3.5 | Solve this system for x:
3.5x + 2y = 8
1x + 3y = 9
FINAL: | 0.705882 | 0.705882 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 45 | 3.53806 | Solve this system for x:
3.5380602337443565x + 2y = 8
1x + 3y = 9
FINAL: | 0.696526 | 0.696526 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 46 | 3.646447 | Solve this system for x:
3.6464466094067256x + 2y = 8
1x + 3y = 9
FINAL: | 0.671191 | 0.671191 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 47 | 3.808658 | Solve this system for x:
3.808658283817455x + 2y = 8
1x + 3y = 9
FINAL: | 0.636539 | 0.636539 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 48 | 4 | Solve this system for x:
3.9999999999999996x + 2y = 8
1x + 3y = 9
FINAL: | 0.6 | 0.6 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 49 | 4.191342 | Solve this system for x:
4.191341716182544x + 2y = 8
1x + 3y = 9
FINAL: | 0.567428 | 0.567428 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 50 | 4.353553 | Solve this system for x:
4.353553390593274x + 2y = 8
1x + 3y = 9
FINAL: | 0.542463 | 0.542463 |
linear_system | 1 | sinusoid | 2.5 | 4 | 0 | 51 | 4.46194 | Solve this system for x:
4.461939766255643x + 2y = 8
1x + 3y = 9
FINAL: | 0.526971 | 0.526971 |
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