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
0
52
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
4
0
53
4.46194
Solve this system for x: 4.461939766255643x + 2y = 8 1x + 3y = 9 FINAL:
0.526971
0.526971
linear_system
1
sinusoid
2.5
4
0
54
4.353553
Solve this system for x: 4.353553390593275x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
4
0
55
4.191342
Solve this system for x: 4.191341716182545x + 2y = 8 1x + 3y = 9 FINAL:
0.567428
0.567428
linear_system
1
sinusoid
2.5
4
0
56
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
4
0
57
3.808658
Solve this system for x: 3.808658283817456x + 2y = 8 1x + 3y = 9 FINAL:
0.636539
0.636539
linear_system
1
sinusoid
2.5
4
0
58
3.646447
Solve this system for x: 3.646446609406726x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
4
0
59
3.53806
Solve this system for x: 3.538060233744357x + 2y = 8 1x + 3y = 9 FINAL:
0.696526
0.696526
linear_system
1
sinusoid
2.5
4
0
60
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
4
0
61
3.53806
Solve this system for x: 3.5380602337443565x + 2y = 8 1x + 3y = 9 FINAL:
0.696526
0.696526
linear_system
1
sinusoid
2.5
4
0
62
3.646447
Solve this system for x: 3.6464466094067256x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
4
0
63
3.808658
Solve this system for x: 3.808658283817455x + 2y = 8 1x + 3y = 9 FINAL:
0.636539
0.636539
linear_system
1
sinusoid
2.5
8
0
0
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
1
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
2
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
8
0
3
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
4
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
5
3.646447
Solve this system for x: 3.646446609406726x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
6
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
8
0
7
3.646447
Solve this system for x: 3.646446609406726x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
8
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
9
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
10
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
8
0
11
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
12
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
13
3.646447
Solve this system for x: 3.646446609406726x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
14
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
8
0
15
3.646447
Solve this system for x: 3.6464466094067256x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
16
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
17
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
18
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
8
0
19
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
20
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
21
3.646447
Solve this system for x: 3.646446609406726x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
22
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
8
0
23
3.646447
Solve this system for x: 3.6464466094067256x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
24
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
25
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
26
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
8
0
27
4.353553
Solve this system for x: 4.353553390593275x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
28
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
29
3.646447
Solve this system for x: 3.646446609406726x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
30
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
8
0
31
3.646447
Solve this system for x: 3.6464466094067256x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
32
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
33
4.353553
Solve this system for x: 4.353553390593274x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
34
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
8
0
35
4.353553
Solve this system for x: 4.353553390593275x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
36
4
Solve this system for x: 4.000000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
37
3.646447
Solve this system for x: 3.6464466094067265x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
38
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
8
0
39
3.646447
Solve this system for x: 3.6464466094067256x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
40
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
41
4.353553
Solve this system for x: 4.353553390593272x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
42
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
8
0
43
4.353553
Solve this system for x: 4.353553390593275x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
44
4
Solve this system for x: 4.000000000000003x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
45
3.646447
Solve this system for x: 3.6464466094067265x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
46
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
8
0
47
3.646447
Solve this system for x: 3.6464466094067265x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
48
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
49
4.353553
Solve this system for x: 4.353553390593272x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
50
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
8
0
51
4.353553
Solve this system for x: 4.353553390593275x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
52
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
53
3.646447
Solve this system for x: 3.6464466094067265x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
54
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
8
0
55
3.646447
Solve this system for x: 3.6464466094067265x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
56
4
Solve this system for x: 3.999999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
57
4.353553
Solve this system for x: 4.353553390593272x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
58
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
8
0
59
4.353553
Solve this system for x: 4.353553390593275x + 2y = 8 1x + 3y = 9 FINAL:
0.542463
0.542463
linear_system
1
sinusoid
2.5
8
0
60
4
Solve this system for x: 4.000000000000003x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
8
0
61
3.646447
Solve this system for x: 3.6464466094067265x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
8
0
62
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
8
0
63
3.646447
Solve this system for x: 3.6464466094067265x + 2y = 8 1x + 3y = 9 FINAL:
0.671191
0.671191
linear_system
1
sinusoid
2.5
16
0
0
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
1
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
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
16
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
17
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
18
4
Solve this system for x: 4.000000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
16
0
19
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
20
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
21
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
22
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
23
3.5
Solve this system for x: 3.5x + 2y = 8 1x + 3y = 9 FINAL:
0.705882
0.705882