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
16
240
44
3.913397
Solve this system for x: 3.913397459621557x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
16
240
45
3.95
Solve this system for x: 3.9499999999999993x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
16
240
46
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
16
240
47
4.05
Solve this system for x: 4.05x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
16
240
48
3.913397
Solve this system for x: 3.9133974596215566x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
16
240
49
3.95
Solve this system for x: 3.949999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
16
240
50
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
16
240
51
4.05
Solve this system for x: 4.050000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
16
240
52
3.913397
Solve this system for x: 3.913397459621556x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
16
240
53
3.95
Solve this system for x: 3.9499999999999993x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
16
240
54
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
16
240
55
4.05
Solve this system for x: 4.05x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
16
240
56
3.913397
Solve this system for x: 3.9133974596215566x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
16
240
57
3.95
Solve this system for x: 3.949999999999999x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
16
240
58
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
16
240
59
4.05
Solve this system for x: 4.050000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
1
sinusoid
0.5
16
240
60
3.913397
Solve this system for x: 3.913397459621557x + 2y = 8 1x + 3y = 9 FINAL:
0.616004
0.616004
linear_system
1
sinusoid
0.5
16
240
61
3.95
Solve this system for x: 3.9499999999999993x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
16
240
62
4.086603
Solve this system for x: 4.086602540378443x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
16
240
63
4.05
Solve this system for x: 4.050000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.591133
0.591133
linear_system
2
sinusoid
0.5
1
0
0
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
0.5
1
0
1
4.009802
Solve this system for x: 4.009801714032956x + 1y = 10 2x + 4y = 12 FINAL:
1.994415
1.994415
linear_system
2
sinusoid
0.5
1
0
2
4.019509
Solve this system for x: 4.019509032201613x + 1y = 10 2x + 4y = 12 FINAL:
1.988914
1.988914
linear_system
2
sinusoid
0.5
1
0
3
4.029028
Solve this system for x: 4.029028467725446x + 1y = 10 2x + 4y = 12 FINAL:
1.983549
1.983549
linear_system
2
sinusoid
0.5
1
0
4
4.038268
Solve this system for x: 4.038268343236509x + 1y = 10 2x + 4y = 12 FINAL:
1.978369
1.978369
linear_system
2
sinusoid
0.5
1
0
5
4.04714
Solve this system for x: 4.0471396736826x + 1y = 10 2x + 4y = 12 FINAL:
1.973421
1.973421
linear_system
2
sinusoid
0.5
1
0
6
4.055557
Solve this system for x: 4.05555702330196x + 1y = 10 2x + 4y = 12 FINAL:
1.968749
1.968749
linear_system
2
sinusoid
0.5
1
0
7
4.063439
Solve this system for x: 4.063439328416364x + 1y = 10 2x + 4y = 12 FINAL:
1.964394
1.964394
linear_system
2
sinusoid
0.5
1
0
8
4.070711
