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
8
0
8
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
9
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
10
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
8
0
11
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
12
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
13
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
14
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
8
0
15
3.929289
Solve this system for x: 3.929289321881345x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
16
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
17
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
18
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
8
0
19
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
20
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
21
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
22
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
8
0
23
3.929289
Solve this system for x: 3.929289321881345x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
24
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
25
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
26
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
8
0
27
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
28
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
29
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
30
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
8
0
31
3.929289
Solve this system for x: 3.929289321881345x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
32
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
33
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
34
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
8
0
35
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
36
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
37
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
38
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
8
0
39
3.929289
Solve this system for x: 3.929289321881345x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
40
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
41
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
42
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
8
0
43
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
44
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
45
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
46
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
8
0
47
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
48
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
49
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
50
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
8
0
51
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
52
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
53
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
54
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
8
0
55
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
56
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
57
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
58
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
8
0
59
4.070711
Solve this system for x: 4.070710678118655x + 1y = 7 1x + 5y = 11 FINAL:
1.240082
1.240082
linear_system
0
sinusoid
0.5
8
0
60
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
8
0
61
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
8
0
62
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
8
0
63
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109
linear_system
0
sinusoid
0.5
16
0
0
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
1
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
2
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
3
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
4
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
5
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
6
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
7
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
8
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
9
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
10
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
11
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
12
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
13
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
14
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
15
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
16
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
17
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
18
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
19
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
20
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
21
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
22
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
23
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
24
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
25
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
26
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
27
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
28
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
29
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
30
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
31
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
32
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
33
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
34
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
35
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
36
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
37
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
38
4
Solve this system for x: 4.000000000000001x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
39
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297
linear_system
0
sinusoid
0.5
16
0
40
4
Solve this system for x: 3.9999999999999996x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
41
4.1
Solve this system for x: 4.1x + 1y = 7 1x + 5y = 11 FINAL:
1.230769
1.230769
linear_system
0
sinusoid
0.5
16
0
42
4
Solve this system for x: 4.0x + 1y = 7 1x + 5y = 11 FINAL:
1.263158
1.263158
linear_system
0
sinusoid
0.5
16
0
43
3.9
Solve this system for x: 3.9x + 1y = 7 1x + 5y = 11 FINAL:
1.297297
1.297297