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
16
0
44
4
Solve this system for x: 3.999999999999999x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
45
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
46
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
47
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
48
4
Solve this system for x: 3.9999999999999996x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
49
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
50
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
51
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
52
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
53
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
54
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
55
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
56
4
Solve this system for x: 3.9999999999999996x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
57
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
58
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
59
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
60
4
Solve this system for x: 3.999999999999999x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
61
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
62
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
63
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
1
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
1
120
1
4.081285
Solve this system for x: 4.081284668459162x + 1y = 7 1x + 5y = 11 FINAL:
1.236704
1.236704
linear_system
0
sinusoid
0.5
1
120
2
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
1
120
3
4.068359
Solve this system for x: 4.0683592302022875x + 1y = 7 1x + 5y = 11 FINAL:
1.240836
1.240836
linear_system
0
sinusoid
0.5
1
120
4
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
1
120
5
4.052807
Solve this system for x: 4.052806785065036x + 1y = 7 1x + 5y = 11 FINAL:
1.245845
1.245845
linear_system
0
sinusoid
0.5
1
120
6
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
1
120
7
4.035225
Solve this system for x: 4.035225004792124x + 1y = 7 1x + 5y = 11 FINAL:
1.251556
1.251556
linear_system
0
sinusoid
0.5
1
120
8
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
1
120
9
4.01629
Solve this system for x: 4.016289547339459x + 1y = 7 1x + 5y = 11 FINAL:
1.257766
1.257766
linear_system
0
sinusoid
0.5
1
120
10
4.00654
Solve this system for x: 4.006540312923014x + 1y = 7 1x + 5y = 11 FINAL:
1.260988
1.260988
linear_system
0
sinusoid
0.5
1
120
11
3.996728
Solve this system for x: 3.9967280917178223x + 1y = 7 1x + 5y = 11 FINAL:
1.264246
1.264246
linear_system
0
sinusoid
0.5
1
120
12
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
1
120
13
3.977292
Solve this system for x: 3.977292373696563x + 1y = 7 1x + 5y = 11 FINAL:
1.270752
1.270752
linear_system
0
sinusoid
0.5
1
120
14
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
1
120
15
3.958729
Solve this system for x: 3.9587292970195604x + 1y = 7 1x + 5y = 11 FINAL:
1.277027
1.277027
linear_system
0
sinusoid
0.5
1
120
16
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
1
120
17
3.941752
Solve this system for x: 3.9417522303132198x + 1y = 7 1x + 5y = 11 FINAL:
1.282821
1.282821
linear_system
0
sinusoid
0.5
1
120
18
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
1
120
19
3.927014
Solve this system for x: 3.9270135927302166x + 1y = 7 1x + 5y = 11 FINAL:
1.287894
1.287894
linear_system
0
sinusoid
0.5
1
120
20
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
1
120
21
3.91508
Solve this system for x: 3.915079781847342x + 1y = 7 1x + 5y = 11 FINAL:
1.292031
1.292031
linear_system
0
sinusoid
0.5
1
120
22
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
1
120
23
3.906409
Solve this system for x: 3.9064094073242677x + 1y = 7 1x + 5y = 11 FINAL:
1.295054
1.295054
linear_system
0
sinusoid
0.5
1
120
24
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
1
120
25
3.901336
Solve this system for x: 3.9013356667915122x + 1y = 7 1x + 5y = 11 FINAL:
1.296829
1.296829
linear_system
0
sinusoid
0.5
1
120
26
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
1
120
27
3.900054
Solve this system for x: 3.9000535412523636x + 1y = 7 1x + 5y = 11 FINAL:
1.297279
1.297279
linear_system
0
sinusoid
