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
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prompt
stringlengths
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ground_truth
float64
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2.33
symbolic_baseline_answer
float64
0.52
2.33
linear_system
0
sinusoid
2.5
1
240
0
3.566987
Solve this system for x: 3.566987298107781x + 1y = 7 1x + 5y = 11 FINAL:
1.425607
1.425607
linear_system
0
sinusoid
2.5
1
240
1
3.544568
Solve this system for x: 3.544568087539412x + 1y = 7 1x + 5y = 11 FINAL:
1.435163
1.435163
linear_system
0
sinusoid
2.5
1
240
2
3.526535
Solve this system for x: 3.5265349352524473x + 1y = 7 1x + 5y = 11 FINAL:
1.442943
1.442943
linear_system
0
sinusoid
2.5
1
240
3
3.513062
Solve this system for x: 3.513061510361333x + 1y = 7 1x + 5y = 11 FINAL:
1.448811
1.448811
linear_system
0
sinusoid
2.5
1
240
4
3.504278
Solve this system for x: 3.504277569313095x + 1y = 7 1x + 5y = 11 FINAL:
1.452662
1.452662
linear_system
0
sinusoid
2.5
1
240
5
3.500268
Solve this system for x: 3.500267706261817x + 1y = 7 1x + 5y = 11 FINAL:
1.454427
1.454427
linear_system
0
sinusoid
2.5
1
240
6
3.501071
Solve this system for x: 3.501070538380698x + 1y = 7 1x + 5y = 11 FINAL:
1.454074
1.454074
linear_system
0
sinusoid
2.5
1
240
7
3.506678
Solve this system for x: 3.5066783339575607x + 1y = 7 1x + 5y = 11 FINAL:
1.451608
1.451608
linear_system
0
sinusoid
2.5
1
240
8
3.517037
Solve this system for x: 3.5170370868554657x + 1y = 7 1x + 5y = 11 FINAL:
1.447075
1.447075
linear_system
0
sinusoid
2.5
1
240
9
3.532047
Solve this system for x: 3.532047036621337x + 1y = 7 1x + 5y = 11 FINAL:
1.440556
1.440556
linear_system
0
sinusoid
2.5
1
240
10
3.551564
Solve this system for x: 3.5515636292336557x + 1y = 7 1x + 5y = 11 FINAL:
1.432167
1.432167
linear_system
0
sinusoid
2.5
1
240
11
3.575399
Solve this system for x: 3.57539890923671x + 1y = 7 1x + 5y = 11 FINAL:
1.422054
1.422054
linear_system
0
sinusoid
2.5
1
240
12
3.603323
Solve this system for x: 3.6033233298543825x + 1y = 7 1x + 5y = 11 FINAL:
1.410386
1.410386
linear_system
0
sinusoid
2.5
1
240
13
3.635068
Solve this system for x: 3.635067963651082x + 1y = 7 1x + 5y = 11 FINAL:
1.397352
1.397352
linear_system
0
sinusoid
2.5
1
240
14
3.670327
Solve this system for x: 3.6703270924499654x + 1y = 7 1x + 5y = 11 FINAL:
1.383155
1.383155
linear_system
0
sinusoid
2.5
1
240
15
3.708761
Solve this system for x: 3.7087611515660983x + 1y = 7 1x + 5y = 11 FINAL:
1.368004
1.368004
linear_system
0
sinusoid
2.5
1
240
16
3.75
Solve this system for x: 3.75x + 1y = 7 1x + 5y = 11 FINAL:
1.352113
1.352113
linear_system
0
sinusoid
2.5
1
240
17
3.793646
Solve this system for x: 3.7936464850978027x + 1y = 7 1x + 5y = 11 FINAL:
1.335691
1.335691
linear_system
0
sinusoid
2.5
1
