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
76
ground_truth
float64
0.52
2.33
symbolic_baseline_answer
float64
0.52
2.33
linear_system
1
sinusoid
2.5
4
120
32
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
4
120
33
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
120
34
4.12941
Solve this system for x: 4.129409522551261x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
4
120
35
3.934737
Solve this system for x: 3.934736903889975x + 2y = 8 1x + 3y = 9 FINAL:
0.611982
0.611982
linear_system
1
sinusoid
2.5
4
120
36
3.75
Solve this system for x: 3.7500000000000004x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
4
120
37
3.603323
Solve this system for x: 3.603323329854382x + 2y = 8 1x + 3y = 9 FINAL:
0.681047
0.681047
linear_system
1
sinusoid
2.5
4
120
38
3.517037
Solve this system for x: 3.517037086855466x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
4
120
39
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
4
120
40
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
120
41
3.695619
Solve this system for x: 3.6956192854956393x + 2y = 8 1x + 3y = 9 FINAL:
0.660294
0.660294
linear_system
1
sinusoid
2.5
4
120
42
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
4
120
43
4.065263
Solve this system for x: 4.065263096110026x + 2y = 8 1x + 3y = 9 FINAL:
0.588478
0.588478
linear_system
1
sinusoid
2.5
4
120
44
4.25
Solve this system for x: 4.249999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
4
120
45
4.396677
Solve this system for x: 4.3966766701456175x + 2y = 8 1x + 3y = 9 FINAL:
0.536192
0.536192
linear_system
1
sinusoid
2.5
4
120
46
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
120
47
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
120
48
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
4
120
49
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
120
50
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
120
51
3.934737
Solve this system for x: 3.9347369038899744x + 2y = 8 1x + 3y = 9 FINAL:
0.611982
0.611982
linear_system
1
sinusoid
2.5
4
120
52
3.75
Solve this system for x: 3.749999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
4
120
53
3.603323
Solve this system for x: 3.603323329854382x + 2y = 8 1x + 3y = 9 FINAL:
0.681047
0.681047
linear_system
1
sinusoid
2.5
4
120
54
3.517037
Solve this system for x: 3.517037086855466x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
4
120
55
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
120
56
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
120
57
3.695619
Solve this system for x: 3.6956192854956393x + 2y = 8 1x + 3y = 9 FINAL:
0.660294
0.660294
linear_system
1
sinusoid
2.5
4
120
58
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
4
120
59
4.065263
Solve this system for x: 4.065263096110026x + 2y = 8 1x + 3y = 9 FINAL:
0.588478
0.588478
linear_system
1
sinusoid
2.5
4
120
60
4.25
Solve this system for x: 4.249999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
4
120
61
4.396677
Solve this system for x: 4.3966766701456175x + 2y = 8 1x + 3y = 9 FINAL:
0.536192
0.536192
linear_system
1
sinusoid
2.5
4
120
62
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
120
63
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
8
120
0
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
1
4.12941
Solve this system for x: 4.129409522551261x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
120
2
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
8
120
3
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
8
120
4
3.566987
Solve this system for x: 3.5669872981077804x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
8
120
5
3.87059
Solve this system for x: 3.8705904774487396x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
8
120
6
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
8
120
7
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
8
120
8
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
9
4.12941
Solve this system for x: 4.129409522551261x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
120
10
3.75
Solve this system for x: 3.7500000000000004x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
120
11
3.517037
Solve this system for x: 3.517037086855466x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
8
120
12
3.566987
Solve this system for x: 3.5669872981077804x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
8
120
13
3.87059
Solve this system for x: 3.8705904774487396x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
8
120
14
4.25
Solve this system for x: 4.249999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
120
15
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
8
120
16
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
17
4.12941
Solve this system for x: 4.129409522551261x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
120
18
3.75
Solve this system for x: 3.7500000000000004x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
120
19
3.517037
Solve this system for x: 3.517037086855466x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
8
120
20
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
8
120
21
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
8
120
22
4.25
Solve this system for x: 4.249999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
120
23
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
8
120
24
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
25
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
8
120
26
3.75
Solve this system for x: 3.749999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
120
27
3.517037
Solve this system for x: 3.517037086855466x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
8
120
28
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
8
120
29
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
8
120
30
4.25
Solve this system for x: 4.249999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
120
31
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
8
120
32
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
33
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
8
120
34
3.75
Solve this system for x: 3.749999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
120
35
3.517037
Solve this system for x: 3.517037086855466x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
8
120
36
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
8
120
37
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
8
120
38
4.25
Solve this system for x: 4.249999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
120
39
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
8
120
40
4.433013
Solve this system for x: 4.4330127018922205x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
41
4.12941
Solve this system for x: 4.1294095225512635x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
120
42
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
120
43
3.517037
Solve this system for x: 3.5170370868554666x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
8
120
44
3.566987
Solve this system for x: 3.5669872981077786x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
8
120
45
3.87059
Solve this system for x: 3.8705904774487383x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
8
120
46
4.25
Solve this system for x: 4.249999999999997x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
120
47
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
8
120
48
4.433013
Solve this system for x: 4.4330127018922205x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
49
4.12941
Solve this system for x: 4.1294095225512635x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
120
50
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
120
51
3.517037
Solve this system for x: 3.5170370868554666x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
8
120
52
3.566987
Solve this system for x: 3.5669872981077804x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
8
120
53
3.87059
Solve this system for x: 3.8705904774487383x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
8
120
54
4.25
Solve this system for x: 4.249999999999997x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
120
55
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
8
120
56
4.433013
Solve this system for x: 4.4330127018922205x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
120
57
4.12941
Solve this system for x: 4.1294095225512635x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
120
58
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
120
59
3.517037
Solve this system for x: 3.5170370868554666x + 2y = 8 1x + 3y = 9 FINAL:
0.701663
0.701663
linear_system
1
sinusoid
2.5
8
120
60
3.566987
Solve this system for x: 3.5669872981077786x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
8
120
61
3.87059
Solve this system for x: 3.870590477448738x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
8
120
62
4.25
Solve this system for x: 4.249999999999997x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
120
63
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
16
120
0
4.433013
Solve this system for x: 4.43301270189222x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
120
1
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
16
120
2
3.566987
Solve this system for x: 3.5669872981077804x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
120
3
4.25
Solve this system for x: 4.25x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814