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
0.5
16
240
4
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
5
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
6
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
7
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
8
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
9
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
10
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
11
4.05
Solve this system for x: 4.050000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
12
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
13
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
14
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
15
4.05
Solve this system for x: 4.050000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
16
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
17
3.95
Solve this system for x: 3.9499999999999997x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
18
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
19
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
20
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
21
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
22
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
23
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
24
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
25
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
26
4.086603
Solve this system for x: 4.086602540378444x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
27
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
28
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
29
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
30
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
31
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
32
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
33
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
34
4.086603
Solve this system for x: 4.086602540378444x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
35
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
36
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
37
3.95
Solve this system for x: 3.95x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
38
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
39
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
40
3.913397
Solve this system for x: 3.9133974596215566x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
41
3.95
Solve this system for x: 3.949999999999999x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
42
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
43
4.05
Solve this system for x: 4.050000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
44
3.913397
Solve this system for x: 3.913397459621557x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
45
3.95
Solve this system for x: 3.9499999999999993x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
46
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
47
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
48
3.913397
Solve this system for x: 3.9133974596215566x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
49
3.95
Solve this system for x: 3.949999999999999x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
50
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
51
4.05
Solve this system for x: 4.050000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
52
3.913397
Solve this system for x: 3.913397459621556x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
53
3.95
Solve this system for x: 3.9499999999999993x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
54
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
55
4.05
Solve this system for x: 4.05x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
56
3.913397
Solve this system for x: 3.9133974596215566x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
57
3.95
Solve this system for x: 3.949999999999999x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
58
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
59
4.05
Solve this system for x: 4.050000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
0
sinusoid
0.5
16
240
60
3.913397
Solve this system for x: 3.913397459621557x + 1y = 7 1x + 5y = 11 FINAL:
1.292617
1.292617
linear_system
0
sinusoid
0.5
16
240
61
3.95
Solve this system for x: 3.9499999999999993x + 1y = 7 1x + 5y = 11 FINAL:
1.28
1.28
linear_system
0
sinusoid
0.5
16
240
62
4.086603
Solve this system for x: 4.086602540378443x + 1y = 7 1x + 5y = 11 FINAL:
1.235012
1.235012
linear_system
0
sinusoid
0.5
16
240
63
4.05
Solve this system for x: 4.050000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.246753
1.246753
linear_system
1
sinusoid
0.5
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
0.5
1
0
1
4.009802
Solve this system for x: 4.009801714032956x + 2y = 8 1x + 3y = 9 FINAL:
0.598241
0.598241
linear_system
1
sinusoid
0.5
1
0
2
4.019509