240
18
3.83928
Solve this system for x: 3.839280267348419x + 1y = 7 1x + 5y = 11 FINAL:
1.318942
1.318942
linear_system
0
sinusoid
2.5
1
240
19
3.886462
Solve this system for x: 3.886461868482813x + 1y = 7 1x + 5y = 11 FINAL:
1.302061
1.302061
linear_system
0
sinusoid
2.5
1
240
20
3.934737
Solve this system for x: 3.9347369038899735x + 1y = 7 1x + 5y = 11 FINAL:
1.285231
1.285231
linear_system
0
sinusoid
2.5
1
240
21
3.98364
Solve this system for x: 3.983640458589112x + 1y = 7 1x + 5y = 11 FINAL:
1.268619
1.268619
linear_system
0
sinusoid
2.5
1
240
22
4.032702
Solve this system for x: 4.0327015646150715x + 1y = 7 1x + 5y = 11 FINAL:
1.25238
1.25238
linear_system
0
sinusoid
2.5
1
240
23
4.081448
Solve this system for x: 4.081447736697294x + 1y = 7 1x + 5y = 11 FINAL:
1.236652
1.236652
linear_system
0
sinusoid
2.5
1
240
24
4.12941
Solve this system for x: 4.12940952255126x + 1y = 7 1x + 5y = 11 FINAL:
1.221558
1.221558
linear_system
0
sinusoid
2.5
1
240
25
4.176125
Solve this system for x: 4.1761250239606165x + 1y = 7 1x + 5y = 11 FINAL:
1.207206
1.207206
linear_system
0
sinusoid
2.5
1
240
26
4.221144
Solve this system for x: 4.221144345109501x + 1y = 7 1x + 5y = 11 FINAL:
1.19369
1.19369
linear_system
0
sinusoid
2.5
1
240
27
4.264034
Solve this system for x: 4.264033925325184x + 1y = 7 1x + 5y = 11 FINAL:
1.181093
1.181093
linear_system
0
sinusoid
2.5
1
240
28
4.304381
Solve this system for x: 4.304380714504361x + 1y = 7 1x + 5y = 11 FINAL:
1.169482
1.169482
linear_system
0
sinusoid
2.5
1
240
29
4.341796
Solve this system for x: 4.341796151011436x + 1y = 7 1x + 5y = 11 FINAL:
1.158917
1.158917
linear_system
0
sinusoid
2.5
1
240
30
4.37592
Solve this system for x: 4.375919903739488x + 1y = 7 1x + 5y = 11 FINAL:
1.149447
1.149447
linear_system
0
sinusoid
2.5
1
240
31
4.406423
Solve this system for x: 4.406423342295807x + 1y = 7 1x + 5y = 11 FINAL:
1.141112
1.141112
linear_system
0
sinusoid
2.5
1
240
32
4.433013
Solve this system for x: 4.433012701892219x + 1y = 7 1x + 5y = 11 FINAL:
1.133944
1.133944
linear_system
0
sinusoid
2.5
1
240
33
4.455432
Solve this system for x: 4.455431912460588x + 1y = 7 1x + 5y = 11 FINAL:
1.12797
1.12797
linear_system
0
sinusoid
2.5
1
240
34
4.473465
Solve this system for x: 4.473465064747553x + 1y = 7 1x + 5y = 11 FINAL:
1.12321
1.12321
linear_system
0
sinusoid
2.5
1
240
35
4.486938
Solve this system for x: 4.486938489638667x + 1y = 7 1x + 5y = 11 FINAL:
1.11968
1.11968
linear_system
0
sinusoid
2.5
1
240
36
4.495722
Solve this system for x: 4.4957224306869055x + 1y = 7 1x + 5y = 11 FINAL:
1.117391
1.117391
linear_system
0
sinusoid
2.5
1
240
37
4.499732
Solve this system for x: 4.499732293738183x + 1y = 7 1x + 5y = 11 FINAL:
1.116349
1.116349
linear_system
0
sinusoid
2.5
1
240
38
4.498929