Solve this system for x: 4.070710678118655x + 1y = 10 2x + 4y = 12 FINAL:
1.960394
1.960394
linear_system
2
sinusoid
0.5
1
0
9
4.077301
Solve this system for x: 4.077301045336274x + 1y = 10 2x + 4y = 12 FINAL:
1.956782
1.956782
linear_system
2
sinusoid
0.5
1
0
10
4.083147
Solve this system for x: 4.083146961230255x + 1y = 10 2x + 4y = 12 FINAL:
1.95359
1.95359
linear_system
2
sinusoid
0.5
1
0
11
4.088192
Solve this system for x: 4.088192126434835x + 1y = 10 2x + 4y = 12 FINAL:
1.950843
1.950843
linear_system
2
sinusoid
0.5
1
0
12
4.092388
Solve this system for x: 4.092387953251128x + 1y = 10 2x + 4y = 12 FINAL:
1.948565
1.948565
linear_system
2
sinusoid
0.5
1
0
13
4.095694
Solve this system for x: 4.095694033573221x + 1y = 10 2x + 4y = 12 FINAL:
1.946773
1.946773
linear_system
2
sinusoid
0.5
1
0
14
4.098079
Solve this system for x: 4.098078528040323x + 1y = 10 2x + 4y = 12 FINAL:
1.945483
1.945483
linear_system
2
sinusoid
0.5
1
0
15
4.099518
Solve this system for x: 4.09951847266722x + 1y = 10 2x + 4y = 12 FINAL:
1.944705
1.944705
linear_system
2
sinusoid
0.5
1
0
16
4.1
Solve this system for x: 4.1x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
0.5
1
0
17
4.099518
Solve this system for x: 4.09951847266722x + 1y = 10 2x + 4y = 12 FINAL:
1.944705
1.944705
linear_system
2
sinusoid
0.5
1
0
18
4.098079
Solve this system for x: 4.098078528040323x + 1y = 10 2x + 4y = 12 FINAL:
1.945483
1.945483
linear_system
2
sinusoid
0.5
1
0
19
4.095694
Solve this system for x: 4.095694033573221x + 1y = 10 2x + 4y = 12 FINAL:
1.946773
1.946773
linear_system
2
sinusoid
0.5
1
0
20
4.092388
Solve this system for x: 4.092387953251128x + 1y = 10 2x + 4y = 12 FINAL:
1.948565
1.948565
linear_system
2
sinusoid
0.5
1
0
21
4.088192
Solve this system for x: 4.088192126434835x + 1y = 10 2x + 4y = 12 FINAL:
1.950843
1.950843
linear_system
2
sinusoid
0.5
1
0
22
4.083147
Solve this system for x: 4.083146961230255x + 1y = 10 2x + 4y = 12 FINAL:
1.95359
1.95359
linear_system
2
sinusoid
0.5
1
0
23
4.077301
Solve this system for x: 4.077301045336274x + 1y = 10 2x + 4y = 12 FINAL:
1.956782
1.956782
linear_system
2
sinusoid
0.5
1
0
24
4.070711
Solve this system for x: 4.070710678118655x + 1y = 10 2x + 4y = 12 FINAL:
1.960394
1.960394
linear_system
2
sinusoid
0.5
1
0
25
4.063439
Solve this system for x: 4.063439328416364x + 1y = 10 2x + 4y = 12 FINAL:
1.964394
1.964394
linear_system
2
sinusoid
0.5
1
0
26
4.055557
Solve this system for x: 4.05555702330196x + 1y = 10 2x + 4y = 12 FINAL:
1.968749
1.968749
linear_system
2
sinusoid
0.5
1
0
27
4.04714
Solve this system for x: 4.0471396736826x + 1y = 10 2x + 4y = 12 FINAL:
1.973421
1.973421
linear_system
2
sinusoid
0.5
1
0
28
4.038268
Solve this system for x: 4.038268343236509x + 1y = 10 2x + 4y = 12 FINAL:
1.978369
1.978369
linear_system
2
sinusoid
0.5
1
0
29
4.029028
Solve this system for x: 4.029028467725446x + 1y = 10 2x + 4y = 12 FINAL:
1.983549
1.983549
linear_system
2
sinusoid
0.5
1
0
30
4.019509
Solve this system for x: 4.019509032201613x + 1y = 10 2x + 4y = 12 FINAL:
1.988914
1.988914
linear_system
2
sinusoid
0.5
1
0
31
4.009802
Solve this system for x: 4.009801714032956x + 1y = 10 2x + 4y = 12 FINAL:
1.994415
