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
2
0
36
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
2
0
37
4.083147
Solve this system for x: 4.083146961230255x + 1y = 7 1x + 5y = 11 FINAL:
1.236111
1.236111
linear_system
0
sinusoid
0.5
2
0
38
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
2
0
39
4.098079
Solve this system for x: 4.098078528040323x + 1y = 7 1x + 5y = 11 FINAL:
1.231376
1.231376
linear_system
0
sinusoid
0.5
2
0
40
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
2
0
41
4.098079
Solve this system for x: 4.098078528040323x + 1y = 7 1x + 5y = 11 FINAL:
1.231376
1.231376
linear_system
0
sinusoid
0.5
2
0
42
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
2
0
43
4.083147
Solve this system for x: 4.083146961230255x + 1y = 7 1x + 5y = 11 FINAL:
1.236111
1.236111
linear_system
0
sinusoid
0.5
2
0
44
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
2
0
45
4.055557
Solve this system for x: 4.055557023301961x + 1y = 7 1x + 5y = 11 FINAL:
1.244956
1.244956
linear_system
0
sinusoid
0.5
2
0
46
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
2
0
47
4.019509
Solve this system for x: 4.019509032201613x + 1y = 7 1x + 5y = 11 FINAL:
1.256706
1.256706
linear_system
0
sinusoid
0.5
2
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
2
0
49
3.980491
Solve this system for x: 3.9804909677983873x + 1y = 7 1x + 5y = 11 FINAL:
1.269676
1.269676
linear_system
0
sinusoid
0.5
2
0
50
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
2
0
51
3.944443
Solve this system for x: 3.94444297669804x + 1y = 7 1x + 5y = 11 FINAL:
1.2819
1.2819
linear_system
0
sinusoid
0.5
2
0
52
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
2
0
53
3.916853
Solve this system for x: 3.9168530387697453x + 1y = 7 1x + 5y = 11 FINAL:
1.291415
1.291415
linear_system
0
sinusoid
0.5
2
0
54
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
2
0
55
3.901921
Solve this system for x: 3.901921471959677x + 1y = 7 1x + 5y = 11 FINAL:
1.296624
1.296624
linear_system
0
sinusoid
0.5
2
0
56
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
2
0
57
3.901921
Solve this system for x: 3.901921471959677x + 1y = 7 1x + 5y = 11 FINAL:
1.296624
1.296624
linear_system
0
sinusoid
0.5
2
0
58
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
2
0
59
3.916853
Solve this system for x: 3.9168530387697453x + 1y = 7 1x + 5y = 11 FINAL:
1.291415
1.291415
linear_system
0
sinusoid
0.5
2
0
60
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
2
0
61
3.944443
Solve this system for x: 3.94444297669804x + 1y = 7 1x + 5y = 11 FINAL:
1.2819
1.2819
linear_system
0
sinusoid
0.5
2
0
62
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
2
0
63
3.980491
Solve this system for x: 3.9804909677983873x + 1y = 7 1x + 5y = 11 FINAL:
1.269676
1.269676
linear_system
0
sinusoid
0.5
4
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
4
0
1
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
0
2
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
4
0
3
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
4
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
4
0
5
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
6
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
4
0
7
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
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
4
0
9
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
4
0
10
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
4
0
11
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
12
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
4
0
13
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
14
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
4
0
15
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
4
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
4
0
17
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
0
18
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
4
0
19
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
20
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
4
0
21
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
22
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
4
0
23
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
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
4
0
25
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
4
0
26
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
4
0
27
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
28
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
4
0
29
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
30
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
4
0
31
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
4
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
4
0
33
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
0
34
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
4
0
35
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
36
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
4
0
37
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
38
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
4
0
39
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
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
4
0
41
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
4
0
42
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
4
0
43
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
44
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
4
0
45
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
46
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
4
0
47
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
4
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
4
0
49
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
0
50
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
4
0
51
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
52
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
4
0
53
4.092388
Solve this system for x: 4.092387953251128x + 1y = 7 1x + 5y = 11 FINAL:
1.233176
1.233176
linear_system
0
sinusoid
0.5
4
0
54
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
4
0
55
4.038268
Solve this system for x: 4.038268343236509x + 1y = 7 1x + 5y = 11 FINAL:
1.250564
1.250564
linear_system
0
sinusoid
0.5
4
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
4
0
57
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
4
0
58
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
4
0
59
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
60
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
4
0
61
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 7 1x + 5y = 11 FINAL:
1.294634
1.294634
linear_system
0
sinusoid
0.5
4
0
62
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
4
0
63
3.961732
Solve this system for x: 3.961731656763491x + 1y = 7 1x + 5y = 11 FINAL:
1.276008
1.276008
linear_system
0
sinusoid
0.5
8
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
8
0
1
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
2
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
3
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
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
8
0
5
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
6
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
7
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 7 1x + 5y = 11 FINAL:
1.287109
1.287109