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
16
0
24
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
25
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
26
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
27
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
28
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
29
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
30
4
Solve this system for x: 4.000000000000003x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
31
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
32
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
33
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
34
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
35
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
36
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
37
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
38
4
Solve this system for x: 4.000000000000003x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
39
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
40
4
Solve this system for x: 3.9999999999999987x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
41
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
42
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
43
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
44
4
Solve this system for x: 3.999999999999995x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
45
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
46
4
Solve this system for x: 4.0000000000000036x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
47
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
48
4
Solve this system for x: 3.9999999999999987x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
49
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
50
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
51
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
52
4
Solve this system for x: 4.000000000000002x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
53
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
54
4
Solve this system for x: 4.0000000000000036x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
55
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
56
4
Solve this system for x: 3.9999999999999982x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
57
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
58
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
59
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
16
0
60
4
Solve this system for x: 3.9999999999999947x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
61
4.5
Solve this system for x: 4.5x + 2y = 8 1x + 3y = 9 FINAL:
0.521739
0.521739
linear_system
1
sinusoid
2.5
16
0
62
4
Solve this system for x: 4.0000000000000036x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
63
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882
linear_system
1
sinusoid
2.5
1
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
1
120
1
4.406423
Solve this system for x: 4.406423342295808x + 2y = 8 1x + 3y = 9 FINAL:
0.534794
0.534794
linear_system
1
sinusoid
2.5
1
120
2
4.37592
Solve this system for x: 4.375919903739489x + 2y = 8 1x + 3y = 9 FINAL:
0.539192
0.539192
linear_system
1
sinusoid
2.5
1
120
3
4.341796
Solve this system for x: 4.341796151011436x + 2y = 8 1x + 3y = 9 FINAL:
0.544199
0.544199
linear_system
1
sinusoid
2.5
1
120
4
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
1
120
5
4.264034
Solve this system for x: 4.264033925325184x + 2y = 8 1x + 3y = 9 FINAL:
0.555962
0.555962
linear_system
1
sinusoid
2.5
1
120
6
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
1
120
7
4.176125
Solve this system for x: 4.176125023960617x + 2y = 8 1x + 3y = 9 FINAL:
0.569889
0.569889
linear_system
1
sinusoid
2.5
1
120
8
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
1
120
9
4.081448
Solve this system for x: 4.081447736697294x + 2y = 8 1x + 3y = 9 FINAL:
0.585689
0.585689
linear_system
1
sinusoid
2.5
1
120
10
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
1
120
11
3.98364
Solve this system for x: 3.9836404585891123x + 2y = 8 1x + 3y = 9 FINAL:
0.602959
0.602959
linear_system
1
sinusoid
2.5
1
120
12
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
1
120
13
3.886462
Solve this system for x: 3.8864618684828134x + 2y = 8 1x + 3y = 9 FINAL:
0.621158
0.621158
linear_system
1
sinusoid
2.5
1
120
14
3.83928
Solve this system for x: 3.8392802673484194x + 2y = 8 1x + 3y = 9 FINAL:
0.630395
0.630395
linear_system
1
sinusoid
2.5
1
120
15
3.793646