Solve this system for x: 4.498929461619301x + 1y = 7 1x + 5y = 11 FINAL:
1.116557
1.116557
linear_system
0
sinusoid
2.5
1
240
39
4.493322
Solve this system for x: 4.49332166604244x + 1y = 7 1x + 5y = 11 FINAL:
1.118015
1.118015
linear_system
0
sinusoid
2.5
1
240
40
4.482963
Solve this system for x: 4.482962913144534x + 1y = 7 1x + 5y = 11 FINAL:
1.120719
1.120719
linear_system
0
sinusoid
2.5
1
240
41
4.467953
Solve this system for x: 4.467952963378663x + 1y = 7 1x + 5y = 11 FINAL:
1.124661
1.124661
linear_system
0
sinusoid
2.5
1
240
42
4.448436
Solve this system for x: 4.448436370766345x + 1y = 7 1x + 5y = 11 FINAL:
1.129827
1.129827
linear_system
0
sinusoid
2.5
1
240
43
4.424601
Solve this system for x: 4.42460109076329x + 1y = 7 1x + 5y = 11 FINAL:
1.136202
1.136202
linear_system
0
sinusoid
2.5
1
240
44
4.396677
Solve this system for x: 4.396676670145618x + 1y = 7 1x + 5y = 11 FINAL:
1.143762
1.143762
linear_system
0
sinusoid
2.5
1
240
45
4.364932
Solve this system for x: 4.364932036348918x + 1y = 7 1x + 5y = 11 FINAL:
1.15248
1.15248
linear_system
0
sinusoid
2.5
1
240
46
4.329673
Solve this system for x: 4.329672907550035x + 1y = 7 1x + 5y = 11 FINAL:
1.16232
1.16232
linear_system
0
sinusoid
2.5
1
240
47
4.291239
Solve this system for x: 4.291238848433901x + 1y = 7 1x + 5y = 11 FINAL:
1.173239
1.173239
linear_system
0
sinusoid
2.5
1
240
48
4.25
Solve this system for x: 4.25x + 1y = 7 1x + 5y = 11 FINAL:
1.185185
1.185185
linear_system
0
sinusoid
2.5
1
240
49
4.206354
Solve this system for x: 4.206353514902197x + 1y = 7 1x + 5y = 11 FINAL:
1.198097
1.198097
linear_system
0
sinusoid
2.5
1
240
50
4.16072
Solve this system for x: 4.160719732651581x + 1y = 7 1x + 5y = 11 FINAL:
1.211901
1.211901
linear_system
0
sinusoid
2.5
1
240
51
4.113538
Solve this system for x: 4.113538131517187x + 1y = 7 1x + 5y = 11 FINAL:
1.226512
1.226512
linear_system
0
sinusoid
2.5
1
240
52
4.065263
Solve this system for x: 4.0652630961100265x + 1y = 7 1x + 5y = 11 FINAL:
1.24183
1.24183
linear_system
0
sinusoid
2.5
1
240
53
4.01636
Solve this system for x: 4.016359541410889x + 1y = 7 1x + 5y = 11 FINAL:
1.257743
1.257743
linear_system
0
sinusoid
2.5
1
240
54
3.967298
Solve this system for x: 3.9672984353849294x + 1y = 7 1x + 5y = 11 FINAL:
1.274123
1.274123
linear_system
0
sinusoid
2.5
1
240
55
3.918552
Solve this system for x: 3.918552263302706x + 1y = 7 1x + 5y = 11 FINAL:
1.290825
1.290825
linear_system
0
sinusoid
2.5
1
240
56
3.87059
Solve this system for x: 3.87059047744874x + 1y = 7 1x + 5y = 11 FINAL:
1.307692
1.307692
linear_system
0
sinusoid
2.5
1
240
57
3.823875
Solve this system for x: 3.8238749760393835x + 1y = 7 1x + 5y = 11 FINAL:
1.324549
1.324549
linear_system
0
sinusoid
2.5
1
240
58
3.778856
Solve this system for x: 3.7788556548904992x + 1y = 7 1x + 5y = 11 FINAL:
1.341211
1.341211
linear_system