1.994415
linear_system
2
sinusoid
0.5
1
0
32
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
0.5
1
0
33
3.990198
Solve this system for x: 3.9901982859670437x + 1y = 10 2x + 4y = 12 FINAL:
2.005617
2.005617
linear_system
2
sinusoid
0.5
1
0
34
3.980491
Solve this system for x: 3.9804909677983873x + 1y = 10 2x + 4y = 12 FINAL:
2.011211
2.011211
linear_system
2
sinusoid
0.5
1
0
35
3.970972
Solve this system for x: 3.970971532274554x + 1y = 10 2x + 4y = 12 FINAL:
2.016726
2.016726
linear_system
2
sinusoid
0.5
1
0
36
3.961732
Solve this system for x: 3.961731656763491x + 1y = 10 2x + 4y = 12 FINAL:
2.022109
2.022109
linear_system
2
sinusoid
0.5
1
0
37
3.95286
Solve this system for x: 3.9528603263174x + 1y = 10 2x + 4y = 12 FINAL:
2.027305
2.027305
linear_system
2
sinusoid
0.5
1
0
38
3.944443
Solve this system for x: 3.94444297669804x + 1y = 10 2x + 4y = 12 FINAL:
2.032259
2.032259
linear_system
2
sinusoid
0.5
1
0
39
3.936561
Solve this system for x: 3.9365606715836354x + 1y = 10 2x + 4y = 12 FINAL:
2.03692
2.03692
linear_system
2
sinusoid
0.5
1
0
40
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 10 2x + 4y = 12 FINAL:
2.041239
2.041239
linear_system
2
sinusoid
0.5
1
0
41
3.922699
Solve this system for x: 3.9226989546637263x + 1y = 10 2x + 4y = 12 FINAL:
2.04517
2.04517
linear_system
2
sinusoid
0.5
1
0
42
3.916853
Solve this system for x: 3.9168530387697453x + 1y = 10 2x + 4y = 12 FINAL:
2.048669
2.048669
linear_system
2
sinusoid
0.5
1
0
43
3.911808
Solve this system for x: 3.9118078735651647x + 1y = 10 2x + 4y = 12 FINAL:
2.051698
2.051698
linear_system
2
sinusoid
0.5
1
0
44
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 10 2x + 4y = 12 FINAL:
2.054224
2.054224
linear_system
2
sinusoid
0.5
1
0
45
3.904306
Solve this system for x: 3.904305966426779x + 1y = 10 2x + 4y = 12 FINAL:
2.056219
2.056219
linear_system
2
sinusoid
0.5
1
0
46
3.901921
Solve this system for x: 3.901921471959677x + 1y = 10 2x + 4y = 12 FINAL:
2.057661
2.057661
linear_system
2
sinusoid
0.5
1
0
47
3.900482
Solve this system for x: 3.90048152733278x + 1y = 10 2x + 4y = 12 FINAL:
2.058532
2.058532
linear_system
2
sinusoid
0.5
1
0
48
3.9
Solve this system for x: 3.9x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
0.5
1
0
49
3.900482
Solve this system for x: 3.90048152733278x + 1y = 10 2x + 4y = 12 FINAL:
2.058532
2.058532
linear_system
2
sinusoid
0.5
1
0
50
3.901921
Solve this system for x: 3.901921471959677x + 1y = 10 2x + 4y = 12 FINAL:
2.057661
2.057661
linear_system
2
sinusoid
0.5
1
0
51
3.904306
Solve this system for x: 3.904305966426779x + 1y = 10 2x + 4y = 12 FINAL:
2.056219
2.056219
linear_system
2
sinusoid
0.5
1
0
52
3.907612
Solve this system for x: 3.9076120467488713x + 1y = 10 2x + 4y = 12 FINAL:
2.054224
2.054224
linear_system
2
sinusoid
0.5
1
0
53
3.911808
Solve this system for x: 3.9118078735651647x + 1y = 10 2x + 4y = 12 FINAL:
2.051698
2.051698
linear_system
2
sinusoid
0.5
1
0
54
3.916853
Solve this system for x: 3.9168530387697453x + 1y = 10 2x + 4y = 12 FINAL:
2.048669
2.048669
linear_system
2
sinusoid
0.5
1
0
55
3.922699
Solve this system for x: 3.9226989546637263x + 1y = 10 2x + 4y = 12 FINAL:
2.04517
2.04517
linear_system
