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
2.33
symbolic_baseline_answer
float64
0.52
2.33
linear_system
0
sinusoid
0.5
2
120
16
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
2
120
17
3.924816
Solve this system for x: 3.9248160192521024x + 1y = 7 1x + 5y = 11 FINAL:
1.288654
1.288654
linear_system
0
sinusoid
0.5
2
120
18
3.939124
Solve this system for x: 3.939123857099128x + 1y = 7 1x + 5y = 11 FINAL:
1.283723
1.283723
linear_system
0
sinusoid
0.5
2
120
19
3.955771
Solve this system for x: 3.9557711309781x + 1y = 7 1x + 5y = 11 FINAL:
1.278033
1.278033
linear_system
0
sinusoid
0.5
2
120
20
3.974118
Solve this system for x: 3.974118095489748x + 1y = 7 1x + 5y = 11 FINAL:
1.27182
1.27182
linear_system
0
sinusoid
0.5
2
120
21
3.99346
Solve this system for x: 3.9934596870769856x + 1y = 7 1x + 5y = 11 FINAL:
1.265336
1.265336
linear_system
0
sinusoid
0.5
2
120
22
4.013053
Solve this system for x: 4.013052619222005x + 1y = 7 1x + 5y = 11 FINAL:
1.258834
1.258834
linear_system
0
sinusoid
0.5
2
120
23
4.032144
Solve this system for x: 4.032143946530316x + 1y = 7 1x + 5y = 11 FINAL:
1.252563
1.252563
linear_system
0
sinusoid
0.5
2
120
24
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
2
120
25
4.065935
Solve this system for x: 4.065934581510007x + 1y = 7 1x + 5y = 11 FINAL:
1.241614
1.241614
linear_system
0
sinusoid
0.5
2
120
26
4.079335
Solve this system for x: 4.079335334029124x + 1y = 7 1x + 5y = 11 FINAL:
1.237325
1.237325
linear_system
0
sinusoid
0.5
2
120
27
4.089687
Solve this system for x: 4.089687274153269x + 1y = 7 1x + 5y = 11 FINAL:
1.234032
1.234032
linear_system
0
sinusoid
0.5
2
120
28
4.096593
Solve this system for x: 4.096592582628907x + 1y = 7 1x + 5y = 11 FINAL:
1.231845
1.231845
linear_system
0
sinusoid
0.5
2
120
29
4.099786
Solve this system for x: 4.09978589232386x + 1y = 7 1x + 5y = 11 FINAL:
1.230837
1.230837
linear_system
0
sinusoid
0.5
2
120
30
4.099144
Solve this system for x: 4.099144486137381x + 1y = 7 1x + 5y = 11 FINAL:
1.231039
1.231039
linear_system
0
sinusoid
0.5
2
120
31
4.094693
Solve this system for x: 4.09469301294951x + 1y = 7 1x + 5y = 11 FINAL:
1.232446
1.232446
linear_system
0
sinusoid
0.5
2
120
32
4.086603
Solve this system for x: 4.086602540378444x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
2
120
33
4.075184
Solve this system for x: 4.075183980747898x + 1y = 7 1x + 5y = 11 FINAL:
1.238651
1.238651
linear_system
0
sinusoid
0.5
2
120
34
4.060876
Solve this system for x: 4.060876142900872x + 1y = 7 1x + 5y = 11 FINAL:
1.243241
1.243241
linear_system
0
sinusoid
0.5
2
120
35
4.044229
Solve this system for x: 4.0442288690219x + 1y = 7 1x + 5y = 11 FINAL:
1.248625
1.248625
linear_system
0
sinusoid
0.5
2
120
36
4.025882
Solve this system for x: 4.0258819045102525x + 1y = 7 1x + 5y = 11 FINAL:
1.254613
1.254613
linear_system
0
sinusoid
0.5
2
120
37
4.00654
Solve this system for x: 4.006540312923015x + 1y = 7 1x + 5y = 11 FINAL:
1.260988
1.260988
linear_system
0
sinusoid
0.5
2
120
38
3.986947
Solve this system for x: 3.986947380777995x + 1y = 7 1x + 5y = 11 FINAL:
1.267512
1.267512
linear_system
0
sinusoid
0.5
2
120
39
3.967856
Solve this system for x: 3.967856053469684x + 1y = 7 1x + 5y = 11 FINAL:
