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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signal_type
stringclasses
2 values
amplitude_scale
float64
0.5
2.5
frequency_cycles
float64
1
16
phase_deg
float64
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240
⌀
time_step
int64
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prompt
stringlengths
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ground_truth
float64
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symbolic_baseline_answer
float64
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linear_system
1
sinusoid
2.5
1
240
40
4.482963
Solve this system for x: 4.482962913144534x + 2y = 8 1x + 3y = 9 FINAL:
0.524068
0.524068
linear_system
1
sinusoid
2.5
1
240
41
4.467953
Solve this system for x: 4.467952963378663x + 2y = 8 1x + 3y = 9 FINAL:
0.526138
0.526138
linear_system
1
sinusoid
2.5
1
240
42
4.448436
Solve this system for x: 4.448436370766345x + 2y = 8 1x + 3y = 9 FINAL:
0.528853
0.528853
linear_system
1
sinusoid
2.5
1
240
43
4.424601
Solve this system for x: 4.42460109076329x + 2y = 8 1x + 3y = 9 FINAL:
0.532207
0.532207
linear_system
1
sinusoid
2.5
1
240
44
4.396677
Solve this system for x: 4.396676670145618x + 2y = 8 1x + 3y = 9 FINAL:
0.536192
0.536192
linear_system
1
sinusoid
2.5
1
240
45
4.364932
Solve this system for x: 4.364932036348918x + 2y = 8 1x + 3y = 9 FINAL:
0.540794
0.540794
linear_system
1
sinusoid
2.5
1
240
46
4.329673
Solve this system for x: 4.329672907550035x + 2y = 8 1x + 3y = 9 FINAL:
0.546
0.546
linear_system
1
sinusoid
2.5
1
240
47
4.291239
Solve this system for x: 4.291238848433901x + 2y = 8 1x + 3y = 9 FINAL:
0.551789
0.551789
linear_system
1
sinusoid
2.5
1
240
48
4.25
Solve this system for x: 4.25x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
1
240
49
4.206354
Solve this system for x: 4.206353514902197x + 2y = 8 1x + 3y = 9 FINAL:
0.565022
0.565022
linear_system
1
sinusoid
2.5
1
240
50
4.16072
Solve this system for x: 4.160719732651581x + 2y = 8 1x + 3y = 9 FINAL:
0.572401
0.572401
linear_system
1
sinusoid
2.5
1
240
51
4.113538
Solve this system for x: 4.113538131517187x + 2y = 8 1x + 3y = 9 FINAL:
0.580236
0.580236
linear_system
1
sinusoid
2.5
1
240
52
4.065263
Solve this system for x: 4.0652630961100265x + 2y = 8 1x + 3y = 9 FINAL:
0.588478
0.588478
linear_system
1
sinusoid
2.5
1
240
53
4.01636
Solve this system for x: 4.016359541410889x + 2y = 8 1x + 3y = 9 FINAL:
0.59707
0.59707
linear_system
1
sinusoid
2.5
1
240
54
3.967298
Solve this system for x: 3.9672984353849294x + 2y = 8 1x + 3y = 9 FINAL:
0.605945
0.605945
linear_system
1
sinusoid
2.5
1
240
55
3.918552
Solve this system for x: 3.918552263302706x + 2y = 8 1x + 3y = 9 FINAL:
0.615028
0.615028
linear_system
1
sinusoid
2.5
1
240
56
3.87059
Solve this system for x: 3.87059047744874x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
1
240
57
3.823875
Solve this system for x: 3.8238749760393835x + 2y = 8 1x + 3y = 9 FINAL:
0.633471
0.633471
linear_system
1
sinusoid
2.5
1
240
58
3.778856
Solve this system for x: 3.7788556548904992x + 2y = 8 1x + 3y = 9 FINAL:
0.642634
0.642634
linear_system
1
sinusoid
2.5
1
240
59
3.735966
Solve this system for x: 3.735966074674816x + 2y = 8 1x + 3y = 9 FINAL:
0.651615
0.651615
linear_system
1
sinusoid
2.5
1
240
60
3.695619
Solve this system for x: 3.69561928549564x + 2y = 8 1x + 3y = 9 FINAL:
0.660294
