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
1
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
1
0
1
4.009802
Solve this system for x: 4.009801714032956x + 1y = 7 1x + 5y = 11 FINAL:
1.259908
1.259908
linear_system
0
sinusoid
0.5
1
0
2
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
1
0
3
4.029028
Solve this system for x: 4.029028467725446x + 1y = 7 1x + 5y = 11 FINAL:
1.253582
1.253582
linear_system
0
sinusoid
0.5
1
0
4
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
1
0
5
4.04714
Solve this system for x: 4.0471396736826x + 1y = 7 1x + 5y = 11 FINAL:
1.24768
1.24768
linear_system
0
sinusoid
0.5
1
0
6
4.055557
Solve this system for x: 4.05555702330196x + 1y = 7 1x + 5y = 11 FINAL:
1.244956
1.244956
linear_system
0
sinusoid
0.5
1
0
7
4.063439
Solve this system for x: 4.063439328416364x + 1y = 7 1x + 5y = 11 FINAL:
1.242416
1.242416
linear_system
0
sinusoid
0.5
1
0
8
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
1
0
9
4.077301
Solve this system for x: 4.077301045336274x + 1y = 7 1x + 5y = 11 FINAL:
1.237975
1.237975
linear_system
0
sinusoid
0.5
1
0
10
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
1
0
11
4.088192
Solve this system for x: 4.088192126434835x + 1y = 7 1x + 5y = 11 FINAL:
1.234507
1.234507
linear_system
0
sinusoid
0.5
1
0
12
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
1
0
13
4.095694
Solve this system for x: 4.095694033573221x + 1y = 7 1x + 5y = 11 FINAL:
1.23213
1.23213
linear_system
0
sinusoid
0.5
1
0
14
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
1
0
15
4.099518
Solve this system for x: 4.09951847266722x + 1y = 7 1x + 5y = 11 FINAL:
1.230921
1.230921
linear_system
0
sinusoid
0.5
1
0
16
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
1
0
17
4.099518
Solve this system for x: 4.09951847266722x + 1y = 7 1x + 5y = 11 FINAL:
1.230921
1.230921
linear_system
0
sinusoid
0.5
1
0
18
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
1
0
19
4.095694
Solve this system for x: 4.095694033573221x + 1y = 7 1x + 5y = 11 FINAL:
1.23213
1.23213
linear_system
0
sinusoid
0.5
1
0
20
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
1
0
21
4.088192
Solve this system for x: 4.088192126434835x + 1y = 7 1x + 5y = 11 FINAL:
1.234507
1.234507
linear_system
0
sinusoid
0.5
1
0
22
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
1
0
23
4.077301
Solve this system for x: 4.077301045336274x + 1y = 7 1x + 5y = 11 FINAL:
1.237975
1.237975
linear_system
0
sinusoid
0.5
1
0
24
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
1
0
25
4.063439
Solve this system for x: 4.063439328416364x + 1y = 7 1x + 5y = 11 FINAL:
1.242416
1.242416
linear_system
0
sinusoid
0.5
1
0
26
4.055557
Solve this system for x: 4.05555702330196x + 1y = 7 1x + 5y = 11 FINAL:
1.244956
1.244956
linear_system
0
sinusoid
0.5
1
0
27
4.04714
Solve this system for x: 4.0471396736826x + 1y = 7 1x + 5y = 11 FINAL:
1.24768
1.24768
linear_system
0
sinusoid
0.5
1
0
28
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
1
0
29
4.029028
Solve this system for x: 4.029028467725446x + 1y = 7 1x + 5y = 11 FINAL:
1.253582
1.253582
linear_system
0
sinusoid
0.5
1
0
30
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
1
0
31
4.009802
Solve this system for x: 4.009801714032956x + 1y = 7 1x + 5y = 11 FINAL:
1.259908
1.259908
linear_system
0
sinusoid
0.5
1
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
1
0
33
3.990198
Solve this system for x: 3.9901982859670437x + 1y = 7 1x + 5y = 11 FINAL:
1.266425
1.266425
linear_system
0
sinusoid
0.5
1
0
34
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
1
0
35
3.970972
Solve this system for x: 3.970971532274554x + 1y = 7 1x + 5y = 11 FINAL:
1.272882
1.272882
linear_system
0
sinusoid
0.5
1
0
36
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
1
0
37
3.95286
Solve this system for x: 3.9528603263174x + 1y = 7 1x + 5y = 11 FINAL:
1.279024
1.279024
linear_system
0
sinusoid
0.5
1
0
38
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
1
0
39
3.936561
Solve this system for x: 3.9365606715836354x + 1y = 7 1x + 5y = 11 FINAL:
1.284604
1.284604
linear_system
0
sinusoid
0.5
1
0
40
