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
2
sinusoid
2.5
1
0
20
4.46194
Solve this system for x: 4.461939766255643x + 1y = 10 2x + 4y = 12 FINAL:
1.766811
1.766811
linear_system
2
sinusoid
2.5
1
0
21
4.440961
Solve this system for x: 4.4409606321741775x + 1y = 10 2x + 4y = 12 FINAL:
1.776217
1.776217
linear_system
2
sinusoid
2.5
1
0
22
4.415735
Solve this system for x: 4.4157348061512725x + 1y = 10 2x + 4y = 12 FINAL:
1.787659
1.787659
linear_system
2
sinusoid
2.5
1
0
23
4.386505
Solve this system for x: 4.386505226681368x + 1y = 10 2x + 4y = 12 FINAL:
1.801104
1.801104
linear_system
2
sinusoid
2.5
1
0
24
4.353553
Solve this system for x: 4.353553390593274x + 1y = 10 2x + 4y = 12 FINAL:
1.816505
1.816505
linear_system
2
sinusoid
2.5
1
0
25
4.317197
Solve this system for x: 4.317196642081822x + 1y = 10 2x + 4y = 12 FINAL:
1.833806
1.833806
linear_system
2
sinusoid
2.5
1
0
26
4.277785
Solve this system for x: 4.277785116509801x + 1y = 10 2x + 4y = 12 FINAL:
1.852938
1.852938
linear_system
2
sinusoid
2.5
1
0
27
4.235698
Solve this system for x: 4.235698368412999x + 1y = 10 2x + 4y = 12 FINAL:
1.873813
1.873813
linear_system
2
sinusoid
2.5
1
0
28
4.191342
Solve this system for x: 4.191341716182545x + 1y = 10 2x + 4y = 12 FINAL:
1.896329
1.896329
linear_system
2
sinusoid
2.5
1
0
29
4.145142
Solve this system for x: 4.145142338627231x + 1y = 10 2x + 4y = 12 FINAL:
1.920364
1.920364
linear_system
2
sinusoid
2.5
1
0
30
4.097545
Solve this system for x: 4.097545161008064x + 1y = 10 2x + 4y = 12 FINAL:
1.945771
1.945771
linear_system
2
sinusoid
2.5
1
0
31
4.049009
Solve this system for x: 4.04900857016478x + 1y = 10 2x + 4y = 12 FINAL:
1.972382
1.972382
linear_system
2
sinusoid
2.5
1
0
32
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
2.5
1
0
33
3.950991
Solve this system for x: 3.9509914298352196x + 1y = 10 2x + 4y = 12 FINAL:
2.028403
2.028403
linear_system
2
sinusoid
2.5
1
0
34
3.902455
Solve this system for x: 3.902454838991936x + 1y = 10 2x + 4y = 12 FINAL:
2.057338
2.057338
linear_system
2
sinusoid
2.5
1
0
35
3.854858
Solve this system for x: 3.854857661372769x + 1y = 10 2x + 4y = 12 FINAL:
2.086527
2.086527
linear_system
2
sinusoid
2.5
1
0
36
3.808658
Solve this system for x: 3.808658283817455x + 1y = 10 2x + 4y = 12 FINAL:
2.115661
2.115661
linear_system
2
sinusoid
2.5
1
0
37
3.764302
Solve this system for x: 3.764301631587001x + 1y = 10 2x + 4y = 12 FINAL:
2.14441
2.14441
linear_system
2
sinusoid
2.5
1
0
38
3.722215
Solve this system for x: 3.722214883490199x + 1y = 10 2x + 4y = 12 FINAL:
2.172419
2.172419
linear_system
2
sinusoid
2.5
1
0
39
3.682803
Solve this system for x: 3.6828033579181776x + 1y = 10 2x + 4y = 12 FINAL:
2.199319
2.199319
linear_system
2
sinusoid
2.5
1
0
40
3.646447
Solve this system for x: 3.646446609406726x + 1y = 10 2x + 4y = 12 FINAL:
2.224732
2.224732
linear_system
2
sinusoid
2.5
1
0
41
3.613495
Solve this system for x: 3.6134947733186316x + 1y = 10 2x + 4y = 12 FINAL:
2.248277
2.248277
linear_system
2
sinusoid
2.5
1
0
42
3.584265
Solve this system for x: 3.5842651938487275x + 1y = 10 2x + 4y = 12 FINAL:
2.269584
2.269584
linear_system
2
sinusoid
2.5
1
0
43
3.559039
Solve this system for x: 3.5590393678258225x + 1y = 10 2x + 4y = 12 FINAL:
2.2883
2.2883
linear_system
2
sinusoid
2.5
1
0
44
3.53806
