Datasets:
ai-metrology-lab
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MathBode-LinearSystem

Dataset card Data Studio Files
xet
Community
1
family
stringclasses
1 value
question_id
int64
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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
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prompt
stringlengths
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ground_truth
float64
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symbolic_baseline_answer
float64
0.52
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linear_system
1
sinusoid
0.5
1
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
1
240
1
3.908914
Solve this system for x: 3.9089136175078822x + 2y = 8 1x + 3y = 9 FINAL:
0.616856
0.616856
linear_system
1
sinusoid
0.5
1
240
2
3.905307
Solve this system for x: 3.9053069870504893x + 2y = 8 1x + 3y = 9 FINAL:
0.617543
0.617543
linear_system
1
sinusoid
0.5
1
240
3
3.902612
Solve this system for x: 3.9026123020722667x + 2y = 8 1x + 3y = 9 FINAL:
0.618057
0.618057
linear_system
1
sinusoid
0.5
1
240
4
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
1
240
5
3.900054
Solve this system for x: 3.9000535412523636x + 2y = 8 1x + 3y = 9 FINAL:
0.618546
0.618546
linear_system
1
sinusoid
0.5
1
240
6
3.900214
Solve this system for x: 3.9002141076761396x + 2y = 8 1x + 3y = 9 FINAL:
0.618516
0.618516
linear_system
1
sinusoid
0.5
1
240
7
3.901336
Solve this system for x: 3.9013356667915122x + 2y = 8 1x + 3y = 9 FINAL:
0.618301
0.618301
linear_system
1
sinusoid
0.5
1
240
8
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
1
240
9
3.906409
Solve this system for x: 3.9064094073242672x + 2y = 8 1x + 3y = 9 FINAL:
0.617333
0.617333
linear_system
1
sinusoid
0.5
1
240
10
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
1
240
11
3.91508
Solve this system for x: 3.915079781847342x + 2y = 8 1x + 3y = 9 FINAL:
0.615685
0.615685
linear_system
1
sinusoid
0.5
1
240
12
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
1
240
13
3.927014
Solve this system for x: 3.9270135927302166x + 2y = 8 1x + 3y = 9 FINAL:
0.613432
0.613432
linear_system
1
sinusoid
0.5
1
240
14
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
1
240
15
3.941752
Solve this system for x: 3.9417522303132198x + 2y = 8 1x + 3y = 9 FINAL:
0.610671
0.610671
linear_system
1
sinusoid
0.5
1
240
16
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
1
240
17
3.958729
Solve this system for x: 3.9587292970195604x + 2y = 8 1x + 3y = 9 FINAL:
0.607522
0.607522
linear_system
1
sinusoid
0.5
1
240
18
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
1
240
19
3.977292
Solve this system for x: 3.9772923736965624x + 2y = 8 1x + 3y = 9 FINAL:
0.604115
0.604115
linear_system
1
sinusoid
0.5
1
240
20
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
1
240
21
3.996728
Solve this system for x: 3.9967280917178223x + 2y = 8 1x + 3y = 9 FINAL:
0.60059
0.60059
linear_system
1
sinusoid
0.5
1
240
22
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
1
240
23
4.01629
Solve this system for x: 4.016289547339459x + 2y = 8 1x + 3y = 9 FINAL:
0.597082
0.597082
linear_system
1
sinusoid
0.5
1
240
24
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
1
240
25
4.035225
Solve this system for x: 4.035225004792124x + 2y = 8 1x + 3y = 9 FINAL:
0.593726
0.593726
linear_system
1
sinusoid
0.5
1
240
26
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
1
240
27
4.052807
Solve this system for x: 4.052806785065036x + 2y = 8 1x + 3y = 9 FINAL:
0.590643
0.590643
linear_system
1
sinusoid
0.5
1
240
28
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
1
240
29
4.068359
Solve this system for x: 4.0683592302022875x + 2y = 8 1x + 3y = 9 FINAL:
0.587943
0.587943
linear_system
1
sinusoid
0.5
1
240
30
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
1
240
31
4.081285
Solve this system for x: 4.081284668459161x + 2y = 8 1x + 3y = 9 FINAL:
0.585717
0.585717
linear_system
1
sinusoid
0.5
1
240
32
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
1
240
33
4.091086
Solve this system for x: 4.091086382492118x + 2y = 8 1x + 3y = 9 FINAL:
0.584041
0.584041
linear_system
1
sinusoid
0.5
1
240
34
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
1
240
35
4.097388
Solve this system for x: 4.097387697927734x + 2y = 8 1x + 3y = 9 FINAL:
0.582968
0.582968
linear_system
1
sinusoid
0.5
1
240
36
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
1
240
37
4.099946
Solve this system for x: 4.099946458747636x + 2y = 8 1x + 3y = 9 FINAL:
0.582533
0.582533
linear_system
1
sinusoid