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
1
0
41
3.922699
Solve this system for x: 3.9226989546637263x + 1y = 7 1x + 5y = 11 FINAL:
1.289387
1.289387
linear_system
0
sinusoid
0.5
1
0
42
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
1
0
43
3.911808
Solve this system for x: 3.9118078735651647x + 1y = 7 1x + 5y = 11 FINAL:
1.29317
1.29317
linear_system
0
sinusoid
0.5
1
0
44
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
1
0
45
3.904306
Solve this system for x: 3.904305966426779x + 1y = 7 1x + 5y = 11 FINAL:
1.295789
1.295789
linear_system
0
sinusoid
0.5
1
0
46
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
1
0
47
3.900482
Solve this system for x: 3.90048152733278x + 1y = 7 1x + 5y = 11 FINAL:
1.297128
1.297128
linear_system
0
sinusoid
0.5
1
0
48
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
1
0
49
3.900482
Solve this system for x: 3.90048152733278x + 1y = 7 1x + 5y = 11 FINAL:
1.297128
1.297128
linear_system
0
sinusoid
0.5
1
0
50
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
1
0
51
3.904306
Solve this system for x: 3.904305966426779x + 1y = 7 1x + 5y = 11 FINAL:
1.295789
1.295789
linear_system
0
sinusoid
0.5
1
0
52
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
1
0
53
3.911808
Solve this system for x: 3.9118078735651647x + 1y = 7 1x + 5y = 11 FINAL:
1.29317
1.29317
linear_system
0
sinusoid
0.5
1
0
54
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
1
0
55
3.922699
Solve this system for x: 3.9226989546637263x + 1y = 7 1x + 5y = 11 FINAL:
1.289387
1.289387
linear_system
0
sinusoid
0.5
1
0
56
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
1
0
57
3.936561
Solve this system for x: 3.9365606715836354x + 1y = 7 1x + 5y = 11 FINAL:
1.284604
1.284604
linear_system
0
sinusoid
0.5
1
0
58
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
1
0
59
3.95286
Solve this system for x: 3.9528603263174x + 1y = 7 1x + 5y = 11 FINAL:
1.279024
1.279024
linear_system
0
sinusoid
0.5
1
0
60
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
1
0
61
3.970972
Solve this system for x: 3.970971532274554x + 1y = 7 1x + 5y = 11 FINAL:
1.272882
1.272882
linear_system
0
sinusoid
0.5
1
0
62
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
1
0
63
3.990198
Solve this system for x: 3.9901982859670437x + 1y = 7 1x + 5y = 11 FINAL:
1.266425
1.266425
linear_system
0
sinusoid
0.5
2
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
2
0
1
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
2
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
3
4.055557
Solve this system for x: 4.05555702330196x + 1y = 7 1x + 5y = 11 FINAL:
1.244956
1.244956
linear_system
0
sinusoid
0.5
2
0
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
4.055557
Solve this system for x: 4.05555702330196x + 1y = 7 1x + 5y = 11 FINAL:
1.244956
1.244956
linear_system
0
sinusoid
0.5
2
0
14
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
15
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
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
2
0
17
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
18
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
19
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
20
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
21
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
22
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
23
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
24
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
25
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
26
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
27
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
28
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
29
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
30
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
31
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
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
2
0
33
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
34
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
35
4.055557
Solve this system for x: 4.05555702330196x + 1y = 7 1x + 5y = 11 FINAL:
1.244956
1.244956