0.660294
linear_system
1
sinusoid
2.5
1
240
61
3.658204
Solve this system for x: 3.6582038489885647x + 2y = 8 1x + 3y = 9 FINAL:
0.668553
0.668553
linear_system
1
sinusoid
2.5
1
240
62
3.62408
Solve this system for x: 3.6240800962605118x + 2y = 8 1x + 3y = 9 FINAL:
0.676267
0.676267
linear_system
1
sinusoid
2.5
1
240
63
3.593577
Solve this system for x: 3.593576657704193x + 2y = 8 1x + 3y = 9 FINAL:
0.683314
0.683314
linear_system
1
sinusoid
2.5
2
240
0
3.566987
Solve this system for x: 3.566987298107781x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
2
240
1
3.526535
Solve this system for x: 3.5265349352524473x + 2y = 8 1x + 3y = 9 FINAL:
0.699333
0.699333
linear_system
1
sinusoid
2.5
2
240
2
3.504278
Solve this system for x: 3.504277569313095x + 2y = 8 1x + 3y = 9 FINAL:
0.704818
0.704818
linear_system
1
sinusoid
2.5
2
240
3
3.501071
Solve this system for x: 3.501070538380698x + 2y = 8 1x + 3y = 9 FINAL:
0.705616
0.705616
linear_system
1
sinusoid
2.5
2
240
4
3.517037
Solve this system for x: 3.5170370868554657x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
2
240
5
3.551564
Solve this system for x: 3.5515636292336557x + 2y = 8 1x + 3y = 9 FINAL:
0.693266
0.693266
linear_system
1
sinusoid
2.5
2
240
6
3.603323
Solve this system for x: 3.6033233298543825x + 2y = 8 1x + 3y = 9 FINAL:
0.681047
0.681047
linear_system
1
sinusoid
2.5
2
240
7
3.670327
Solve this system for x: 3.6703270924499654x + 2y = 8 1x + 3y = 9 FINAL:
0.665854
0.665854
linear_system
1
sinusoid
2.5
2
240
8
3.75
Solve this system for x: 3.75x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
2
240
9
3.83928
Solve this system for x: 3.839280267348419x + 2y = 8 1x + 3y = 9 FINAL:
0.630395
0.630395
linear_system
1
sinusoid
2.5
2
240
10
3.934737
Solve this system for x: 3.9347369038899735x + 2y = 8 1x + 3y = 9 FINAL:
0.611982
0.611982
linear_system
1
sinusoid
2.5
2
240
11
4.032702
Solve this system for x: 4.0327015646150715x + 2y = 8 1x + 3y = 9 FINAL:
0.594171
0.594171
linear_system
1
sinusoid
2.5
2
240
12
4.12941
Solve this system for x: 4.12940952255126x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
2
240
13
4.221144
Solve this system for x: 4.221144345109501x + 2y = 8 1x + 3y = 9 FINAL:
0.562671
0.562671
linear_system
1
sinusoid
2.5
2
240
14
4.304381
Solve this system for x: 4.304380714504361x + 2y = 8 1x + 3y = 9 FINAL:
0.549796
0.549796
linear_system
1
sinusoid
2.5
2
240
15
4.37592
Solve this system for x: 4.375919903739488x + 2y = 8 1x + 3y = 9 FINAL:
0.539192
0.539192
linear_system
1
sinusoid
2.5
2
240
16
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
2
240
17
4.473465
Solve this system for x: 4.473465064747553x + 2y = 8 1x + 3y = 9 FINAL:
0.525376
0.525376
linear_system
1
sinusoid
2.5
2
240
18
4.495722
Solve this system for x: 4.4957224306869055x + 2y = 8 1x + 3y = 9 FINAL:
0.522322
0.522322
linear_system
1
sinusoid
2.5
2
240
19
4.498929
Solve this system for x: 4.498929461619301x + 2y = 8 1x + 3y = 9 FINAL:
0.521885
0.521885
linear_system
1
sinusoid
2.5
2
240
20
4.482963
Solve this system for x: 4.482962913144534x + 2y = 8 1x + 3y = 9 FINAL:
0.524068
0.524068
linear_system
1
sinusoid
2.5
2
240
21
4.448436
Solve this system for x: 4.448436370766345x + 2y = 8 1x + 3y = 9 FINAL:
0.528853
0.528853
linear_system
1
sinusoid
2.5
2
240
22
4.396677
Solve this system for x: 4.396676670145618x + 2y = 8 1x + 3y = 9 FINAL:
0.536192
0.536192
