Datasets:
ai-metrology-lab
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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
2
sinusoid
1
16
240
4
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
5
3.9
Solve this system for x: 3.9x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
6
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
7
4.1
Solve this system for x: 4.1x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
8
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
9
3.9
Solve this system for x: 3.9x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
10
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
11
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
12
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
13
3.9
Solve this system for x: 3.9x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
14
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
15
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
16
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
17
3.9
Solve this system for x: 3.9x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
18
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
19
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
20
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
21
3.9
Solve this system for x: 3.9000000000000004x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
22
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
23
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
24
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
25
3.9
Solve this system for x: 3.9000000000000004x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
26
4.173205
Solve this system for x: 4.173205080756889x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
27
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
28
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
29
3.9
Solve this system for x: 3.9000000000000004x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
30
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
31
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
32
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
33
3.9
Solve this system for x: 3.9000000000000004x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
34
4.173205
Solve this system for x: 4.173205080756889x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
35
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
36
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
37
3.9
Solve this system for x: 3.9000000000000004x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
38
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
39
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
40
3.826795
Solve this system for x: 3.826794919243113x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
41
3.9
Solve this system for x: 3.8999999999999977x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
42
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
43
4.1
Solve this system for x: 4.100000000000001x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
44
3.826795
Solve this system for x: 3.8267949192431137x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
45
3.9
Solve this system for x: 3.899999999999999x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
46
4.173205
Solve this system for x: 4.173205080756887x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
47
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
48
3.826795
Solve this system for x: 3.826794919243113x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
49
3.9
Solve this system for x: 3.8999999999999977x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
50
4.173205
Solve this system for x: 4.173205080756888x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
51
4.1
Solve this system for x: 4.100000000000001x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
52
3.826795
Solve this system for x: 3.8267949192431123x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
53
3.9
Solve this system for x: 3.899999999999999x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
54
4.173205
Solve this system for x: 4.173205080756887x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
55
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
56
3.826795
Solve this system for x: 3.826794919243113x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
57
3.9
Solve this system for x: 3.8999999999999977x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
58
4.173205
Solve this system for x: 4.173205080756887x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
59
4.1
Solve this system for x: 4.100000000000001x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
2
sinusoid
1
16
240
60
3.826795
Solve this system for x: 3.8267949192431137x + 1y = 10 2x + 4y = 12 FINAL:
2.104127
2.104127
linear_system
2
sinusoid
1
16
240
61
3.9
Solve this system for x: 3.8999999999999986x + 1y = 10 2x + 4y = 12 FINAL:
2.058824
2.058824
linear_system
2
sinusoid
1
16
240
62
4.173205
Solve this system for x: 4.173205080756887x + 1y = 10 2x + 4y = 12 FINAL:
1.905693
1.905693
linear_system
2
sinusoid
1
16
240
63
4.1
Solve this system for x: 4.1000000000000005x + 1y = 10 2x + 4y = 12 FINAL:
1.944444
1.944444
linear_system
