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 | 4 | 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 | 4 | 120 | 33 | 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 | 4 | 120 | 34 | 4.025882 | Solve this system for x:
4.0258819045102525x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 35 | 3.986947 | Solve this system for x:
3.986947380777995x + 1y = 10
2x + 4y = 12
FINAL: | 2.007487 | 2.007487 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 36 | 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 | 4 | 120 | 37 | 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 | 4 | 120 | 38 | 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 | 4 | 120 | 39 | 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 | 4 | 120 | 40 | 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 | 4 | 120 | 41 | 3.939124 | Solve this system for x:
3.939123857099128x + 1y = 10
2x + 4y = 12
FINAL: | 2.035402 | 2.035402 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 42 | 3.974118 | Solve this system for x:
3.974118095489748x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 43 | 4.013053 | Solve this system for x:
4.013052619222005x + 1y = 10
2x + 4y = 12
FINAL: | 1.992569 | 1.992569 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 44 | 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 | 4 | 120 | 45 | 4.079335 | Solve this system for x:
4.079335334029124x + 1y = 10
2x + 4y = 12
FINAL: | 1.95567 | 1.95567 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 46 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 47 | 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 | 4 | 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 | 4 | 120 | 49 | 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 | 4 | 120 | 50 | 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 | 4 | 120 | 51 | 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 | 4 | 120 | 52 | 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 | 4 | 120 | 53 | 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 | 4 | 120 | 54 | 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 | 4 | 120 | 55 | 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 | 4 | 120 | 56 | 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 | 4 | 120 | 57 | 3.939124 | Solve this system for x:
3.939123857099128x + 1y = 10
2x + 4y = 12
FINAL: | 2.035402 | 2.035402 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 58 | 3.974118 | Solve this system for x:
3.974118095489748x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 59 | 4.013053 | Solve this system for x:
4.013052619222005x + 1y = 10
2x + 4y = 12
FINAL: | 1.992569 | 1.992569 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 60 | 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 | 4 | 120 | 61 | 4.079335 | Solve this system for x:
4.079335334029124x + 1y = 10
2x + 4y = 12
FINAL: | 1.95567 | 1.95567 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 62 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 4 | 120 | 63 | 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 | 8 | 120 | 0 | 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 | 8 | 120 | 1 | 4.025882 | Solve this system for x:
4.0258819045102525x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 2 | 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 | 8 | 120 | 3 | 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 | 8 | 120 | 4 | 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 | 8 | 120 | 5 | 3.974118 | Solve this system for x:
3.974118095489748x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 6 | 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 | 8 | 120 | 7 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 8 | 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 | 8 | 120 | 9 | 4.025882 | Solve this system for x:
4.0258819045102525x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 10 | 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 | 8 | 120 | 11 | 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 | 8 | 120 | 12 | 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 | 8 | 120 | 13 | 3.974118 | Solve this system for x:
3.974118095489748x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 14 | 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 | 8 | 120 | 15 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 8 | 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 | 8 | 120 | 17 | 4.025882 | Solve this system for x:
4.0258819045102525x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 18 | 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 | 8 | 120 | 19 | 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 | 8 | 120 | 20 | 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 | 8 | 120 | 21 | 3.974118 | Solve this system for x:
3.974118095489748x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 22 | 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 | 8 | 120 | 23 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 8 | 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 | 8 | 120 | 25 | 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 | 8 | 120 | 26 | 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 | 8 | 120 | 27 | 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 | 8 | 120 | 28 | 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 | 8 | 120 | 29 | 3.974118 | Solve this system for x:
3.974118095489748x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 30 | 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 | 8 | 120 | 31 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 8 | 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 | 8 | 120 | 33 | 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 | 8 | 120 | 34 | 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 | 8 | 120 | 35 | 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 | 8 | 120 | 36 | 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 | 8 | 120 | 37 | 3.974118 | Solve this system for x:
3.974118095489748x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 38 | 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 | 8 | 120 | 39 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 8 | 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 | 8 | 120 | 41 | 4.025882 | Solve this system for x:
4.0258819045102525x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 42 | 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 | 8 | 120 | 43 | 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 | 8 | 120 | 44 | 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 | 8 | 120 | 45 | 3.974118 | Solve this system for x:
3.9741180954897475x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 46 | 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 | 8 | 120 | 47 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 8 | 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 | 8 | 120 | 49 | 4.025882 | Solve this system for x:
4.0258819045102525x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 50 | 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 | 8 | 120 | 51 | 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 | 8 | 120 | 52 | 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 | 8 | 120 | 53 | 3.974118 | Solve this system for x:
3.9741180954897475x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 54 | 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 | 8 | 120 | 55 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 8 | 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 | 8 | 120 | 57 | 4.025882 | Solve this system for x:
4.0258819045102525x + 1y = 10
2x + 4y = 12
FINAL: | 1.985319 | 1.985319 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 58 | 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 | 8 | 120 | 59 | 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 | 8 | 120 | 60 | 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 | 8 | 120 | 61 | 3.974118 | Solve this system for x:
3.9741180954897475x + 1y = 10
2x + 4y = 12
FINAL: | 2.0149 | 2.0149 |
linear_system | 2 | sinusoid | 0.5 | 8 | 120 | 62 | 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 | 8 | 120 | 63 | 4.096593 | Solve this system for x:
4.096592582628907x + 1y = 10
2x + 4y = 12
FINAL: | 1.946287 | 1.946287 |
linear_system | 2 | sinusoid | 0.5 | 16 | 120 | 0 | 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 | 1 | 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 | 2 | 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 | 3 | 4.05 | Solve this system for x:
4.05x + 1y = 10
2x + 4y = 12
FINAL: | 1.971831 | 1.971831 |
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