linear_system
1
sinusoid
2.5
2
240
23
4.329673
Solve this system for x: 4.329672907550035x + 2y = 8 1x + 3y = 9 FINAL:
0.546
0.546
linear_system
1
sinusoid
2.5
2
240
24
4.25
Solve this system for x: 4.25x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
2
240
25
4.16072
Solve this system for x: 4.160719732651581x + 2y = 8 1x + 3y = 9 FINAL:
0.572401
0.572401
linear_system
1
sinusoid
2.5
2
240
26
4.065263
Solve this system for x: 4.0652630961100265x + 2y = 8 1x + 3y = 9 FINAL:
0.588478
0.588478
linear_system
1
sinusoid
2.5
2
240
27
3.967298
Solve this system for x: 3.9672984353849294x + 2y = 8 1x + 3y = 9 FINAL:
0.605945
0.605945
linear_system
1
sinusoid
2.5
2
240
28
3.87059
Solve this system for x: 3.87059047744874x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
2
240
29
3.778856
Solve this system for x: 3.7788556548904992x + 2y = 8 1x + 3y = 9 FINAL:
0.642634
0.642634
linear_system
1
sinusoid
2.5
2
240
30
3.695619
Solve this system for x: 3.69561928549564x + 2y = 8 1x + 3y = 9 FINAL:
0.660294
0.660294
linear_system
1
sinusoid
2.5
2
240
31
3.62408
Solve this system for x: 3.6240800962605118x + 2y = 8 1x + 3y = 9 FINAL:
0.676267
0.676267
linear_system
1
sinusoid
2.5
2
240
32
3.566987
Solve this system for x: 3.5669872981077813x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
2
240
33
3.526535
Solve this system for x: 3.5265349352524473x + 2y = 8 1x + 3y = 9 FINAL:
0.699333
0.699333
linear_system
1
sinusoid
2.5
2
240
34
3.504278
Solve this system for x: 3.5042775693130945x + 2y = 8 1x + 3y = 9 FINAL:
0.704818
0.704818
linear_system
1
sinusoid
2.5
2
240
35
3.501071
Solve this system for x: 3.501070538380698x + 2y = 8 1x + 3y = 9 FINAL:
0.705616
0.705616
linear_system
1
sinusoid
2.5
2
240
36
3.517037
Solve this system for x: 3.5170370868554657x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
2
240
37
3.551564
Solve this system for x: 3.5515636292336557x + 2y = 8 1x + 3y = 9 FINAL:
0.693266
0.693266
linear_system
1
sinusoid
2.5
2
240
38
3.603323
Solve this system for x: 3.6033233298543816x + 2y = 8 1x + 3y = 9 FINAL:
0.681047
0.681047
linear_system
1
sinusoid
2.5
2
240
39
3.670327
Solve this system for x: 3.6703270924499654x + 2y = 8 1x + 3y = 9 FINAL:
0.665854
0.665854
linear_system
1
sinusoid
2.5
2
240
40
3.75
Solve this system for x: 3.75x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
2
240
41
3.83928
Solve this system for x: 3.839280267348419x + 2y = 8 1x + 3y = 9 FINAL:
0.630395
0.630395
linear_system
1
sinusoid
2.5
2
240
42
3.934737
Solve this system for x: 3.9347369038899735x + 2y = 8 1x + 3y = 9 FINAL:
0.611982
0.611982
linear_system
1
sinusoid
2.5
2
240
43
4.032702
Solve this system for x: 4.032701564615071x + 2y = 8 1x + 3y = 9 FINAL:
0.594171
0.594171
linear_system
1
sinusoid
2.5
2
240
44
4.12941
Solve this system for x: 4.129409522551259x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
2
240
45
4.221144
Solve this system for x: 4.221144345109501x + 2y = 8 1x + 3y = 9 FINAL:
0.562671
0.562671
linear_system
1
sinusoid
2.5
2
240
46
4.304381
Solve this system for x: 4.30438071450436x + 2y = 8 1x + 3y = 9 FINAL:
0.549796
0.549796
linear_system
1
sinusoid
2.5
2
240
47
4.37592
Solve this system for x: 4.375919903739488x + 2y = 8 1x + 3y = 9 FINAL:
0.539192
0.539192
linear_system
1
sinusoid
2.5
2
240
48
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
2
240
49
4.473465