Solve this system for x: 4.019509032201613x + 2y = 8 1x + 3y = 9 FINAL:
0.596509
0.596509
linear_system
1
sinusoid
0.5
1
0
3
4.029028
Solve this system for x: 4.029028467725446x + 2y = 8 1x + 3y = 9 FINAL:
0.59482
0.59482
linear_system
1
sinusoid
0.5
1
0
4
4.038268
Solve this system for x: 4.038268343236509x + 2y = 8 1x + 3y = 9 FINAL:
0.59319
0.59319
linear_system
1
sinusoid
0.5
1
0
5
4.04714
Solve this system for x: 4.0471396736826x + 2y = 8 1x + 3y = 9 FINAL:
0.591633
0.591633
linear_system
1
sinusoid
0.5
1
0
6
4.055557
Solve this system for x: 4.05555702330196x + 2y = 8 1x + 3y = 9 FINAL:
0.590164
0.590164
linear_system
1
sinusoid
0.5
1
0
7
4.063439
Solve this system for x: 4.063439328416364x + 2y = 8 1x + 3y = 9 FINAL:
0.588794
0.588794
linear_system
1
sinusoid
0.5
1
0
8
4.070711
Solve this system for x: 4.070710678118655x + 2y = 8 1x + 3y = 9 FINAL:
0.587536
0.587536
linear_system
1
sinusoid
0.5
1
0
9
4.077301
Solve this system for x: 4.077301045336274x + 2y = 8 1x + 3y = 9 FINAL:
0.586401
0.586401
linear_system
1
sinusoid
0.5
1
0
10
4.083147
Solve this system for x: 4.083146961230255x + 2y = 8 1x + 3y = 9 FINAL:
0.585398
0.585398
linear_system
1
sinusoid
0.5
1
0
11
4.088192
Solve this system for x: 4.088192126434835x + 2y = 8 1x + 3y = 9 FINAL:
0.584535
0.584535
linear_system
1
sinusoid
0.5
1
0
12
4.092388
Solve this system for x: 4.092387953251128x + 2y = 8 1x + 3y = 9 FINAL:
0.583819
0.583819
linear_system
1
sinusoid
0.5
1
0
13
4.095694
Solve this system for x: 4.095694033573221x + 2y = 8 1x + 3y = 9 FINAL:
0.583256
0.583256
linear_system
1
sinusoid
0.5
1
0
14
4.098079
Solve this system for x: 4.098078528040323x + 2y = 8 1x + 3y = 9 FINAL:
0.58285
0.58285
linear_system
1
sinusoid
0.5
1
0
15
4.099518
Solve this system for x: 4.09951847266722x + 2y = 8 1x + 3y = 9 FINAL:
0.582606
0.582606
linear_system
1
sinusoid
0.5
1
0
16
4.1
Solve this system for x: 4.1x + 2y = 8 1x + 3y = 9 FINAL:
0.582524
0.582524
linear_system
1
sinusoid
0.5
1
0
17
4.099518
Solve this system for x: 4.09951847266722x + 2y = 8 1x + 3y = 9 FINAL:
0.582606
0.582606
linear_system
1
sinusoid
0.5
1
0
18
4.098079
Solve this system for x: 4.098078528040323x + 2y = 8 1x + 3y = 9 FINAL:
0.58285
0.58285
linear_system
1
sinusoid
0.5
1
0
19
4.095694
Solve this system for x: 4.095694033573221x + 2y = 8 1x + 3y = 9 FINAL:
0.583256
0.583256
linear_system
1
sinusoid
0.5
1
0
20
4.092388
Solve this system for x: 4.092387953251128x + 2y = 8 1x + 3y = 9 FINAL:
0.583819
0.583819
linear_system
1
sinusoid
0.5
1
0
21
4.088192
Solve this system for x: 4.088192126434835x + 2y = 8 1x + 3y = 9 FINAL:
0.584535
0.584535
linear_system
1
sinusoid
0.5
1
0
22
4.083147
Solve this system for x: 4.083146961230255x + 2y = 8 1x + 3y = 9 FINAL:
0.585398
0.585398
linear_system
1
sinusoid
0.5
1
0
23
4.077301
Solve this system for x: 4.077301045336274x + 2y = 8 1x + 3y = 9 FINAL:
0.586401
0.586401
linear_system
1
sinusoid
0.5
1
0
24
4.070711
Solve this system for x: 4.070710678118655x + 2y = 8 1x + 3y = 9 FINAL:
0.587536
0.587536
linear_system
1
sinusoid
0.5
1
0
25
4.063439
Solve this system for x: 4.063439328416364x + 2y = 8 1x + 3y = 9 FINAL:
0.588794
0.588794
linear_system
1
sinusoid
0.5
1
0
26
4.055557
Solve this system for x: 4.05555702330196x + 2y = 8 1x + 3y = 9 FINAL:
0.590164
0.590164
linear_system
1
sinusoid
0.5
1
0
27
4.04714
Solve this system for x: 4.0471396736826x + 2y = 8 1x + 3y = 9 FINAL:
0.591633
0.591633
linear_system
1
sinusoid
0.5
1
0
28
4.038268
Solve this system for x: 4.038268343236509x + 2y = 8 1x + 3y = 9 FINAL:
0.59319
0.59319
linear_system
1
sinusoid
0.5
1
0
29
4.029028
Solve this system for x: 4.029028467725446x + 2y = 8 1x + 3y = 9 FINAL:
0.59482
0.59482
linear_system
1
sinusoid
0.5
1
0
30
4.019509
Solve this system for x: 4.019509032201613x + 2y = 8 1x + 3y = 9 FINAL:
0.596509
0.596509
linear_system
1
sinusoid
0.5
1
0
31
4.009802
Solve this system for x: 4.009801714032956x + 2y = 8 1x + 3y = 9 FINAL:
0.598241
0.598241
linear_system
1
sinusoid
0.5
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
0.5
1
0
33
3.990198
Solve this system for x: 3.9901982859670437x + 2y = 8 1x + 3y = 9 FINAL:
0.60177
0.60177
linear_system
1
sinusoid
0.5
1
0
34
3.980491
Solve this system for x: 3.9804909677983873x + 2y = 8 1x + 3y = 9 FINAL:
0.603532
0.603532
linear_system
1
sinusoid
0.5
1
0
35
3.970972
Solve this system for x: 3.970971532274554x + 2y = 8 1x + 3y = 9 FINAL:
0.605271
0.605271
linear_system
1
sinusoid
0.5
1
0
36
3.961732
Solve this system for x: 3.961731656763491x + 2y = 8 1x + 3y = 9 FINAL:
0.606968
0.606968
linear_system
1
sinusoid
0.5
1
0
37
3.95286
Solve this system for x: 3.9528603263174x + 2y = 8 1x + 3y = 9 FINAL:
0.608607
0.608607
linear_system
1
sinusoid
0.5
1
0
38
3.944443
Solve this system for x: 3.94444297669804x + 2y = 8 1x + 3y = 9 FINAL:
0.61017
0.61017
linear_system
1
sinusoid
0.5
1
0
39
3.936561
Solve this system for x: 3.9365606715836354x + 2y = 8 1x + 3y = 9 FINAL:
0.611641
0.611641