0
sinusoid
2.5
1
240
59
3.735966
Solve this system for x: 3.735966074674816x + 1y = 7 1x + 5y = 11 FINAL:
1.357479
1.357479
linear_system
0
sinusoid
2.5
1
240
60
3.695619
Solve this system for x: 3.69561928549564x + 1y = 7 1x + 5y = 11 FINAL:
1.373147
1.373147
linear_system
0
sinusoid
2.5
1
240
61
3.658204
Solve this system for x: 3.6582038489885647x + 1y = 7 1x + 5y = 11 FINAL:
1.388004
1.388004
linear_system
0
sinusoid
2.5
1
240
62
3.62408
Solve this system for x: 3.6240800962605118x + 1y = 7 1x + 5y = 11 FINAL:
1.401836
1.401836
linear_system
0
sinusoid
2.5
1
240
63
3.593577
Solve this system for x: 3.593576657704193x + 1y = 7 1x + 5y = 11 FINAL:
1.414437
1.414437
linear_system
0
sinusoid
2.5
2
240
0
3.566987
Solve this system for x: 3.566987298107781x + 1y = 7 1x + 5y = 11 FINAL:
1.425607
1.425607
linear_system
0
sinusoid
2.5
2
240
1
3.526535
Solve this system for x: 3.5265349352524473x + 1y = 7 1x + 5y = 11 FINAL:
1.442943
1.442943
linear_system
0
sinusoid
2.5
2
240
2
3.504278
Solve this system for x: 3.504277569313095x + 1y = 7 1x + 5y = 11 FINAL:
1.452662
1.452662
linear_system
0
sinusoid
2.5
2
240
3
3.501071
Solve this system for x: 3.501070538380698x + 1y = 7 1x + 5y = 11 FINAL:
1.454074
1.454074
linear_system
0
sinusoid
2.5
2
240
4
3.517037
Solve this system for x: 3.5170370868554657x + 1y = 7 1x + 5y = 11 FINAL:
1.447075
1.447075
linear_system
0
sinusoid
2.5
2
240
5
3.551564
Solve this system for x: 3.5515636292336557x + 1y = 7 1x + 5y = 11 FINAL:
1.432167
1.432167
linear_system
0
sinusoid
2.5
2
240
6
3.603323
Solve this system for x: 3.6033233298543825x + 1y = 7 1x + 5y = 11 FINAL:
1.410386
1.410386
linear_system
0
sinusoid
2.5
2
240
7
3.670327
Solve this system for x: 3.6703270924499654x + 1y = 7 1x + 5y = 11 FINAL:
1.383155
1.383155
linear_system
0
sinusoid
2.5
2
240
8
3.75
Solve this system for x: 3.75x + 1y = 7 1x + 5y = 11 FINAL:
1.352113
1.352113
linear_system
0
sinusoid
2.5
2
240
9
3.83928
Solve this system for x: 3.839280267348419x + 1y = 7 1x + 5y = 11 FINAL:
1.318942
1.318942
linear_system
0
sinusoid
2.5
2
240
10
3.934737
Solve this system for x: 3.9347369038899735x + 1y = 7 1x + 5y = 11 FINAL:
1.285231
1.285231
linear_system
0
sinusoid
2.5
2
240
11
4.032702
Solve this system for x: 4.0327015646150715x + 1y = 7 1x + 5y = 11 FINAL:
1.25238
1.25238
linear_system
0
sinusoid
2.5
2
240
12
4.12941
Solve this system for x: 4.12940952255126x + 1y = 7 1x + 5y = 11 FINAL:
1.221558
1.221558
linear_system
0
sinusoid
2.5
2
240
13
4.221144
Solve this system for x: 4.221144345109501x + 1y = 7 1x + 5y = 11 FINAL:
1.19369
1.19369
linear_system
0
sinusoid
2.5
2
240
14
4.304381
Solve this system for x: 4.304380714504361x + 1y = 7 1x + 5y = 11 FINAL:
1.169482
1.169482
linear_system
0
sinusoid
2.5
2
240
15
4.37592