1.273934
1.273934
linear_system
0
sinusoid
0.5
2
120
40
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
2
120
41
3.934065
Solve this system for x: 3.9340654184899932x + 1y = 7 1x + 5y = 11 FINAL:
1.285462
1.285462
linear_system
0
sinusoid
0.5
2
120
42
3.920665
Solve this system for x: 3.9206646659708766x + 1y = 7 1x + 5y = 11 FINAL:
1.290092
1.290092
linear_system
0
sinusoid
0.5
2
120
43
3.910313
Solve this system for x: 3.9103127258467314x + 1y = 7 1x + 5y = 11 FINAL:
1.293691
1.293691
linear_system
0
sinusoid
0.5
2
120
44
3.903407
Solve this system for x: 3.9034074173710933x + 1y = 7 1x + 5y = 11 FINAL:
1.296104
1.296104
linear_system
0
sinusoid
0.5
2
120
45
3.900214
Solve this system for x: 3.9002141076761396x + 1y = 7 1x + 5y = 11 FINAL:
1.297222
1.297222
linear_system
0
sinusoid
0.5
2
120
46
3.900856
Solve this system for x: 3.900855513862619x + 1y = 7 1x + 5y = 11 FINAL:
1.296997
1.296997
linear_system
0
sinusoid
0.5
2
120
47
3.905307
Solve this system for x: 3.9053069870504893x + 1y = 7 1x + 5y = 11 FINAL:
1.295439
1.295439
linear_system
0
sinusoid
0.5
2
120
48
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
2
120
49
3.924816
Solve this system for x: 3.924816019252102x + 1y = 7 1x + 5y = 11 FINAL:
1.288654
1.288654
linear_system
0
sinusoid
0.5
2
120
50
3.939124
Solve this system for x: 3.939123857099128x + 1y = 7 1x + 5y = 11 FINAL:
1.283723
1.283723
linear_system
0
sinusoid
0.5
2
120
51
3.955771
Solve this system for x: 3.9557711309781x + 1y = 7 1x + 5y = 11 FINAL:
1.278033
1.278033
linear_system
0
sinusoid
0.5
2
120
52
3.974118
Solve this system for x: 3.974118095489748x + 1y = 7 1x + 5y = 11 FINAL:
1.27182
1.27182
linear_system
0
sinusoid
0.5
2
120
53
3.99346
Solve this system for x: 3.9934596870769856x + 1y = 7 1x + 5y = 11 FINAL:
1.265336
1.265336
linear_system
0
sinusoid
0.5
2
120
54
4.013053
Solve this system for x: 4.013052619222005x + 1y = 7 1x + 5y = 11 FINAL:
1.258834
1.258834
linear_system
0
sinusoid
0.5
2
120
55
4.032144
Solve this system for x: 4.032143946530316x + 1y = 7 1x + 5y = 11 FINAL:
1.252563
1.252563
linear_system
0
sinusoid
0.5
2
120
56
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
2
120
57
4.065935
Solve this system for x: 4.065934581510007x + 1y = 7 1x + 5y = 11 FINAL:
1.241614
1.241614
linear_system
0
sinusoid
0.5
2
120
58
4.079335
Solve this system for x: 4.079335334029124x + 1y = 7 1x + 5y = 11 FINAL:
1.237325
1.237325
linear_system
0
sinusoid
0.5
2
120
59
4.089687
Solve this system for x: 4.089687274153269x + 1y = 7 1x + 5y = 11 FINAL:
1.234032
1.234032
linear_system
0
sinusoid
0.5
2
120
60
4.096593
Solve this system for x: 4.096592582628907x + 1y = 7 1x + 5y = 11 FINAL:
1.231845
1.231845
linear_system
0
sinusoid
0.5
2
120
61
4.099786
Solve this system for x: 4.09978589232386x + 1y = 7 1x + 5y = 11 FINAL:
1.230837
1.230837
linear_system
0
sinusoid
0.5
2
120
62
4.099144
Solve this system for x: 4.099144486137381x + 1y = 7 1x + 5y = 11 FINAL:
1.231039
1.231039
linear_system
0
sinusoid
0.5
2
120
63
4.094693
Solve this system for x: 4.09469301294951x + 1y = 7 1x + 5y = 11 FINAL:
1.232446
1.232446
linear_system
0
sinusoid
0.5
4
120
0