0
sinusoid
2.5
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
2.5
1
0
1
4.049009
Solve this system for x: 4.04900857016478x + 1y = 7 1x + 5y = 11 FINAL:
1.247074
1.247074
linear_system
0
sinusoid
2.5
1
0
2
4.097545
Solve this system for x: 4.097545161008064x + 1y = 7 1x + 5y = 11 FINAL:
1.231544
1.231544
linear_system
0
sinusoid
2.5
1
0
3
4.145142
Solve this system for x: 4.145142338627231x + 1y = 7 1x + 5y = 11 FINAL:
1.216686
1.216686
linear_system
0
sinusoid
2.5
1
0
4
4.191342
Solve this system for x: 4.191341716182545x + 1y = 7 1x + 5y = 11 FINAL:
1.202603
1.202603
linear_system
0
sinusoid
2.5
1
0
5
4.235698
Solve this system for x: 4.235698368412999x + 1y = 7 1x + 5y = 11 FINAL:
1.189385
1.189385
linear_system
0
sinusoid
2.5
1
0
6
4.277785
Solve this system for x: 4.277785116509801x + 1y = 7 1x + 5y = 11 FINAL:
1.17711
1.17711
linear_system
0
sinusoid
2.5
1
0
7
4.317197
Solve this system for x: 4.317196642081822x + 1y = 7 1x + 5y = 11 FINAL:
1.165842
1.165842
linear_system
0
sinusoid
2.5
1
0
8
4.353553
Solve this system for x: 4.353553390593274x + 1y = 7 1x + 5y = 11 FINAL:
1.155637
1.155637
linear_system
0
sinusoid
2.5
1
0
9
4.386505
Solve this system for x: 4.386505226681368x + 1y = 7 1x + 5y = 11 FINAL:
1.146541
1.146541
linear_system
0
sinusoid
2.5
1
0
10
4.415735
Solve this system for x: 4.4157348061512725x + 1y = 7 1x + 5y = 11 FINAL:
1.138592
1.138592
linear_system
0
sinusoid
2.5
1
0
11
4.440961
Solve this system for x: 4.4409606321741775x + 1y = 7 1x + 5y = 11 FINAL:
1.131819
1.131819
linear_system
0
sinusoid
2.5
1
0
12
4.46194
Solve this system for x: 4.461939766255643x + 1y = 7 1x + 5y = 11 FINAL:
1.126248
1.126248
linear_system
0
sinusoid
2.5
1
0
13
4.47847
Solve this system for x: 4.478470167866105x + 1y = 7 1x + 5y = 11 FINAL:
1.121896
1.121896
linear_system
0
sinusoid
2.5
1
0
14
4.490393
Solve this system for x: 4.490392640201615x + 1y = 7 1x + 5y = 11 FINAL:
1.118779
1.118779
linear_system
0
sinusoid
2.5
1
0
15
4.497592
Solve this system for x: 4.497592363336098x + 1y = 7 1x + 5y = 11 FINAL:
1.116904
1.116904
linear_system
0
sinusoid
2.5
1
0
16
4.5
Solve this system for x: 4.5x + 1y = 7 1x + 5y = 11 FINAL:
1.116279
1.116279
linear_system
0
sinusoid
2.5
1
0
17
4.497592
Solve this system for x: 4.497592363336098x + 1y = 7 1x + 5y = 11 FINAL:
1.116904
1.116904
linear_system
0
sinusoid
2.5
1
0
18
4.490393
Solve this system for x: 4.490392640201615x + 1y = 7 1x + 5y = 11 FINAL:
1.118779
1.118779
linear_system
0
sinusoid
2.5
1
0
19
4.47847
Solve this system for x: 4.478470167866105x + 1y = 7 1x + 5y = 11 FINAL:
1.121896
1.121896
linear_system
0
sinusoid
2.5
1
0
20
4.46194
Solve this system for x: 4.461939766255643x + 1y = 7 1x + 5y = 11 FINAL:
1.126248
1.126248
linear_system
0
sinusoid
2.5
1
0
21
4.440961
Solve this system for x: 4.4409606321741775x + 1y = 7 1x + 5y = 11 FINAL:
1.131819
1.131819
linear_system
0
sinusoid
2.5
1
0
22
4.415735
Solve this system for x: 4.4157348061512725x + 1y = 7 1x + 5y = 11 FINAL:
1.138592
1.138592
linear_system
0
sinusoid
2.5
1
0
23
4.386505
Solve this system for x: 4.386505226681368x + 1y = 7 1x + 5y = 11 FINAL:
1.146541
1.146541
linear_system
0
sinusoid
2.5
1
0
24
4.353553
Solve this system for x: 4.353553390593274x + 1y = 7 1x + 5y = 11 FINAL:
1.155637
1.155637
linear_system
0
sinusoid
2.5
1
0
25
4.317197
Solve this system for x: 4.317196642081822x + 1y = 7 1x + 5y = 11 FINAL:
1.165842
1.165842
linear_system
0
sinusoid
2.5
1
0
26
4.277785
Solve this system for x: 4.277785116509801x + 1y = 7 1x + 5y = 11 FINAL:
1.17711
1.17711
linear_system
0
sinusoid
2.5
1
0
27
4.235698
Solve this system for x: 4.235698368412999x + 1y = 7 1x + 5y = 11 FINAL:
1.189385
1.189385
linear_system
0
sinusoid
2.5
1
0
28
4.191342
Solve this system for x: 4.191341716182545x + 1y = 7 1x + 5y = 11 FINAL:
1.202603
1.202603
linear_system
0
sinusoid
2.5
1
0
29
4.145142
Solve this system for x: 4.145142338627231x + 1y = 7 1x + 5y = 11 FINAL:
1.216686
1.216686
linear_system
0
sinusoid
2.5
1
0
30
4.097545
Solve this system for x: 4.097545161008064x + 1y = 7 1x + 5y = 11 FINAL:
1.231544
1.231544
linear_system
0
sinusoid
2.5
1
0
31
4.049009
Solve this system for x: 4.04900857016478x + 1y = 7 1x + 5y = 11 FINAL:
1.247074
1.247074
linear_system
0
sinusoid
2.5
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
2.5
1
0
33
3.950991
Solve this system for x: 3.9509914298352196x + 1y = 7 1x + 5y = 11 FINAL:
1.279662
1.279662
linear_system
0
sinusoid
2.5
1
0
34
3.902455
Solve this system for x: 3.902454838991936x + 1y = 7 1x + 5y = 11 FINAL:
1.296437
1.296437
linear_system
0
sinusoid
2.5
1
0
35
3.854858
Solve this system for x: 3.854857661372769x + 1y = 7 1x + 5y = 11 FINAL:
1.313321
1.313321
linear_system
0
sinusoid
2.5
1
0
36
3.808658
Solve this system for x: 3.808658283817455x + 1y = 7 1x + 5y = 11 FINAL:
1.330134
1.330134
linear_system
0
sinusoid
2.5
1
0
37
3.764302
Solve this system for x: 3.764301631587001x + 1y = 7 1x + 5y = 11 FINAL:
1.346687
1.346687
linear_system
0
sinusoid
2.5
1
0
38
3.722215
Solve this system for x: 3.722214883490199x + 1y = 7 1x + 5y = 11 FINAL:
1.362779
1.362779
linear_system
0
sinusoid
2.5
1
0
39
3.682803
Solve this system for x: 3.6828033579181776x + 1y = 7 1x + 5y = 11 FINAL:
1.3782
1.3782