Solve this system for x: 3.538060233744357x + 1y = 10 2x + 4y = 12 FINAL:
2.304102
2.304102
linear_system
2
sinusoid
2.5
1
0
45
3.52153
Solve this system for x: 3.5215298321338957x + 1y = 10 2x + 4y = 12 FINAL:
2.316707
2.316707
linear_system
2
sinusoid
2.5
1
0
46
3.509607
Solve this system for x: 3.509607359798385x + 1y = 10 2x + 4y = 12 FINAL:
2.325885
2.325885
linear_system
2
sinusoid
2.5
1
0
47
3.502408
Solve this system for x: 3.5024076366639014x + 1y = 10 2x + 4y = 12 FINAL:
2.331462
2.331462
linear_system
2
sinusoid
2.5
1
0
48
3.5
Solve this system for x: 3.5x + 1y = 10 2x + 4y = 12 FINAL:
2.333333
2.333333
linear_system
2
sinusoid
2.5
1
0
49
3.502408
Solve this system for x: 3.5024076366639014x + 1y = 10 2x + 4y = 12 FINAL:
2.331462
2.331462
linear_system
2
sinusoid
2.5
1
0
50
3.509607
Solve this system for x: 3.509607359798385x + 1y = 10 2x + 4y = 12 FINAL:
2.325885
2.325885
linear_system
2
sinusoid
2.5
1
0
51
3.52153
Solve this system for x: 3.5215298321338957x + 1y = 10 2x + 4y = 12 FINAL:
2.316707
2.316707
linear_system
2
sinusoid
2.5
1
0
52
3.53806
Solve this system for x: 3.5380602337443565x + 1y = 10 2x + 4y = 12 FINAL:
2.304102
2.304102
linear_system
2
sinusoid
2.5
1
0
53
3.559039
Solve this system for x: 3.5590393678258225x + 1y = 10 2x + 4y = 12 FINAL:
2.2883
2.2883
linear_system
2
sinusoid
2.5
1
0
54
3.584265
Solve this system for x: 3.584265193848727x + 1y = 10 2x + 4y = 12 FINAL:
2.269584
2.269584
linear_system
2
sinusoid
2.5
1
0
55
3.613495
Solve this system for x: 3.6134947733186316x + 1y = 10 2x + 4y = 12 FINAL:
2.248277
2.248277
linear_system
2
sinusoid
2.5
1
0
56
3.646447
Solve this system for x: 3.646446609406726x + 1y = 10 2x + 4y = 12 FINAL:
2.224732
2.224732
linear_system
2
sinusoid
2.5
1
0
57
3.682803
Solve this system for x: 3.682803357918177x + 1y = 10 2x + 4y = 12 FINAL:
2.199319
2.199319
linear_system
2
sinusoid
2.5
1
0
58
3.722215
Solve this system for x: 3.722214883490199x + 1y = 10 2x + 4y = 12 FINAL:
2.172419
2.172419
linear_system
2
sinusoid
2.5
1
0
59
3.764302
Solve this system for x: 3.764301631587001x + 1y = 10 2x + 4y = 12 FINAL:
2.14441
2.14441
linear_system
2
sinusoid
2.5
1
0
60
3.808658
Solve this system for x: 3.8086582838174547x + 1y = 10 2x + 4y = 12 FINAL:
2.115661
2.115661
linear_system
2
sinusoid
2.5
1
0
61
3.854858
Solve this system for x: 3.854857661372769x + 1y = 10 2x + 4y = 12 FINAL:
2.086527
2.086527
linear_system
2
sinusoid
2.5
1
0
62
3.902455
Solve this system for x: 3.9024548389919356x + 1y = 10 2x + 4y = 12 FINAL:
2.057338
2.057338
linear_system
2
sinusoid
2.5
1
0
63
3.950991
Solve this system for x: 3.9509914298352196x + 1y = 10 2x + 4y = 12 FINAL:
2.028403
2.028403
linear_system
2
sinusoid
2.5
2
0
0
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
2.5
2
0
1
4.097545
Solve this system for x: 4.097545161008064x + 1y = 10 2x + 4y = 12 FINAL:
1.945771
1.945771
linear_system
2
sinusoid
2.5
2
0
2
4.191342
Solve this system for x: 4.191341716182545x + 1y = 10 2x + 4y = 12 FINAL:
1.896329
1.896329
linear_system
2
sinusoid
2.5
2
0
3
4.277785
Solve this system for x: 4.277785116509801x + 1y = 10 2x + 4y = 12 FINAL:
1.852938
1.852938
linear_system
2
sinusoid
2.5
2
0
4
4.353553
Solve this system for x: 4.353553390593274x + 1y = 10 2x + 4y = 12 FINAL:
1.816505
1.816505
linear_system
2
sinusoid
2.5
2
0
5
4.415735