4.086603
Solve this system for x: 4.086602540378444x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
4
120
1
4.060876
Solve this system for x: 4.060876142900872x + 1y = 7 1x + 5y = 11 FINAL:
1.243241
1.243241
linear_system
0
sinusoid
0.5
4
120
2
4.025882
Solve this system for x: 4.0258819045102525x + 1y = 7 1x + 5y = 11 FINAL:
1.254613
1.254613
linear_system
0
sinusoid
0.5
4
120
3
3.986947
Solve this system for x: 3.9869473807779947x + 1y = 7 1x + 5y = 11 FINAL:
1.267512
1.267512
linear_system
0
sinusoid
0.5
4
120
4
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
4
120
5
3.920665
Solve this system for x: 3.9206646659708766x + 1y = 7 1x + 5y = 11 FINAL:
1.290092
1.290092
linear_system
0
sinusoid
0.5
4
120
6
3.903407
Solve this system for x: 3.9034074173710933x + 1y = 7 1x + 5y = 11 FINAL:
1.296104
1.296104
linear_system
0
sinusoid
0.5
4
120
7
3.900856
Solve this system for x: 3.900855513862619x + 1y = 7 1x + 5y = 11 FINAL:
1.296997
1.296997
linear_system
0
sinusoid
0.5
4
120
8
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
4
120
9
3.939124
Solve this system for x: 3.939123857099128x + 1y = 7 1x + 5y = 11 FINAL:
1.283723
1.283723
linear_system
0
sinusoid
0.5
4
120
10
3.974118
Solve this system for x: 3.974118095489748x + 1y = 7 1x + 5y = 11 FINAL:
1.27182
1.27182
linear_system
0
sinusoid
0.5
4
120
11
4.013053
Solve this system for x: 4.013052619222005x + 1y = 7 1x + 5y = 11 FINAL:
1.258834
1.258834
linear_system
0
sinusoid
0.5
4
120
12
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
4
120
13
4.079335
Solve this system for x: 4.079335334029124x + 1y = 7 1x + 5y = 11 FINAL:
1.237325
1.237325
linear_system
0
sinusoid
0.5
4
120
14
4.096593
Solve this system for x: 4.096592582628907x + 1y = 7 1x + 5y = 11 FINAL:
1.231845
1.231845
linear_system
0
sinusoid
0.5
4
120
15
4.099144
Solve this system for x: 4.099144486137381x + 1y = 7 1x + 5y = 11 FINAL:
1.231039
1.231039
linear_system
0
sinusoid
0.5
4
120
16
4.086603
Solve this system for x: 4.086602540378444x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
4
120
17
4.060876
Solve this system for x: 4.060876142900872x + 1y = 7 1x + 5y = 11 FINAL:
1.243241
1.243241
linear_system
0
sinusoid
0.5
4
120
18
4.025882
Solve this system for x: 4.0258819045102525x + 1y = 7 1x + 5y = 11 FINAL:
1.254613
1.254613
linear_system
0
sinusoid
0.5
4
120
19
3.986947
Solve this system for x: 3.986947380777995x + 1y = 7 1x + 5y = 11 FINAL:
1.267512
1.267512
linear_system
0
sinusoid
0.5
4
120
20
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
4
120
21
3.920665
Solve this system for x: 3.9206646659708766x + 1y = 7 1x + 5y = 11 FINAL:
1.290092
1.290092
linear_system
0
sinusoid
0.5
4
120
22
3.903407
Solve this system for x: 3.9034074173710933x + 1y = 7 1x + 5y = 11 FINAL:
1.296104
1.296104
linear_system
0
sinusoid
0.5
4
120
23
3.900856
Solve this system for x: 3.900855513862619x + 1y = 7 1x + 5y = 11 FINAL:
1.296997
1.296997
linear_system
0
sinusoid
0.5
4
120
24
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
4
120
25
3.939124
Solve this system for x: 3.939123857099128x + 1y = 7 1x + 5y = 11 FINAL:
1.283723
1.283723
linear_system
0
sinusoid
0.5
4
120
26
3.974118
