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
0.5
4
0
12
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
4
0
13
3.907612
Solve this system for x: 3.9076120467488713x + 2y = 8 1x + 3y = 9 FINAL:
0.617104
0.617104
linear_system
1
sinusoid
0.5
4
0
14
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
4
0
15
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
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
0.5
4
0
17
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
4
0
18
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
4
0
19
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
4
0
20
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
4
0
21
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
4
0
22
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
4
0
23
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
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
0.5
4
0
25
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
4
0
26
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
4
0
27
3.907612
Solve this system for x: 3.9076120467488713x + 2y = 8 1x + 3y = 9 FINAL:
0.617104
0.617104
linear_system
1
sinusoid
0.5
4
0
28
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
4
0
29
3.907612
Solve this system for x: 3.9076120467488713x + 2y = 8 1x + 3y = 9 FINAL:
0.617104
0.617104
linear_system
1
sinusoid
0.5
4
0
30
3.929289
Solve this system for x: 3.929289321881345x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
4
0
31
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
4
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
4
0
33
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
4
0
34
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
4
0
35
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
4
0
36
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
4
0
37
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
4
0
38
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
4
0
39
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
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
0.5
4
0
41
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
4
0
42
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
4
0
43
3.907612
Solve this system for x: 3.9076120467488713x + 2y = 8 1x + 3y = 9 FINAL:
0.617104
0.617104
linear_system
1
sinusoid
0.5
4
0
44
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
4
0
45
3.907612
Solve this system for x: 3.9076120467488713x + 2y = 8 1x + 3y = 9 FINAL:
0.617104
0.617104
linear_system
1
sinusoid
0.5
4
0
46
3.929289
Solve this system for x: 3.929289321881345x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
4
0
47
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
4
0
48
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
4
0
49
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
4
0
50
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
4
0
51
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
4
0
52
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
4
0
53
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
4
0
54
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
4
0
55
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
4
0
56
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
4
0
57
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
4
0
58
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
4
0
59
3.907612
Solve this system for x: 3.9076120467488713x + 2y = 8 1x + 3y = 9 FINAL:
0.617104
0.617104
linear_system
1
sinusoid
0.5
4
0
60
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
4
0
61
3.907612
Solve this system for x: 3.9076120467488713x + 2y = 8 1x + 3y = 9 FINAL:
0.617104
0.617104
linear_system
1
sinusoid
0.5
4
0
62
3.929289
Solve this system for x: 3.929289321881345x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
4
0
63
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
8
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
8
0
1
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
8
0
2
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
8
0
3
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
8
0
4
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
5
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
6
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
8
0
7
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
8
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
9
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
8
0
10
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
8
0
11
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
8
0
12
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
13
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
14
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
8
0
15
3.929289
Solve this system for x: 3.929289321881345x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
16
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
17
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
8
0
18
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
8
0
19
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
8
0
20
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
21
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
22
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
8
0
23
3.929289
Solve this system for x: 3.929289321881345x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
24
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
25
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
8
0
26
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
8
0
27
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
8
0
28
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
29
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
30
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
8
0
31
3.929289
Solve this system for x: 3.929289321881345x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
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
8
0
33
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
8
0
34
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
8
0
35
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
8
0
36
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
37
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
38
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
8
0
39
3.929289
Solve this system for x: 3.929289321881345x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
40
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
41
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
8
0
42
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
8
0
43
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
8
0
44
4
Solve this system for x: 4.000000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
0.5
8
0
45
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004
linear_system
1
sinusoid
0.5
8
0
46
3.9
Solve this system for x: 3.9x + 2y = 8 1x + 3y = 9 FINAL:
0.618557
0.618557
linear_system
1
sinusoid
0.5
8
0
47
3.929289
Solve this system for x: 3.9292893218813454x + 2y = 8 1x + 3y = 9 FINAL:
0.613004
0.613004