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 | 0.5 | 16 | 120 | 4 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 5 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 6 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 7 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 8 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 9 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 10 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 11 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 12 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 13 | 3.95 | Solve this system for x:
3.9499999999999997x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 14 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 15 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 16 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 17 | 3.95 | Solve this system for x:
3.9499999999999997x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 18 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 19 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 20 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 21 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 22 | 3.913397 | Solve this system for x:
3.9133974596215557x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 23 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 24 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 25 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 26 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 27 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 28 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 29 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 30 | 3.913397 | Solve this system for x:
3.9133974596215557x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 31 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 32 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 33 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 34 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 35 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 36 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 37 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 38 | 3.913397 | Solve this system for x:
3.9133974596215557x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 39 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 40 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 41 | 3.95 | Solve this system for x:
3.950000000000001x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 42 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 43 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 44 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 45 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 46 | 3.913397 | Solve this system for x:
3.9133974596215557x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 47 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 48 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 49 | 3.95 | Solve this system for x:
3.950000000000001x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 50 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 51 | 4.05 | Solve this system for x:
4.049999999999999x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 52 | 4.086603 | Solve this system for x:
4.086602540378443x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 53 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 54 | 3.913397 | Solve this system for x:
3.9133974596215557x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 55 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 56 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 57 | 3.95 | Solve this system for x:
3.950000000000001x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 58 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 59 | 4.05 | Solve this system for x:
4.049999999999999x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 60 | 4.086603 | Solve this system for x:
4.086602540378444x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 61 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 62 | 3.913397 | Solve this system for x:
3.9133974596215557x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 63 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 0 | 3.913397 | Solve this system for x:
3.913397459621556x + 1y = 10
2x + 4y = 12
FINAL: | 2.050743 | 2.050743 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 1 | 3.908914 | Solve this system for x:
3.9089136175078822x + 1y = 10
2x + 4y = 12
FINAL: | 2.05344 | 2.05344 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 2 | 3.905307 | Solve this system for x:
3.9053069870504893x + 1y = 10
2x + 4y = 12
FINAL: | 2.055615 | 2.055615 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 3 | 3.902612 | Solve this system for x:
3.9026123020722667x + 1y = 10
2x + 4y = 12
FINAL: | 2.057243 | 2.057243 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 4 | 3.900856 | Solve this system for x:
3.900855513862619x + 1y = 10
2x + 4y = 12
FINAL: | 2.058306 | 2.058306 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 5 | 3.900054 | Solve this system for x:
3.9000535412523636x + 1y = 10
2x + 4y = 12
FINAL: | 2.058791 | 2.058791 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 6 | 3.900214 | Solve this system for x:
3.9002141076761396x + 1y = 10
2x + 4y = 12