0.5
1
240
38
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
1
240
39
4.098664
Solve this system for x: 4.098664333208488x + 2y = 8 1x + 3y = 9 FINAL:
0.582751
0.582751
linear_system
1
sinusoid
0.5
1
240
40
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
1
240
41
4.093591
Solve this system for x: 4.093590592675732x + 2y = 8 1x + 3y = 9 FINAL:
0.583614
0.583614
linear_system
1
sinusoid
0.5
1
240
42
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
1
240
43
4.08492
Solve this system for x: 4.084920218152658x + 2y = 8 1x + 3y = 9 FINAL:
0.585094
0.585094
linear_system
1
sinusoid
0.5
1
240
44
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
1
240
45
4.072986
Solve this system for x: 4.0729864072697834x + 2y = 8 1x + 3y = 9 FINAL:
0.587144
0.587144
linear_system
1
sinusoid
0.5
1
240
46
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
1
240
47
4.058248
Solve this system for x: 4.05824776968678x + 2y = 8 1x + 3y = 9 FINAL:
0.589695
0.589695
linear_system
1
sinusoid
0.5
1
240
48
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
1
240
49
4.041271
Solve this system for x: 4.041270702980439x + 2y = 8 1x + 3y = 9 FINAL:
0.592662
0.592662
linear_system
1
sinusoid
0.5
1
240
50
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
1
240
51
4.022708
Solve this system for x: 4.022707626303437x + 2y = 8 1x + 3y = 9 FINAL:
0.59594
0.59594
linear_system
1
sinusoid
0.5
1
240
52
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
1
240
53
4.003272
Solve this system for x: 4.003271908282178x + 2y = 8 1x + 3y = 9 FINAL:
0.599412
0.599412
linear_system
1
sinusoid
0.5
1
240
54
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
1
240
55
3.98371
Solve this system for x: 3.9837104526605414x + 2y = 8 1x + 3y = 9 FINAL:
0.602947
0.602947
linear_system
1
sinusoid
0.5
1
240
56
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
1
240
57
3.964775
Solve this system for x: 3.964774995207877x + 2y = 8 1x + 3y = 9 FINAL:
0.606408
0.606408
linear_system
1
sinusoid
0.5
1
240
58
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
1
240
59
3.947193
Solve this system for x: 3.947193214934963x + 2y = 8 1x + 3y = 9 FINAL:
0.609658
0.609658
linear_system
1
sinusoid
0.5
1
240
60
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
1
240
61
3.931641
Solve this system for x: 3.931640769797713x + 2y = 8 1x + 3y = 9 FINAL:
0.612562
0.612562
linear_system
1
sinusoid
0.5
1
240
62
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
1
240
63
3.918715
Solve this system for x: 3.9187153315408385x + 2y = 8 1x + 3y = 9 FINAL:
0.614997
0.614997
linear_system
1
sinusoid
0.5
2
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
2
240
1
3.905307
Solve this system for x: 3.9053069870504893x + 2y = 8 1x + 3y = 9 FINAL:
0.617543
0.617543
linear_system
1
sinusoid
0.5
2
240
2
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
2
240
3
3.900214
Solve this system for x: 3.9002141076761396x + 2y = 8 1x + 3y = 9 FINAL:
0.618516
0.618516
linear_system
1
sinusoid
0.5
2
240
4
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
5
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
6
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
2
240
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
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
16
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
17
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
18
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
19
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
20
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
21
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
22
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
23
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
24
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
25
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
26
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
27
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
28
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
2
240
29
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
30
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
31
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
2
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
2
240
33
3.905307
Solve this system for x: 3.9053069870504893x + 2y = 8 1x + 3y = 9 FINAL:
0.617543
0.617543
linear_system
1
sinusoid
0.5
2
240
34
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
2
240
35
3.900214
Solve this system for x: 3.9002141076761396x + 2y = 8 1x + 3y = 9 FINAL:
0.618516
0.618516