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
0
sinusoid
2.5
16
240
44
3.566987
Solve this system for x: 3.5669872981077844x + 1y = 7 1x + 5y = 11 FINAL:
1.425607
1.425607
linear_system
0
sinusoid
2.5
16
240
45
3.75
Solve this system for x: 3.7499999999999973x + 1y = 7 1x + 5y = 11 FINAL:
1.352113
1.352113
linear_system
0
sinusoid
2.5
16
240
46
4.433013
Solve this system for x: 4.433012701892217x + 1y = 7 1x + 5y = 11 FINAL:
1.133944
1.133944
linear_system
0
sinusoid
2.5
16
240
47
4.25
Solve this system for x: 4.250000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.185185
1.185185
linear_system
0
sinusoid
2.5
16
240
48
3.566987
Solve this system for x: 3.5669872981077826x + 1y = 7 1x + 5y = 11 FINAL:
1.425607
1.425607
linear_system
0
sinusoid
2.5
16
240
49
3.75
Solve this system for x: 3.7499999999999942x + 1y = 7 1x + 5y = 11 FINAL:
1.352113
1.352113
linear_system
0
sinusoid
2.5
16
240
50
4.433013
Solve this system for x: 4.433012701892218x + 1y = 7 1x + 5y = 11 FINAL:
1.133944
1.133944
linear_system
0
sinusoid
2.5
16
240
51
4.25
Solve this system for x: 4.250000000000004x + 1y = 7 1x + 5y = 11 FINAL:
1.185185
1.185185
linear_system
0
sinusoid
2.5
16
240
52
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
16
240
53
3.75
Solve this system for x: 3.7499999999999973x + 1y = 7 1x + 5y = 11 FINAL:
1.352113
1.352113
linear_system
0
sinusoid
2.5
16
240
54
4.433013
Solve this system for x: 4.433012701892216x + 1y = 7 1x + 5y = 11 FINAL:
1.133944
1.133944
linear_system
0
sinusoid
2.5
16
240
55
4.25
Solve this system for x: 4.250000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.185185
1.185185
linear_system
0
sinusoid
2.5
16
240
56
3.566987
Solve this system for x: 3.5669872981077826x + 1y = 7 1x + 5y = 11 FINAL:
1.425607
1.425607
linear_system
0
sinusoid
2.5
16
240
57
3.75
Solve this system for x: 3.7499999999999942x + 1y = 7 1x + 5y = 11 FINAL:
1.352113
1.352113
linear_system
0
sinusoid
2.5
16
240
58
4.433013
Solve this system for x: 4.433012701892218x + 1y = 7 1x + 5y = 11 FINAL:
1.133944
1.133944
linear_system
0
sinusoid
2.5
16
240
59
4.25
Solve this system for x: 4.250000000000004x + 1y = 7 1x + 5y = 11 FINAL:
1.185185
1.185185
linear_system
0
sinusoid
2.5
16
240
60
3.566987
Solve this system for x: 3.566987298107785x + 1y = 7 1x + 5y = 11 FINAL:
1.425607
1.425607
linear_system
0
sinusoid
2.5
16
240
61
3.75
Solve this system for x: 3.749999999999997x + 1y = 7 1x + 5y = 11 FINAL:
1.352113
1.352113
linear_system
0
sinusoid
2.5
16
240
62
4.433013
Solve this system for x: 4.433012701892216x + 1y = 7 1x + 5y = 11 FINAL:
1.133944
1.133944
linear_system
0
sinusoid
2.5
16
240
63
4.25
Solve this system for x: 4.250000000000002x + 1y = 7 1x + 5y = 11 FINAL:
1.185185
1.185185
linear_system
1
sinusoid
2.5
1
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
1
0
1
4.049009
Solve this system for x: 4.04900857016478x + 2y = 8 1x + 3y = 9 FINAL:
0.591306
0.591306
linear_system
1
sinusoid
2.5
1
0
2
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
1
0
3
4.145142
Solve this system for x: 4.145142338627231x + 2y = 8 1x + 3y = 9 FINAL:
0.574964
0.574964
linear_system
1
sinusoid
2.5
1
0
4
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
1
0
5
4.235698
Solve this system for x: 4.235698368412999x + 2y = 8 1x + 3y = 9 FINAL:
0.560376
0.560376
linear_system
1
sinusoid
2.5
1
0
6
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
1
0
7
4.317197
Solve this system for x: 4.317196642081822x + 2y = 8 1x + 3y = 9 FINAL:
0.547866
0.547866
linear_system
1
sinusoid
2.5
1
0
8
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
1
0
9
4.386505
Solve this system for x: 4.386505226681368x + 2y = 8 1x + 3y = 9 FINAL:
0.537658
0.537658
linear_system
1
sinusoid
2.5
1
0
10
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
1
0
11
4.440961
Solve this system for x: 4.4409606321741775x + 2y = 8 1x + 3y = 9 FINAL:
0.5299
0.5299
linear_system
1
sinusoid
2.5
1
0
12
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
1
0
13
4.47847
Solve this system for x: 4.478470167866105x + 2y = 8 1x + 3y = 9 FINAL:
0.524686
0.524686
linear_system
1
sinusoid
2.5
1
0
14
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
1
0
15
4.497592
Solve this system for x: 4.497592363336098x + 2y = 8 1x + 3y = 9 FINAL:
0.522067
0.522067
linear_system
1
sinusoid
2.5
1
0
16
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
1
0
17
4.497592
Solve this system for x: 4.497592363336098x + 2y = 8 1x + 3y = 9 FINAL:
0.522067
0.522067
linear_system
1
sinusoid
2.5
1
0
18
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
1
0
19
4.47847