Solve this system for x: 4.4157348061512725x + 1y = 10 2x + 4y = 12 FINAL:
1.787659
1.787659
linear_system
2
sinusoid
2.5
2
0
6
4.46194
Solve this system for x: 4.461939766255643x + 1y = 10 2x + 4y = 12 FINAL:
1.766811
1.766811
linear_system
2
sinusoid
2.5
2
0
7
4.490393
Solve this system for x: 4.490392640201615x + 1y = 10 2x + 4y = 12 FINAL:
1.754213
1.754213
linear_system
2
sinusoid
2.5
2
0
8
4.5
Solve this system for x: 4.5x + 1y = 10 2x + 4y = 12 FINAL:
1.75
1.75
linear_system
2
sinusoid
2.5
2
0
9
4.490393
Solve this system for x: 4.490392640201615x + 1y = 10 2x + 4y = 12 FINAL:
1.754213
1.754213
linear_system
2
sinusoid
2.5
2
0
10
4.46194
Solve this system for x: 4.461939766255643x + 1y = 10 2x + 4y = 12 FINAL:
1.766811
1.766811
linear_system
2
sinusoid
2.5
2
0
11
4.415735
Solve this system for x: 4.4157348061512725x + 1y = 10 2x + 4y = 12 FINAL:
1.787659
1.787659
linear_system
2
sinusoid
2.5
2
0
12
4.353553
Solve this system for x: 4.353553390593274x + 1y = 10 2x + 4y = 12 FINAL:
1.816505
1.816505
linear_system
2
sinusoid
2.5
2
0
13
4.277785
Solve this system for x: 4.277785116509801x + 1y = 10 2x + 4y = 12 FINAL:
1.852938
1.852938
linear_system
2
sinusoid
2.5
2
0
14
4.191342
Solve this system for x: 4.191341716182545x + 1y = 10 2x + 4y = 12 FINAL:
1.896329
1.896329
linear_system
2
sinusoid
2.5
2
0
15
4.097545
Solve this system for x: 4.097545161008064x + 1y = 10 2x + 4y = 12 FINAL:
1.945771
1.945771
linear_system
2
sinusoid
2.5
2
0
16
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
2.5
2
0
17
3.902455
Solve this system for x: 3.902454838991936x + 1y = 10 2x + 4y = 12 FINAL:
2.057338
2.057338
linear_system
2
sinusoid
2.5
2
0
18
3.808658
Solve this system for x: 3.808658283817455x + 1y = 10 2x + 4y = 12 FINAL:
2.115661
2.115661
linear_system
2
sinusoid
2.5
2
0
19
3.722215
Solve this system for x: 3.722214883490199x + 1y = 10 2x + 4y = 12 FINAL:
2.172419
2.172419
linear_system
2
sinusoid
2.5
2
0
20
3.646447
Solve this system for x: 3.646446609406726x + 1y = 10 2x + 4y = 12 FINAL:
2.224732
2.224732
linear_system
2
sinusoid
2.5
2
0
21
3.584265
Solve this system for x: 3.5842651938487275x + 1y = 10 2x + 4y = 12 FINAL:
2.269584
2.269584
linear_system
2
sinusoid
2.5
2
0
22
3.53806
Solve this system for x: 3.538060233744357x + 1y = 10 2x + 4y = 12 FINAL:
2.304102
2.304102
linear_system
2
sinusoid
2.5
2
0
23
3.509607
Solve this system for x: 3.509607359798385x + 1y = 10 2x + 4y = 12 FINAL:
2.325885
2.325885
linear_system
2
sinusoid
2.5
2
0
24
3.5
Solve this system for x: 3.5x + 1y = 10 2x + 4y = 12 FINAL:
2.333333
2.333333
linear_system
2
sinusoid
2.5
2
0
25
3.509607
Solve this system for x: 3.509607359798385x + 1y = 10 2x + 4y = 12 FINAL:
2.325885
2.325885
linear_system
2
sinusoid
2.5
2
0
26
3.53806
Solve this system for x: 3.5380602337443565x + 1y = 10 2x + 4y = 12 FINAL:
2.304102
2.304102
linear_system
2
sinusoid
2.5
2
0
27
3.584265
Solve this system for x: 3.584265193848727x + 1y = 10 2x + 4y = 12 FINAL:
2.269584
2.269584
linear_system
2
sinusoid
2.5
2
0
28
3.646447
Solve this system for x: 3.646446609406726x + 1y = 10 2x + 4y = 12 FINAL:
2.224732
2.224732
linear_system
2
sinusoid
2.5
2
0
29
3.722215
Solve this system for x: 3.722214883490199x + 1y = 10 2x + 4y = 12 FINAL:
2.172419
2.172419
linear_system
2
sinusoid
2.5
2
0
30
3.808658