Solve this system for x: 3.7936464850978027x + 2y = 8 1x + 3y = 9 FINAL:
0.639595
0.639595
linear_system
1
sinusoid
2.5
1
120
16
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
1
120
17
3.708761
Solve this system for x: 3.708761151566099x + 2y = 8 1x + 3y = 9 FINAL:
0.657442
0.657442
linear_system
1
sinusoid
2.5
1
120
18
3.670327
Solve this system for x: 3.670327092449966x + 2y = 8 1x + 3y = 9 FINAL:
0.665854
0.665854
linear_system
1
sinusoid
2.5
1
120
19
3.635068
Solve this system for x: 3.6350679636510823x + 2y = 8 1x + 3y = 9 FINAL:
0.673763
0.673763
linear_system
1
sinusoid
2.5
1
120
20
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
1
120
21
3.575399
Solve this system for x: 3.5753989092367107x + 2y = 8 1x + 3y = 9 FINAL:
0.687585
0.687585
linear_system
1
sinusoid
2.5
1
120
22
3.551564
Solve this system for x: 3.551563629233656x + 2y = 8 1x + 3y = 9 FINAL:
0.693266
0.693266
linear_system
1
sinusoid
2.5
1
120
23
3.532047
Solve this system for x: 3.5320470366213375x + 2y = 8 1x + 3y = 9 FINAL:
0.697988
0.697988
linear_system
1
sinusoid
2.5
1
120
24
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
1
120
25
3.506678
Solve this system for x: 3.5066783339575607x + 2y = 8 1x + 3y = 9 FINAL:
0.704222
0.704222
linear_system
1
sinusoid
2.5
1
120
26
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
1
120
27
3.500268
Solve this system for x: 3.500267706261817x + 2y = 8 1x + 3y = 9 FINAL:
0.705816
0.705816
linear_system
1
sinusoid
2.5
1
120
28
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
1
120
29
3.513062
Solve this system for x: 3.513061510361333x + 2y = 8 1x + 3y = 9 FINAL:
0.702643
0.702643
linear_system
1
sinusoid
2.5
1
120
30
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
1
120
31
3.544568
Solve this system for x: 3.544568087539412x + 2y = 8 1x + 3y = 9 FINAL:
0.694951
0.694951
linear_system
1
sinusoid
2.5
1
120
32
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
1
120
33
3.593577
Solve this system for x: 3.593576657704192x + 2y = 8 1x + 3y = 9 FINAL:
0.683314
0.683314
linear_system
1
sinusoid
2.5
1
120
34
3.62408
Solve this system for x: 3.6240800962605113x + 2y = 8 1x + 3y = 9 FINAL:
0.676267
0.676267
linear_system
1
sinusoid
2.5
1
120
35
3.658204
Solve this system for x: 3.658203848988564x + 2y = 8 1x + 3y = 9 FINAL:
0.668553
0.668553
linear_system
1
sinusoid
2.5
1
120
36
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
1
120
37
3.735966
Solve this system for x: 3.7359660746748156x + 2y = 8 1x + 3y = 9 FINAL:
0.651615
0.651615
linear_system
1
sinusoid
2.5
1
120
38
3.778856
Solve this system for x: 3.778855654890499x + 2y = 8 1x + 3y = 9 FINAL:
0.642634
0.642634
linear_system
1
sinusoid
2.5
1
120
39
3.823875
Solve this system for x: 3.823874976039383x + 2y = 8 1x + 3y = 9 FINAL:
0.633471
0.633471
linear_system
1
sinusoid
2.5
1
120
40
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
1
120
41
3.918552
Solve this system for x: 3.9185522633027055x + 2y = 8 1x + 3y = 9 FINAL:
0.615028
0.615028
linear_system
1
sinusoid
2.5
1
120
42
3.967298
Solve this system for x: 3.967298435384928x + 2y = 8 1x + 3y = 9 FINAL:
0.605945
0.605945
linear_system
1
sinusoid
2.5
1
120
43
4.01636
Solve this system for x: 4.016359541410887x + 2y = 8 1x + 3y = 9 FINAL:
0.59707
0.59707
linear_system
1
sinusoid
2.5
1
120
44
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
1
120
45
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
120
46
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
120
47
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
120
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
120
49
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
120
50
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
120
51
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
120
52
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
1
120
53
4.424601
Solve this system for x: 4.424601090763289x + 2y = 8 1x + 3y = 9 FINAL:
0.532207
0.532207
linear_system
1
sinusoid
2.5
1
120
54
4.448436
Solve this system for x: 4.448436370766344x + 2y = 8 1x + 3y = 9 FINAL:
0.528853
0.528853
linear_system
1
sinusoid
2.5
1
120
55
4.467953
Solve this system for x: 4.4679529633786625x + 2y = 8 1x + 3y = 9 FINAL:
0.526138
0.526138
linear_system
1
sinusoid
2.5
1
120
56
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
120
57
4.493322
Solve this system for x: 4.49332166604244x + 2y = 8 1x + 3y = 9 FINAL:
0.52265
0.52265
linear_system
1
sinusoid
2.5
1
120
58
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
1
120
59
4.499732
Solve this system for x: 4.499732293738183x + 2y = 8 1x + 3y = 9 FINAL:
0.521776
0.521776