Solve this system for x: 4.473465064747552x + 2y = 8 1x + 3y = 9 FINAL:
0.525376
0.525376
linear_system
1
sinusoid
2.5
2
240
50
4.495722
Solve this system for x: 4.4957224306869055x + 2y = 8 1x + 3y = 9 FINAL:
0.522322
0.522322
linear_system
1
sinusoid
2.5
2
240
51
4.498929
Solve this system for x: 4.498929461619301x + 2y = 8 1x + 3y = 9 FINAL:
0.521885
0.521885
linear_system
1
sinusoid
2.5
2
240
52
4.482963
Solve this system for x: 4.482962913144534x + 2y = 8 1x + 3y = 9 FINAL:
0.524068
0.524068
linear_system
1
sinusoid
2.5
2
240
53
4.448436
Solve this system for x: 4.448436370766345x + 2y = 8 1x + 3y = 9 FINAL:
0.528853
0.528853
linear_system
1
sinusoid
2.5
2
240
54
4.396677
Solve this system for x: 4.396676670145618x + 2y = 8 1x + 3y = 9 FINAL:
0.536192
0.536192
linear_system
1
sinusoid
2.5
2
240
55
4.329673
Solve this system for x: 4.329672907550034x + 2y = 8 1x + 3y = 9 FINAL:
0.546
0.546
linear_system
1
sinusoid
2.5
2
240
56
4.25
Solve this system for x: 4.25x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
2
240
57
4.16072
Solve this system for x: 4.1607197326515815x + 2y = 8 1x + 3y = 9 FINAL:
0.572401
0.572401
linear_system
1
sinusoid
2.5
2
240
58
4.065263
Solve this system for x: 4.0652630961100265x + 2y = 8 1x + 3y = 9 FINAL:
0.588478
0.588478
linear_system
1
sinusoid
2.5
2
240
59
3.967298
Solve this system for x: 3.9672984353849294x + 2y = 8 1x + 3y = 9 FINAL:
0.605945
0.605945
linear_system
1
sinusoid
2.5
2
240
60
3.87059
Solve this system for x: 3.870590477448741x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
2
240
61
3.778856
Solve this system for x: 3.7788556548904992x + 2y = 8 1x + 3y = 9 FINAL:
0.642634
0.642634
linear_system
1
sinusoid
2.5
2
240
62
3.695619
Solve this system for x: 3.69561928549564x + 2y = 8 1x + 3y = 9 FINAL:
0.660294
0.660294
linear_system
1
sinusoid
2.5
2
240
63
3.62408
Solve this system for x: 3.6240800962605118x + 2y = 8 1x + 3y = 9 FINAL:
0.676267
0.676267
linear_system
1
sinusoid
2.5
4
240
0
3.566987
Solve this system for x: 3.566987298107781x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
4
240
1
3.504278
Solve this system for x: 3.504277569313095x + 2y = 8 1x + 3y = 9 FINAL:
0.704818
0.704818
linear_system
1
sinusoid
2.5
4
240
2
3.517037
Solve this system for x: 3.5170370868554657x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
4
240
3
3.603323
Solve this system for x: 3.6033233298543825x + 2y = 8 1x + 3y = 9 FINAL:
0.681047
0.681047
linear_system
1
sinusoid
2.5
4
240
4
3.75
Solve this system for x: 3.75x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
4
240
5
3.934737
Solve this system for x: 3.9347369038899735x + 2y = 8 1x + 3y = 9 FINAL:
0.611982
0.611982
linear_system
1
sinusoid
2.5
4
240
6
4.12941
Solve this system for x: 4.12940952255126x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
4
240
7
4.304381
Solve this system for x: 4.304380714504361x + 2y = 8 1x + 3y = 9 FINAL:
0.549796
0.549796
linear_system
1
sinusoid
2.5
4
240
8
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
4
240
9
4.495722
Solve this system for x: 4.4957224306869055x + 2y = 8 1x + 3y = 9 FINAL:
0.522322
0.522322
linear_system
1
sinusoid
2.5
4
240
10
4.482963
Solve this system for x: 4.482962913144534x + 2y = 8 1x + 3y = 9 FINAL:
0.524068
0.524068
linear_system
1
sinusoid
2.5
4
240
11
4.396677
Solve this system for x: 4.396676670145618x + 2y = 8 1x + 3y = 9 FINAL:
0.536192
0.536192