0.5
1
120
28
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
1
120
29
3.902612
Solve this system for x: 3.9026123020722667x + 1y = 7 1x + 5y = 11 FINAL:
1.296382
1.296382
linear_system
0
sinusoid
0.5
1
120
30
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
1
120
31
3.908914
Solve this system for x: 3.9089136175078822x + 1y = 7 1x + 5y = 11 FINAL:
1.29418
1.29418
linear_system
0
sinusoid
0.5
1
120
32
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
1
120
33
3.918715
Solve this system for x: 3.9187153315408385x + 1y = 7 1x + 5y = 11 FINAL:
1.290768
1.290768
linear_system
0
sinusoid
0.5
1
120
34
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
1
120
35
3.931641
Solve this system for x: 3.931640769797713x + 1y = 7 1x + 5y = 11 FINAL:
1.286297
1.286297
linear_system
0
sinusoid
0.5
1
120
36
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
1
120
37
3.947193
Solve this system for x: 3.947193214934963x + 1y = 7 1x + 5y = 11 FINAL:
1.280959
1.280959
linear_system
0
sinusoid
0.5
1
120
38
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
1
120
39
3.964775
Solve this system for x: 3.964774995207877x + 1y = 7 1x + 5y = 11 FINAL:
1.274977
1.274977
linear_system
0
sinusoid
0.5
1
120
40
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
1
120
41
3.98371
Solve this system for x: 3.983710452660541x + 1y = 7 1x + 5y = 11 FINAL:
1.268596
1.268596
linear_system
0
sinusoid
0.5
1
120
42
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
1
120
43
4.003272
Solve this system for x: 4.003271908282177x + 1y = 7 1x + 5y = 11 FINAL:
1.262071
1.262071
linear_system
0
sinusoid
0.5
1
120
44
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
1
120
45
4.022708
Solve this system for x: 4.022707626303437x + 1y = 7 1x + 5y = 11 FINAL:
1.255654
1.255654
linear_system
0
sinusoid
0.5
1
120
46
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
1
120
47
4.041271
Solve this system for x: 4.041270702980439x + 1y = 7 1x + 5y = 11 FINAL:
1.249586
1.249586
linear_system
0
sinusoid
0.5
1
120
48
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
1
120
49
4.058248
Solve this system for x: 4.05824776968678x + 1y = 7 1x + 5y = 11 FINAL:
1.244088
1.244088
linear_system
0
sinusoid
0.5
1
120
50
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
1
120
51
4.072986
Solve this system for x: 4.0729864072697834x + 1y = 7 1x + 5y = 11 FINAL:
1.239354
1.239354
linear_system
0
sinusoid
0.5
1
120
52
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
1
120
53
4.08492
Solve this system for x: 4.084920218152658x + 1y = 7 1x + 5y = 11 FINAL:
1.235547
1.235547
linear_system
0
sinusoid
0.5
1
120
54
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
1
120
55
4.093591
Solve this system for x: 4.093590592675732x + 1y = 7 1x + 5y = 11 FINAL:
1.232795
1.232795
linear_system
0
sinusoid
0.5
1
120
56
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
1
120
57
4.098664
Solve this system for x: 4.098664333208488x + 1y = 7 1x + 5y = 11 FINAL:
1.231191
1.231191
linear_system
0
sinusoid
0.5
1
120
58
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
1
120
59
4.099946
Solve this system for x: 4.099946458747636x + 1y = 7 1x + 5y = 11 FINAL:
1.230786
1.230786
linear_system
0
sinusoid
0.5
1
120
60
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
1
120
61
4.097388
Solve this system for x: 4.097387697927734x + 1y = 7 1x + 5y = 11 FINAL:
1.231594
1.231594
linear_system
0
sinusoid
0.5
1
120
62
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
1
120
63
4.091086
Solve this system for x: 4.091086382492118x + 1y = 7 1x + 5y = 11 FINAL:
1.233589
1.233589
linear_system
0
sinusoid
0.5
2
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
2
120
1
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
2
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
3
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
4
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
5
4.00654
Solve this system for x: 4.006540312923014x + 1y = 7 1x + 5y = 11 FINAL:
1.260988
1.260988
linear_system
0
sinusoid
0.5
2
120
6
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
2
120
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
3.905307
Solve this system for x: 3.9053069870504893x + 1y = 7 1x + 5y = 11 FINAL:
1.295439
1.295439