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
2
0
16
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
2
0
17
3.902455
Solve this system for x: 3.902454838991936x + 2y = 8 1x + 3y = 9 FINAL:
0.618087
0.618087
linear_system
1
sinusoid
2.5
2
0
18
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
2
0
19
3.722215
Solve this system for x: 3.722214883490199x + 2y = 8 1x + 3y = 9 FINAL:
0.654547
0.654547
linear_system
1
sinusoid
2.5
2
0
20
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
2
0
21
3.584265
Solve this system for x: 3.5842651938487275x + 2y = 8 1x + 3y = 9 FINAL:
0.685495
0.685495
linear_system
1
sinusoid
2.5
2
0
22
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
2
0
23
3.509607
Solve this system for x: 3.509607359798385x + 2y = 8 1x + 3y = 9 FINAL:
0.703497
0.703497
linear_system
1
sinusoid
2.5
2
0
24
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
2
0
25
3.509607
Solve this system for x: 3.509607359798385x + 2y = 8 1x + 3y = 9 FINAL:
0.703497
0.703497
linear_system
1
sinusoid
2.5
2
0
26
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
2
0
27
3.584265
Solve this system for x: 3.584265193848727x + 2y = 8 1x + 3y = 9 FINAL:
0.685495
0.685495
linear_system
1
sinusoid
2.5
2
0
28
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
2
0
29
3.722215
Solve this system for x: 3.722214883490199x + 2y = 8 1x + 3y = 9 FINAL:
0.654547
0.654547
linear_system
1
sinusoid
2.5
2
0
30
3.808658
Solve this system for x: 3.8086582838174547x + 2y = 8 1x + 3y = 9 FINAL:
0.636539
0.636539
linear_system
1
sinusoid
2.5
2
0
31
3.902455
Solve this system for x: 3.9024548389919356x + 2y = 8 1x + 3y = 9 FINAL:
0.618087
0.618087
linear_system
1
sinusoid
2.5
2
0
32
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
2
0
33
4.097545
Solve this system for x: 4.097545161008064x + 2y = 8 1x + 3y = 9 FINAL:
0.582941
0.582941
linear_system
1
sinusoid
2.5
2
0
34
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
2
0
35
4.277785
Solve this system for x: 4.277785116509801x + 2y = 8 1x + 3y = 9 FINAL:
0.553845
0.553845
linear_system
1
sinusoid
2.5
2
0
36
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
2
0
37
4.415735
Solve this system for x: 4.4157348061512725x + 2y = 8 1x + 3y = 9 FINAL:
0.533466
0.533466
linear_system
1
sinusoid
2.5
2
0
38
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
2
0
39
4.490393
Solve this system for x: 4.490392640201615x + 2y = 8 1x + 3y = 9 FINAL:
0.52305
0.52305
linear_system
1
sinusoid
2.5
2
0
40
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
2
0
41
4.490393
Solve this system for x: 4.490392640201615x + 2y = 8 1x + 3y = 9 FINAL:
0.52305
0.52305
linear_system
1
sinusoid
2.5
2
0
42
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
2
0
43
4.415735
Solve this system for x: 4.4157348061512725x + 2y = 8 1x + 3y = 9 FINAL:
0.533466
0.533466
linear_system
1
sinusoid
2.5
2
0
44
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
2
0
45
4.277785
Solve this system for x: 4.2777851165098015x + 2y = 8 1x + 3y = 9 FINAL:
0.553845
0.553845
linear_system
1
sinusoid
2.5
2
0
46
4.191342
Solve this system for x: 4.191341716182546x + 2y = 8 1x + 3y = 9 FINAL:
0.567428
0.567428
linear_system
1
sinusoid
2.5
2
0
47
4.097545
Solve this system for x: 4.097545161008064x + 2y = 8 1x + 3y = 9 FINAL:
0.582941
0.582941
linear_system
1
sinusoid
2.5
2
0
48
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
2
0
49
3.902455
Solve this system for x: 3.9024548389919365x + 2y = 8 1x + 3y = 9 FINAL:
0.618087
0.618087
linear_system
1
sinusoid
2.5
2
0
50
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
2
0
51
3.722215
Solve this system for x: 3.7222148834901994x + 2y = 8 1x + 3y = 9 FINAL:
0.654547
0.654547
linear_system
1
sinusoid
2.5
2
0
52
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
2
0
53
3.584265
Solve this system for x: 3.5842651938487275x + 2y = 8 1x + 3y = 9 FINAL:
0.685495
0.685495
linear_system
1
sinusoid
2.5
2
0
54
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
2
0
55
3.509607
Solve this system for x: 3.509607359798385x + 2y = 8 1x + 3y = 9 FINAL:
0.703497
0.703497
linear_system
1
sinusoid
2.5
2
0
56
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
2
0
57
3.509607
Solve this system for x: 3.509607359798385x + 2y = 8 1x + 3y = 9 FINAL:
0.703497
0.703497
linear_system
1
sinusoid
2.5
2
0
58
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
2
0
59
3.584265
Solve this system for x: 3.584265193848727x + 2y = 8 1x + 3y = 9 FINAL:
0.685495
0.685495
linear_system
1
sinusoid
2.5
2
0
60
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
2
0
61
3.722215
Solve this system for x: 3.722214883490199x + 2y = 8 1x + 3y = 9 FINAL:
0.654547
0.654547
linear_system
1
sinusoid
2.5
2
0
62
3.808658
Solve this system for x: 3.8086582838174547x + 2y = 8 1x + 3y = 9 FINAL:
0.636539
0.636539
linear_system
1
sinusoid
2.5
2
0
63
3.902455
Solve this system for x: 3.902454838991936x + 2y = 8 1x + 3y = 9 FINAL:
0.618087
0.618087
linear_system
1
sinusoid
2.5
4
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
4
0
1
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
2
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
4
0
3
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
4
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
5
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
6
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
4
0
7
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
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
4
0
9
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
4
0
10
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
11
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
12
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
13
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
14
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
15
3.808658
Solve this system for x: 3.8086582838174547x + 2y = 8 1x + 3y = 9 FINAL:
0.636539
0.636539
linear_system
1
sinusoid
2.5
4
0
16
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
17
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
18
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
4
0
19
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
20
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
21
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
22
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
4
0
23
4.191342
Solve this system for x: 4.191341716182546x + 2y = 8 1x + 3y = 9 FINAL:
0.567428
0.567428
linear_system
1
sinusoid
2.5
4
0
24
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
25
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
4
0
26
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
27
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
28
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
29
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
30
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
31
3.808658
Solve this system for x: 3.8086582838174547x + 2y = 8 1x + 3y = 9 FINAL:
0.636539
0.636539
linear_system
1
sinusoid
2.5
4
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
4
0
33
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
34
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
4
0
35
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
36
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
37
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
38
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
4
0
39
4.191342
Solve this system for x: 4.191341716182546x + 2y = 8 1x + 3y = 9 FINAL:
0.567428
0.567428
linear_system
1
sinusoid
2.5
4
0
40
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
41
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
42
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
43
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
44
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
45
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
46
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
47
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
4
0
48
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
2.5
4
0
49
4.191342
Solve this system for x: 4.191341716182544x + 2y = 8 1x + 3y = 9 FINAL:
0.567428
0.567428
linear_system
1
sinusoid
2.5
4
0
50
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
4
0
51
4.46194
Solve this system for x: 4.461939766255643x + 2y = 8 1x + 3y = 9 FINAL:
0.526971
0.526971