Datasets:
ai-metrology-lab
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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
8
240
48
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
8
240
49
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
8
240
50
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
240
51
4.12941
Solve this system for x: 4.12940952255126x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
240
52
4.433013
Solve this system for x: 4.4330127018922205x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
240
53
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
8
240
54
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
240
55
3.87059
Solve this system for x: 3.8705904774487383x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
8
240
56
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
8
240
57
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
8
240
58
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
8
240
59
4.12941
Solve this system for x: 4.12940952255126x + 2y = 8 1x + 3y = 9 FINAL:
0.577577
0.577577
linear_system
1
sinusoid
2.5
8
240
60
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
8
240
61
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
8
240
62
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
8
240
63
3.87059
Solve this system for x: 3.8705904774487383x + 2y = 8 1x + 3y = 9 FINAL:
0.624235
0.624235
linear_system
1
sinusoid
2.5
16
240
0
3.566987
Solve this system for x: 3.566987298107781x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
1
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
16
240
2
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
3
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
16
240
4
3.566987
Solve this system for x: 3.5669872981077813x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
5
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
16
240
6
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
7
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
16
240
8
3.566987
Solve this system for x: 3.5669872981077813x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
9
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
16
240
10
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
11
4.25
Solve this system for x: 4.250000000000002x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
12
3.566987
Solve this system for x: 3.5669872981077813x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
13
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
16
240
14
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
15
4.25
Solve this system for x: 4.250000000000002x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
16
3.566987
Solve this system for x: 3.5669872981077813x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
17
3.75
Solve this system for x: 3.7499999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
18
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
19
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
16
240
20
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
16
240
21
3.75
Solve this system for x: 3.7500000000000013x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
22
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
23
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
16
240
24
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
16
240
25
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
26
4.433013
Solve this system for x: 4.4330127018922205x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
27
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
28
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
16
240
29
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
30
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
31
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
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
16
240
33
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
34
4.433013
Solve this system for x: 4.4330127018922205x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
35
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
36
3.566987
Solve this system for x: 3.566987298107781x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
37
3.75
Solve this system for x: 3.750000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
38
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
39
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
40
3.566987
Solve this system for x: 3.5669872981077826x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
41
3.75
Solve this system for x: 3.7499999999999947x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
42
4.433013
Solve this system for x: 4.433012701892219x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
43
4.25
Solve this system for x: 4.250000000000004x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
44
3.566987
Solve this system for x: 3.5669872981077844x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
45
3.75
Solve this system for x: 3.7499999999999973x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
46
4.433013
Solve this system for x: 4.433012701892217x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
47
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
48
3.566987
Solve this system for x: 3.5669872981077826x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
49
3.75
Solve this system for x: 3.7499999999999942x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
50
4.433013
Solve this system for x: 4.433012701892218x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
51
4.25
Solve this system for x: 4.250000000000004x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
52
3.566987
Solve this system for x: 3.566987298107781x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
53
3.75
Solve this system for x: 3.7499999999999973x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
54
4.433013
Solve this system for x: 4.433012701892216x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
55
4.25
Solve this system for x: 4.250000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
56
3.566987
Solve this system for x: 3.5669872981077826x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
57
3.75
Solve this system for x: 3.7499999999999942x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
58
4.433013
Solve this system for x: 4.433012701892218x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
59
4.25
Solve this system for x: 4.250000000000004x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
1
sinusoid
2.5
16
240
60
3.566987
Solve this system for x: 3.566987298107785x + 2y = 8 1x + 3y = 9 FINAL:
0.689579
0.689579
linear_system
1
sinusoid
2.5
16
240
61
3.75
Solve this system for x: 3.749999999999997x + 2y = 8 1x + 3y = 9 FINAL:
0.648649
0.648649
linear_system
1
sinusoid
2.5
16
240
62
4.433013
Solve this system for x: 4.433012701892216x + 2y = 8 1x + 3y = 9 FINAL:
0.531019
0.531019
linear_system
1
sinusoid
2.5
16
240
63
4.25
Solve this system for x: 4.250000000000002x + 2y = 8 1x + 3y = 9 FINAL:
0.55814
0.55814
linear_system
2
sinusoid
2.5
1
0
0
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
2.5
1
0
1
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
4.47847
Solve this system for x: 4.478470167866105x + 1y = 10 2x + 4y = 12 FINAL:
1.75947
1.75947
linear_system
2
sinusoid
2.5
1
0
14
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
1
0
15
4.497592
Solve this system for x: 4.497592363336098x + 1y = 10 2x + 4y = 12 FINAL:
1.751054
1.751054
linear_system
2
sinusoid
2.5
1
0
16
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
1
0
17
4.497592
Solve this system for x: 4.497592363336098x + 1y = 10 2x + 4y = 12 FINAL:
1.751054
1.751054
linear_system
2
sinusoid
2.5
1
0
18
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
1
0
19
4.47847
Solve this system for x: 4.478470167866105x + 1y = 10 2x + 4y = 12 FINAL:
1.75947
1.75947