Solve this system for x: 4.478470167866105x + 2y = 8 1x + 3y = 9 FINAL:
0.524686
0.524686
linear_system
1
sinusoid
2.5
1
0
20
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
1
0
21
4.440961
Solve this system for x: 4.4409606321741775x + 2y = 8 1x + 3y = 9 FINAL:
0.5299
0.5299
linear_system
1
sinusoid
2.5
1
0
22
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
1
0
23
4.386505
Solve this system for x: 4.386505226681368x + 2y = 8 1x + 3y = 9 FINAL:
0.537658
0.537658
linear_system
1
sinusoid
2.5
1
0
24
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
1
0
25
4.317197
Solve this system for x: 4.317196642081822x + 2y = 8 1x + 3y = 9 FINAL:
0.547866
0.547866
linear_system
1
sinusoid
2.5
1
0
26
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
1
0
27
4.235698
Solve this system for x: 4.235698368412999x + 2y = 8 1x + 3y = 9 FINAL:
0.560376
0.560376
linear_system
1
sinusoid
2.5
1
0
28
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
1
0
29
4.145142
Solve this system for x: 4.145142338627231x + 2y = 8 1x + 3y = 9 FINAL:
0.574964
0.574964
linear_system
1
sinusoid
2.5
1
0
30
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
1
0
31
4.049009
Solve this system for x: 4.04900857016478x + 2y = 8 1x + 3y = 9 FINAL:
0.591306
0.591306
linear_system
1
sinusoid
2.5
1
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
1
0
33
3.950991
Solve this system for x: 3.9509914298352196x + 2y = 8 1x + 3y = 9 FINAL:
0.608953
0.608953
linear_system
1
sinusoid
2.5
1
0
34
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
1
0
35
3.854858
Solve this system for x: 3.854857661372769x + 2y = 8 1x + 3y = 9 FINAL:
0.627315
0.627315
linear_system
1
sinusoid
2.5
1
0
36
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
1
0
37
3.764302
Solve this system for x: 3.764301631587001x + 2y = 8 1x + 3y = 9 FINAL:
0.645654
0.645654
linear_system
1
sinusoid
2.5
1
0
38
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
1
0
39
3.682803
Solve this system for x: 3.6828033579181776x + 2y = 8 1x + 3y = 9 FINAL:
0.6631
0.6631
linear_system
1
sinusoid
2.5
1
0
40
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
1
0
41
3.613495
Solve this system for x: 3.6134947733186316x + 2y = 8 1x + 3y = 9 FINAL:
0.678696
0.678696
linear_system
1
sinusoid
2.5
1
0
42
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
1
0
43
3.559039
Solve this system for x: 3.5590393678258225x + 2y = 8 1x + 3y = 9 FINAL:
0.691474
0.691474
linear_system
1
sinusoid
2.5
1
0
44
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
1
0
45
3.52153
Solve this system for x: 3.5215298321338957x + 2y = 8 1x + 3y = 9 FINAL:
0.700559
0.700559
linear_system
1
sinusoid
2.5
1
0
46
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
1
0
47
3.502408
Solve this system for x: 3.5024076366639014x + 2y = 8 1x + 3y = 9 FINAL:
0.705283
0.705283
linear_system
1
sinusoid
2.5
1
0
48
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
0
49
3.502408
Solve this system for x: 3.5024076366639014x + 2y = 8 1x + 3y = 9 FINAL:
0.705283
0.705283
linear_system
1
sinusoid
2.5
1
0
50
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
1
0
51
3.52153
Solve this system for x: 3.5215298321338957x + 2y = 8 1x + 3y = 9 FINAL:
0.700559
0.700559
linear_system
1
sinusoid
2.5
1
0
52
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
1
0
53
3.559039
Solve this system for x: 3.5590393678258225x + 2y = 8 1x + 3y = 9 FINAL:
0.691474
0.691474
linear_system
1
sinusoid
2.5
1
0
54
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
1
0
55
3.613495
Solve this system for x: 3.6134947733186316x + 2y = 8 1x + 3y = 9 FINAL:
0.678696
0.678696
linear_system
1
sinusoid
2.5
1
0
56
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
1
0
57
3.682803
Solve this system for x: 3.682803357918177x + 2y = 8 1x + 3y = 9 FINAL:
0.6631
0.6631
linear_system
1
sinusoid
2.5
1
0
58
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
1
0
59
3.764302
Solve this system for x: 3.764301631587001x + 2y = 8 1x + 3y = 9 FINAL:
0.645654
0.645654
linear_system
1
sinusoid
2.5
1
0
60
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
1
0
61
3.854858
Solve this system for x: 3.854857661372769x + 2y = 8 1x + 3y = 9 FINAL:
0.627315
0.627315
linear_system
1
sinusoid
2.5
1
0
62
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
1
0
63
3.950991
Solve this system for x: 3.9509914298352196x + 2y = 8 1x + 3y = 9 FINAL:
0.608953
0.608953
linear_system
1
sinusoid
2.5
2
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
2
0
1
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
4.097545
Solve this system for x: 4.097545161008064x + 2y = 8 1x + 3y = 9 FINAL:
0.582941
0.582941