Solve this system for x: 3.8086582838174547x + 1y = 10 2x + 4y = 12 FINAL:
2.115661
2.115661
linear_system
2
sinusoid
2.5
2
0
31
3.902455
Solve this system for x: 3.9024548389919356x + 1y = 10 2x + 4y = 12 FINAL:
2.057338
2.057338
linear_system
2
sinusoid
2.5
2
0
32
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
2.5
2
0
33
4.097545
Solve this system for x: 4.097545161008064x + 1y = 10 2x + 4y = 12 FINAL:
1.945771
1.945771
linear_system
2
sinusoid
2.5
2
0
34
4.191342
Solve this system for x: 4.191341716182545x + 1y = 10 2x + 4y = 12 FINAL:
1.896329
1.896329
linear_system
2
sinusoid
2.5
2
0
35
4.277785
Solve this system for x: 4.277785116509801x + 1y = 10 2x + 4y = 12 FINAL:
1.852938
1.852938
linear_system
2
sinusoid
2.5
2
0
36
4.353553
Solve this system for x: 4.353553390593274x + 1y = 10 2x + 4y = 12 FINAL:
1.816505
1.816505
linear_system
2
sinusoid
2.5
2
0
37
4.415735
Solve this system for x: 4.4157348061512725x + 1y = 10 2x + 4y = 12 FINAL:
1.787659
1.787659
linear_system
2
sinusoid
2.5
2
0
38
4.46194
Solve this system for x: 4.461939766255643x + 1y = 10 2x + 4y = 12 FINAL:
1.766811
1.766811
linear_system
2
sinusoid
2.5
2
0
39
4.490393
Solve this system for x: 4.490392640201615x + 1y = 10 2x + 4y = 12 FINAL:
1.754213
1.754213
linear_system
2
sinusoid
2.5
2
0
40
4.5
Solve this system for x: 4.5x + 1y = 10 2x + 4y = 12 FINAL:
1.75
1.75
linear_system
2
sinusoid
2.5
2
0
41
4.490393
Solve this system for x: 4.490392640201615x + 1y = 10 2x + 4y = 12 FINAL:
1.754213
1.754213
linear_system
2
sinusoid
2.5
2
0
42
4.46194
Solve this system for x: 4.461939766255643x + 1y = 10 2x + 4y = 12 FINAL:
1.766811
1.766811
linear_system
2
sinusoid
2.5
2
0
43
4.415735
Solve this system for x: 4.4157348061512725x + 1y = 10 2x + 4y = 12 FINAL:
1.787659
1.787659
linear_system
2
sinusoid
2.5
2
0
44
4.353553
Solve this system for x: 4.353553390593274x + 1y = 10 2x + 4y = 12 FINAL:
1.816505
1.816505
linear_system
2
sinusoid
2.5
2
0
45
4.277785
Solve this system for x: 4.2777851165098015x + 1y = 10 2x + 4y = 12 FINAL:
1.852938
1.852938
linear_system
2
sinusoid
2.5
2
0
46
4.191342
Solve this system for x: 4.191341716182546x + 1y = 10 2x + 4y = 12 FINAL:
1.896329
1.896329
linear_system
2
sinusoid
2.5
2
0
47
4.097545
Solve this system for x: 4.097545161008064x + 1y = 10 2x + 4y = 12 FINAL:
1.945771
1.945771
linear_system
2
sinusoid
2.5
2
0
48
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
2.5
2
0
49
3.902455
Solve this system for x: 3.9024548389919365x + 1y = 10 2x + 4y = 12 FINAL:
2.057338
2.057338
linear_system
2
sinusoid
2.5
2
0
50
3.808658
Solve this system for x: 3.808658283817455x + 1y = 10 2x + 4y = 12 FINAL:
2.115661
2.115661
linear_system
2
sinusoid
2.5
2
0
51
3.722215
Solve this system for x: 3.7222148834901994x + 1y = 10 2x + 4y = 12 FINAL:
2.172419
2.172419
linear_system
2
sinusoid
2.5
2
0
52
3.646447
Solve this system for x: 3.646446609406726x + 1y = 10 2x + 4y = 12 FINAL:
2.224732
2.224732
linear_system
2
sinusoid
2.5
2
0
53
3.584265
Solve this system for x: 3.5842651938487275x + 1y = 10 2x + 4y = 12 FINAL:
2.269584
2.269584
linear_system
2
sinusoid
2.5
2
0
54
3.53806
Solve this system for x: 3.538060233744357x + 1y = 10 2x + 4y = 12 FINAL:
2.304102
2.304102
linear_system
2
sinusoid
2.5
2
0
55
3.509607
Solve this system for x: 3.509607359798385x + 1y = 10 2x + 4y = 12 FINAL:
2.325885
2.325885