Solve this system for x: 4.375919903739488x + 1y = 7 1x + 5y = 11 FINAL:
1.149447
1.149447
linear_system
0
sinusoid
2.5
2
240
16
4.433013
Solve this system for x: 4.433012701892219x + 1y = 7 1x + 5y = 11 FINAL:
1.133944
1.133944
linear_system
0
sinusoid
2.5
2
240
17
4.473465
Solve this system for x: 4.473465064747553x + 1y = 7 1x + 5y = 11 FINAL:
1.12321
1.12321
linear_system
0
sinusoid
2.5
2
240
18
4.495722
Solve this system for x: 4.4957224306869055x + 1y = 7 1x + 5y = 11 FINAL:
1.117391
1.117391
linear_system
0
sinusoid
2.5
2
240
19
4.498929
Solve this system for x: 4.498929461619301x + 1y = 7 1x + 5y = 11 FINAL:
1.116557
1.116557
linear_system
0
sinusoid
2.5
2
240
20
4.482963
Solve this system for x: 4.482962913144534x + 1y = 7 1x + 5y = 11 FINAL:
1.120719
1.120719
linear_system
0
sinusoid
2.5
2
240
21
4.448436
Solve this system for x: 4.448436370766345x + 1y = 7 1x + 5y = 11 FINAL:
1.129827
1.129827
linear_system
0
sinusoid
2.5
2
240
22
4.396677
Solve this system for x: 4.396676670145618x + 1y = 7 1x + 5y = 11 FINAL:
1.143762
1.143762
linear_system
0
sinusoid
2.5
2
240
23
4.329673
Solve this system for x: 4.329672907550035x + 1y = 7 1x + 5y = 11 FINAL:
1.16232
1.16232
linear_system
0
sinusoid
2.5
2
240
24
4.25
Solve this system for x: 4.25x + 1y = 7 1x + 5y = 11 FINAL:
1.185185
1.185185
linear_system
0
sinusoid
2.5
2
240
25
4.16072
Solve this system for x: 4.160719732651581x + 1y = 7 1x + 5y = 11 FINAL:
1.211901
1.211901
linear_system
0
sinusoid
2.5
2
240
26
4.065263
Solve this system for x: 4.0652630961100265x + 1y = 7 1x + 5y = 11 FINAL:
1.24183
1.24183
linear_system
0
sinusoid
2.5
2
240
27
3.967298
Solve this system for x: 3.9672984353849294x + 1y = 7 1x + 5y = 11 FINAL:
1.274123
1.274123
linear_system
0
sinusoid
2.5
2
240
28
3.87059
Solve this system for x: 3.87059047744874x + 1y = 7 1x + 5y = 11 FINAL:
1.307692
1.307692
linear_system
0
sinusoid
2.5
2
240
29
3.778856
Solve this system for x: 3.7788556548904992x + 1y = 7 1x + 5y = 11 FINAL:
1.341211
1.341211
linear_system
0
sinusoid
2.5
2
240
30
3.695619
Solve this system for x: 3.69561928549564x + 1y = 7 1x + 5y = 11 FINAL:
1.373147
1.373147
linear_system
0
sinusoid
2.5
2
240
31
3.62408
Solve this system for x: 3.6240800962605118x + 1y = 7 1x + 5y = 11 FINAL:
1.401836
1.401836
linear_system
0
sinusoid
2.5
2
240
32
3.566987
Solve this system for x: 3.5669872981077813x + 1y = 7 1x + 5y = 11 FINAL:
1.425607
1.425607
linear_system
0
sinusoid
2.5
2
240
33
3.526535
Solve this system for x: 3.5265349352524473x + 1y = 7 1x + 5y = 11 FINAL:
1.442943
1.442943
linear_system
0
sinusoid
2.5
2
240
34
3.504278
Solve this system for x: 3.5042775693130945x + 1y = 7 1x + 5y = 11 FINAL:
1.452662
1.452662
linear_system
0
sinusoid
2.5
2
240
35
3.501071
Solve this system for x: 3.501070538380698x + 1y = 7 1x + 5y = 11 FINAL:
1.454074
1.454074