2
sinusoid
0.5
1
0
56
3.929289
Solve this system for x: 3.9292893218813454x + 1y = 10 2x + 4y = 12 FINAL:
2.041239
2.041239
linear_system
2
sinusoid
0.5
1
0
57
3.936561
Solve this system for x: 3.9365606715836354x + 1y = 10 2x + 4y = 12 FINAL:
2.03692
2.03692
linear_system
2
sinusoid
0.5
1
0
58
3.944443
Solve this system for x: 3.94444297669804x + 1y = 10 2x + 4y = 12 FINAL:
2.032259
2.032259
linear_system
2
sinusoid
0.5
1
0
59
3.95286
Solve this system for x: 3.9528603263174x + 1y = 10 2x + 4y = 12 FINAL:
2.027305
2.027305
linear_system
2
sinusoid
0.5
1
0
60
3.961732
Solve this system for x: 3.961731656763491x + 1y = 10 2x + 4y = 12 FINAL:
2.022109
2.022109
linear_system
2
sinusoid
0.5
1
0
61
3.970972
Solve this system for x: 3.970971532274554x + 1y = 10 2x + 4y = 12 FINAL:
2.016726
2.016726
linear_system
2
sinusoid
0.5
1
0
62
3.980491
Solve this system for x: 3.9804909677983873x + 1y = 10 2x + 4y = 12 FINAL:
2.011211
2.011211
linear_system
2
sinusoid
0.5
1
0
63
3.990198
Solve this system for x: 3.9901982859670437x + 1y = 10 2x + 4y = 12 FINAL:
2.005617
2.005617
linear_system
2
sinusoid
0.5
2
0
0
4
Solve this system for x: 4.0x + 1y = 10 2x + 4y = 12 FINAL:
2
2
linear_system
2
sinusoid
0.5
2
0
1
4.019509
Solve this system for x: 4.019509032201613x + 1y = 10 2x + 4y = 12 FINAL:
1.988914
1.988914
linear_system
2
sinusoid
0.5
2
0
2
4.038268
Solve this system for x: 4.038268343236509x + 1y = 10 2x + 4y = 12 FINAL:
1.978369
1.978369
linear_system
2
sinusoid
0.5
2
0
3
4.055557
Solve this system for x: 4.05555702330196x + 1y = 10 2x + 4y = 12 FINAL:
1.968749
1.968749
linear_system
2
sinusoid
0.5
2
0
4
4.070711
Solve this system for x: 4.070710678118655x + 1y = 10 2x + 4y = 12 FINAL:
1.960394
1.960394
linear_system
2
sinusoid
0.5
2
0
5
4.083147
Solve this system for x: 4.083146961230255x + 1y = 10 2x + 4y = 12 FINAL:
1.95359
1.95359
linear_system
2
sinusoid
0.5
2
0
6
4.092388
Solve this system for x: 4.092387953251128x + 1y = 10 2x + 4y = 12 FINAL:
1.948565
1.948565
linear_system
2
sinusoid
0.5
2
0
7
4.098079
Solve this system for x: 4.098078528040323x + 1y = 10 2x + 4y = 12 FINAL:
1.945483
1.945483
linear_system
2
sinusoid
0.5
2
0
8
4.1
Solve this system for x: 4.1x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
0.5
2
0
9
4.098079
Solve this system for x: 4.098078528040323x + 1y = 10 2x + 4y = 12 FINAL:
1.945483
1.945483
linear_system
2
sinusoid
0.5
2
0
10
4.092388
Solve this system for x: 4.092387953251128x + 1y = 10 2x + 4y = 12 FINAL:
1.948565
1.948565
linear_system
2
sinusoid
0.5
2
0
11
4.083147
Solve this system for x: 4.083146961230255x + 1y = 10 2x + 4y = 12 FINAL:
1.95359
1.95359
linear_system
2
sinusoid
0.5
2
0
12
4.070711
Solve this system for x: 4.070710678118655x + 1y = 10 2x + 4y = 12 FINAL:
1.960394
1.960394
linear_system
2
sinusoid
0.5
2
0
13
4.055557
Solve this system for x: 4.05555702330196x + 1y = 10 2x + 4y = 12 FINAL:
1.968749
1.968749
linear_system
2
sinusoid
0.5
2
0
14
4.038268
Solve this system for x: 4.038268343236509x + 1y = 10 2x + 4y = 12 FINAL:
1.978369
1.978369
linear_system
2
sinusoid
0.5
2
0
15
4.019509
Solve this system for x: 4.019509032201613x + 1y = 10 2x + 4y = 12 FINAL:
1.988914
1.988914