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
2
120
56
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
2
120
57
4.065935
Solve this system for x: 4.065934581510007x + 2y = 8 1x + 3y = 9 FINAL:
0.588362
0.588362
linear_system
1
sinusoid
0.5
2
120
58
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
2
120
59
4.089687
Solve this system for x: 4.089687274153269x + 2y = 8 1x + 3y = 9 FINAL:
0.584279
0.584279
linear_system
1
sinusoid
0.5
2
120
60
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
2
120
61
4.099786
Solve this system for x: 4.09978589232386x + 2y = 8 1x + 3y = 9 FINAL:
0.582561
0.582561
linear_system
1
sinusoid
0.5
2
120
62
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
2
120
63
4.094693
Solve this system for x: 4.09469301294951x + 2y = 8 1x + 3y = 9 FINAL:
0.583426
0.583426
linear_system
1
sinusoid
0.5
4
120
0
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
120
1
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
120
2
4.025882
Solve this system for x: 4.0258819045102525x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
120
3
3.986947
Solve this system for x: 3.9869473807779947x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
120
4
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
120
5
3.920665
Solve this system for x: 3.9206646659708766x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
120
6
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
120
7
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
120
8
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
4
120
9
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
4
120
10
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
120
11
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
120
12
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
4
120
13
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
120
14
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
120
15
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
4
120
16
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
120
17
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
120
18
4.025882
Solve this system for x: 4.0258819045102525x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
120
19
3.986947
Solve this system for x: 3.986947380777995x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
120
20
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
120
21
3.920665
Solve this system for x: 3.9206646659708766x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
120
22
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
120
23
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
120
24
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
4
120
25
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
4
120
26
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
120
27
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
120
28
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
4
120
29
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
120
30
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
120
31
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
4
120
32
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
120
33
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
120
34
4.025882
Solve this system for x: 4.0258819045102525x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
120
35
3.986947
Solve this system for x: 3.986947380777995x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
120
36
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
120
37
3.920665
Solve this system for x: 3.9206646659708766x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
120
38
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
120
39
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
120
40
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
4
120
41
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
4
120
42
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
120
43
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
120
44
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
4
120
45
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
120
46
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
120
47
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
4
120
48
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
4
120
49
4.060876
Solve this system for x: 4.060876142900872x + 2y = 8 1x + 3y = 9 FINAL:
0.589239
0.589239
linear_system
1
sinusoid
0.5
4
120
50
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
4
120
51
3.986947
Solve this system for x: 3.9869473807779947x + 2y = 8 1x + 3y = 9 FINAL:
0.602359
0.602359
linear_system
1
sinusoid
0.5
4
120
52
3.95
Solve this system for x: 3.9499999999999997x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
4
120
53
3.920665
Solve this system for x: 3.9206646659708766x + 2y = 8 1x + 3y = 9 FINAL:
0.614629
0.614629
linear_system
1
sinusoid
0.5
4
120
54
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
4
120
55
3.900856
Solve this system for x: 3.900855513862619x + 2y = 8 1x + 3y = 9 FINAL:
0.618393
0.618393
linear_system
1
sinusoid
0.5
4
120
56
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
4
120
57
3.939124
Solve this system for x: 3.939123857099128x + 2y = 8 1x + 3y = 9 FINAL:
0.611162
0.611162
linear_system
1
sinusoid
0.5
4
120
58
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
4
120
59
4.013053
Solve this system for x: 4.013052619222005x + 2y = 8 1x + 3y = 9 FINAL:
0.59766
0.59766
linear_system
1
sinusoid
0.5
4
120
60
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
4
120
61
4.079335
Solve this system for x: 4.079335334029124x + 2y = 8 1x + 3y = 9 FINAL:
0.586052
0.586052
linear_system
1
sinusoid
0.5
4
120
62
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
4
120
63
4.099144
Solve this system for x: 4.099144486137381x + 2y = 8 1x + 3y = 9 FINAL:
0.582669
0.582669
linear_system
1
sinusoid
0.5
8
120
0
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
8
120
1
4.025882
Solve this system for x: 4.0258819045102525x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
8
120
2
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
8
120
3
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
8
120
4
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
8
120
5
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
8
120
6
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
8
120
7
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
8
120
8
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
8
120
9
4.025882
Solve this system for x: 4.0258819045102525x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
8
120
10
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
8
120
11
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
8
120
12
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
8
120
13
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
8
120
14
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
8
120
15
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
8
120
16
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
8
120
17
4.025882
Solve this system for x: 4.0258819045102525x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
8
120
18
3.95
Solve this system for x: 3.95x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
8
120
19
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906
linear_system
1
sinusoid
0.5
8
120
20
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
8
120
21
3.974118
Solve this system for x: 3.974118095489748x + 2y = 8 1x + 3y = 9 FINAL:
0.604695
0.604695
linear_system
1
sinusoid
0.5
8
120
22
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
8
120
23
4.096593
Solve this system for x: 4.096592582628907x + 2y = 8 1x + 3y = 9 FINAL:
0.583103
0.583103
linear_system
1
sinusoid
0.5
8
120
24
4.086603
Solve this system for x: 4.086602540378444x + 2y = 8 1x + 3y = 9 FINAL:
0.584806
0.584806
linear_system
1
sinusoid
0.5
8
120
25
4.025882
Solve this system for x: 4.025881904510252x + 2y = 8 1x + 3y = 9 FINAL:
0.595377
0.595377
linear_system
1
sinusoid
0.5
8
120
26
3.95
Solve this system for x: 3.9499999999999997x + 2y = 8 1x + 3y = 9 FINAL:
0.609137
0.609137
linear_system
1
sinusoid
0.5
8
120
27
3.903407
Solve this system for x: 3.9034074173710933x + 2y = 8 1x + 3y = 9 FINAL:
0.617906
0.617906