Solve this system for x: 3.974118095489748x + 1y = 7 1x + 5y = 11 FINAL:
1.27182
1.27182
linear_system
0
sinusoid
0.5
4
120
27
4.013053
Solve this system for x: 4.013052619222005x + 1y = 7 1x + 5y = 11 FINAL:
1.258834
1.258834
linear_system
0
sinusoid
0.5
4
120
28
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
4
120
29
4.079335
Solve this system for x: 4.079335334029124x + 1y = 7 1x + 5y = 11 FINAL:
1.237325
1.237325
linear_system
0
sinusoid
0.5
4
120
30
4.096593
Solve this system for x: 4.096592582628907x + 1y = 7 1x + 5y = 11 FINAL:
1.231845
1.231845
linear_system
0
sinusoid
0.5
4
120
31
4.099144
Solve this system for x: 4.099144486137381x + 1y = 7 1x + 5y = 11 FINAL:
1.231039
1.231039
linear_system
0
sinusoid
0.5
4
120
32
4.086603
Solve this system for x: 4.086602540378444x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
4
120
33
4.060876
Solve this system for x: 4.060876142900872x + 1y = 7 1x + 5y = 11 FINAL:
1.243241
1.243241
linear_system
0
sinusoid
0.5
4
120
34
4.025882
Solve this system for x: 4.0258819045102525x + 1y = 7 1x + 5y = 11 FINAL:
1.254613
1.254613
linear_system
0
sinusoid
0.5
4
120
35
3.986947
Solve this system for x: 3.986947380777995x + 1y = 7 1x + 5y = 11 FINAL:
1.267512
1.267512
linear_system
0
sinusoid
0.5
4
120
36
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
4
120
37
3.920665
Solve this system for x: 3.9206646659708766x + 1y = 7 1x + 5y = 11 FINAL:
1.290092
1.290092
linear_system
0
sinusoid
0.5
4
120
38
3.903407
Solve this system for x: 3.9034074173710933x + 1y = 7 1x + 5y = 11 FINAL:
1.296104
1.296104
linear_system
0
sinusoid
0.5
4
120
39
3.900856
Solve this system for x: 3.900855513862619x + 1y = 7 1x + 5y = 11 FINAL:
1.296997
1.296997
linear_system
0
sinusoid
0.5
4
120
40
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
4
120
41
3.939124
Solve this system for x: 3.939123857099128x + 1y = 7 1x + 5y = 11 FINAL:
1.283723
1.283723
linear_system
0
sinusoid
0.5
4
120
42
3.974118
Solve this system for x: 3.974118095489748x + 1y = 7 1x + 5y = 11 FINAL:
1.27182
1.27182
linear_system
0
sinusoid
0.5
4
120
43
4.013053
Solve this system for x: 4.013052619222005x + 1y = 7 1x + 5y = 11 FINAL:
1.258834
1.258834
linear_system
0
sinusoid
0.5
4
120
44
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
4
120
45
4.079335
Solve this system for x: 4.079335334029124x + 1y = 7 1x + 5y = 11 FINAL:
1.237325
1.237325
linear_system
0
sinusoid
0.5
4
120
46
4.096593
Solve this system for x: 4.096592582628907x + 1y = 7 1x + 5y = 11 FINAL:
1.231845
1.231845
linear_system
0
sinusoid
0.5
4
120
47
4.099144
Solve this system for x: 4.099144486137381x + 1y = 7 1x + 5y = 11 FINAL:
1.231039
1.231039
linear_system
0
sinusoid
0.5
4
120
48
4.086603
Solve this system for x: 4.086602540378444x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
4
120
49
4.060876
Solve this system for x: 4.060876142900872x + 1y = 7 1x + 5y = 11 FINAL:
1.243241
1.243241
linear_system
0
sinusoid
0.5
4
120
50
4.025882
Solve this system for x: 4.025881904510252x + 1y = 7 1x + 5y = 11 FINAL:
1.254613
1.254613
linear_system
0
sinusoid
0.5
4
120
51
3.986947
Solve this system for x: 3.9869473807779947x + 1y = 7 1x + 5y = 11 FINAL:
1.267512
1.267512