Datasets:
ai-metrology-lab
/
MathBode-LinearSystem

Dataset card Data Studio Files
xet
Community
1
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
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ground_truth
float64
0.52
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symbolic_baseline_answer
float64
0.52
2.33
linear_system
1
sinusoid
0.5
2
240
36
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
2
240
37
3.910313
Solve this system for x: 3.910312725846731x + 2y = 8 1x + 3y = 9 FINAL:
0.61659
0.61659
linear_system
1
sinusoid
0.5
2
240
38
3.920665
Solve this system for x: 3.920664665970876x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
2
240
39
3.934065
Solve this system for x: 3.9340654184899932x + 2y = 8 1x + 3y = 9 FINAL:
0.612108
0.612108
linear_system
1
sinusoid
0.5
2
240
40
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
2
240
41
3.967856
Solve this system for x: 3.9678560534696836x + 2y = 8 1x + 3y = 9 FINAL:
0.605842
0.605842
linear_system
1
sinusoid
0.5
2
240
42
3.986947
Solve this system for x: 3.9869473807779947x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
2
240
43
4.00654
Solve this system for x: 4.006540312923014x + 2y = 8 1x + 3y = 9 FINAL:
0.598825
0.598825
linear_system
1
sinusoid
0.5
2
240
44
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
2
240
45
4.044229
Solve this system for x: 4.0442288690219x + 2y = 8 1x + 3y = 9 FINAL:
0.592143
0.592143
linear_system
1
sinusoid
0.5
2
240
46
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
2
240
47
4.075184
Solve this system for x: 4.075183980747898x + 2y = 8 1x + 3y = 9 FINAL:
0.586765
0.586765
linear_system
1
sinusoid
0.5
2
240
48
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
2
240
49
4.094693
Solve this system for x: 4.09469301294951x + 2y = 8 1x + 3y = 9 FINAL:
0.583426
0.583426
linear_system
1
sinusoid
0.5
2
240
50
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
2
240
51
4.099786
Solve this system for x: 4.09978589232386x + 2y = 8 1x + 3y = 9 FINAL:
0.582561
0.582561
linear_system
1
sinusoid
0.5
2
240
52
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
2
240
53
4.089687
Solve this system for x: 4.089687274153269x + 2y = 8 1x + 3y = 9 FINAL:
0.584279
0.584279
linear_system
1
sinusoid
0.5
2
240
54
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
2
240
55
4.065935
Solve this system for x: 4.065934581510007x + 2y = 8 1x + 3y = 9 FINAL:
0.588362
0.588362
linear_system
1
sinusoid
0.5
2
240
56
4.05
Solve this system for x: 4.05x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
2
240
57
4.032144
Solve this system for x: 4.032143946530316x + 2y = 8 1x + 3y = 9 FINAL:
0.594269
0.594269
linear_system
1
sinusoid
0.5
2
240
58
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
2
240
59
3.99346
Solve this system for x: 3.993459687076986x + 2y = 8 1x + 3y = 9 FINAL:
0.60118
0.60118
linear_system
1
sinusoid
0.5
2
240
60
3.974118
Solve this system for x: 3.9741180954897484x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
2
240
61
3.955771
Solve this system for x: 3.9557711309781x + 2y = 8 1x + 3y = 9 FINAL:
0.608068
0.608068
linear_system
1
sinusoid
0.5
2
240
62
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
2
240
63
3.924816
Solve this system for x: 3.9248160192521024x + 2y = 8 1x + 3y = 9 FINAL:
0.613845
0.613845
linear_system
1
sinusoid
0.5
4
240
0
3.913397
Solve this system for x: 3.913397459621556x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
4
240
1
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
240
2
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
240
3
3.920665
Solve this system for x: 3.9206646659708766x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
240
4
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
240
5
3.986947
Solve this system for x: 3.9869473807779947x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
240
6
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
240
7
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
240
8
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
240
9
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
4
240
10
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
240
11
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
240
12
4.05
Solve this system for x: 4.05x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
4
240
13
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
240
14
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
240
15
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
4
240
16
3.913397
Solve this system for x: 3.913397459621556x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
4
240
17
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
240
18
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
240
19
3.920665
Solve this system for x: 3.920664665970876x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
240
20
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
240
21
3.986947
Solve this system for x: 3.9869473807779947x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
240
22
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
240
23
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
240
24
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
240
25
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
4
240
26
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
240
27
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
240
28
4.05
Solve this system for x: 4.05x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
4
240
29
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
240
30
3.974118
Solve this system for x: 3.9741180954897484x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
240
31
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
4
240
32
3.913397
Solve this system for x: 3.913397459621556x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
4
240
33
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
240
34
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
240
35
3.920665
Solve this system for x: 3.920664665970876x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
240
36
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
240
37
3.986947
Solve this system for x: 3.9869473807779947x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
240
38
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
240
39
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
240
40
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
240
41
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
4
240
42
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
240
43
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
240
44
4.05
Solve this system for x: 4.050000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
4
240
45
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
240
46
3.974118
Solve this system for x: 3.9741180954897484x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
240
47
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
4
240
48
3.913397
Solve this system for x: 3.913397459621556x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
4
240
49
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
240
50
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
240
51
3.920665
Solve this system for x: 3.920664665970876x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
240
52
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
240
53
3.986947
Solve this system for x: 3.9869473807779947x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
240
54
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
240
55
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
240
56
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
240
57
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
4
240
58
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
240
59
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
240
60
4.05
Solve this system for x: 4.050000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
4
240
61
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
240
62
3.974118
Solve this system for x: 3.9741180954897484x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
240
63
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
8
240
0
3.913397
Solve this system for x: 3.913397459621556x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
8
240
1
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
8
240
2
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
8
240
3
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
8
240
4
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
8
240
5
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
8
240
6
4.05
Solve this system for x: 4.05x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
8
240
7
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695