FINAL: | 2.058694 | 2.058694 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 7 | 3.901336 | Solve this system for x:
3.9013356667915122x + 1y = 10
2x + 4y = 12
FINAL: | 2.058015 | 2.058015 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 8 | 3.903407 | Solve this system for x:
3.9034074173710933x + 1y = 10
2x + 4y = 12
FINAL: | 2.056762 | 2.056762 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 9 | 3.906409 | Solve this system for x:
3.9064094073242672x + 1y = 10
2x + 4y = 12
FINAL: | 2.05495 | 2.05495 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 10 | 3.910313 | Solve this system for x:
3.910312725846731x + 1y = 10
2x + 4y = 12
FINAL: | 2.052598 | 2.052598 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 11 | 3.91508 | Solve this system for x:
3.915079781847342x + 1y = 10
2x + 4y = 12
FINAL: | 2.049732 | 2.049732 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 12 | 3.920665 | Solve this system for x:
3.9206646659708766x + 1y = 10
2x + 4y = 12
FINAL: | 2.046386 | 2.046386 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 13 | 3.927014 | Solve this system for x:
3.9270135927302166x + 1y = 10
2x + 4y = 12
FINAL: | 2.042595 | 2.042595 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 14 | 3.934065 | Solve this system for x:
3.9340654184899932x + 1y = 10
2x + 4y = 12
FINAL: | 2.0384 | 2.0384 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 15 | 3.941752 | Solve this system for x:
3.9417522303132198x + 1y = 10
2x + 4y = 12
FINAL: | 2.033848 | 2.033848 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 16 | 3.95 | Solve this system for x:
3.95x + 1y = 10
2x + 4y = 12
FINAL: | 2.028986 | 2.028986 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 17 | 3.958729 | Solve this system for x:
3.9587292970195604x + 1y = 10
2x + 4y = 12
FINAL: | 2.023865 | 2.023865 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 18 | 3.967856 | Solve this system for x:
3.9678560534696836x + 1y = 10
2x + 4y = 12
FINAL: | 2.018538 | 2.018538 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 19 | 3.977292 | Solve this system for x:
3.9772923736965624x + 1y = 10
2x + 4y = 12
FINAL: | 2.013061 | 2.013061 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 20 | 3.986947 | Solve this system for x:
3.9869473807779947x + 1y = 10
2x + 4y = 12
FINAL: | 2.007487 | 2.007487 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 21 | 3.996728 | Solve this system for x:
3.9967280917178223x + 1y = 10
2x + 4y = 12
FINAL: | 2.001871 | 2.001871 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 22 | 4.00654 | Solve this system for x:
4.006540312923014x + 1y = 10
2x + 4y = 12
FINAL: | 1.99627 | 1.99627 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 23 | 4.01629 | Solve this system for x:
4.016289547339459x + 1y = 10
2x + 4y = 12
FINAL: | 1.990735 | 1.990735 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 24 | 4.025882 | Solve this system for x:
4.025881904510252x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 25 | 4.035225 | Solve this system for x:
4.035225004792124x + 1y = 10
2x + 4y = 12
FINAL: | 1.980072 | 1.980072 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 26 | 4.044229 | Solve this system for x:
4.0442288690219x + 1y = 10
2x + 4y = 12
FINAL: | 1.975042 | 1.975042 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 27 | 4.052807 | Solve this system for x:
4.052806785065036x + 1y = 10
2x + 4y = 12
FINAL: | 1.970273 | 1.970273 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 28 | 4.060876 | Solve this system for x:
4.060876142900872x + 1y = 10
2x + 4y = 12
FINAL: | 1.965808 | 1.965808 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 29 | 4.068359 | Solve this system for x:
4.0683592302022875x + 1y = 10
2x + 4y = 12
FINAL: | 1.961686 | 1.961686 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 30 | 4.075184 | Solve this system for x:
4.075183980747898x + 1y = 10
2x + 4y = 12
FINAL: | 1.957941 | 1.957941 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 31 | 4.081285 | Solve this system for x:
4.081284668459161x + 1y = 10
2x + 4y = 12
FINAL: | 1.954606 | 1.954606 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 32 | 4.086603 | Solve this system for x:
4.086602540378443x + 1y = 10
2x + 4y = 12
FINAL: | 1.951708 | 1.951708 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 33 | 4.091086 | Solve this system for x:
4.091086382492118x + 1y = 10
2x + 4y = 12
FINAL: | 1.949271 | 1.949271 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 34 | 4.094693 | Solve this system for x:
4.09469301294951x + 1y = 10
2x + 4y = 12
FINAL: | 1.947315 | 1.947315 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 35 | 4.097388 | Solve this system for x:
4.097387697927734x + 1y = 10
2x + 4y = 12
FINAL: | 1.945856 | 1.945856 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 36 | 4.099144 | Solve this system for x:
4.099144486137381x + 1y = 10
2x + 4y = 12
FINAL: | 1.944907 | 1.944907 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 37 | 4.099946 | Solve this system for x:
4.099946458747636x + 1y = 10
2x + 4y = 12
FINAL: | 1.944473 | 1.944473 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 38 | 4.099786 | Solve this system for x:
4.09978589232386x + 1y = 10
2x + 4y = 12
FINAL: | 1.94456 | 1.94456 |
linear_system | 2 | sinusoid | 0.5 | 1 | 240 | 39 | 4.098664 | Solve this system for x:
4.098664333208488x + 1y = 10
2x + 4y = 12
FINAL: | 1.945166 | 1.945166 |
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