id
stringlengths
26
26
index
int64
1
200
difficulty
stringclasses
1 value
eq1_id
int64
24
3.36k
eq2_id
int64
8
4.69k
equation1
stringclasses
26 values
equation2
stringlengths
15
27
answer
bool
2 classes
evaluation_extra_hard_0001
1
extra_hard
1,487
449
x = (y * x) * (x * (z * w))
x = x * (y * (z * (x * w)))
false
evaluation_extra_hard_0002
2
extra_hard
336
3,690
x * y = y * (y * y)
x * x = (y * y) * (z * x)
true
evaluation_extra_hard_0003
3
extra_hard
1,487
638
x = (y * x) * (x * (z * w))
x = x * (y * ((x * z) * w))
false
evaluation_extra_hard_0004
4
extra_hard
336
3,334
x * y = y * (y * y)
x * y = x * (z * (z * y))
true
evaluation_extra_hard_0005
5
extra_hard
1,487
652
x = (y * x) * (x * (z * w))
x = x * (y * ((z * x) * w))
false
evaluation_extra_hard_0006
6
extra_hard
3,356
3,363
x * y = y * (y * (y * y))
x * y = y * (z * (x * y))
true
evaluation_extra_hard_0007
7
extra_hard
1,487
661
x = (y * x) * (x * (z * w))
x = x * (y * ((z * w) * x))
false
evaluation_extra_hard_0008
8
extra_hard
332
4,358
x * y = y * (x * x)
x * (y * z) = x * (z * y)
true
evaluation_extra_hard_0009
9
extra_hard
1,487
675
x = (y * x) * (x * (z * w))
x = y * (x * ((x * z) * w))
false
evaluation_extra_hard_0010
10
extra_hard
382
4,136
x * y = (x * z) * z
x * y = ((x * y) * z) * w
true
evaluation_extra_hard_0011
11
extra_hard
1,487
752
x = (y * x) * (x * (z * w))
x = y * (z * ((x * w) * x))
false
evaluation_extra_hard_0012
12
extra_hard
336
3,499
x * y = y * (y * y)
x * x = y * ((z * z) * x)
true
evaluation_extra_hard_0013
13
extra_hard
1,487
855
x = (y * x) * (x * (z * w))
x = x * ((y * z) * (x * w))
false
evaluation_extra_hard_0014
14
extra_hard
3,356
4,035
x * y = y * (y * (y * y))
x * y = (z * (z * w)) * y
true
evaluation_extra_hard_0015
15
extra_hard
1,487
864
x = (y * x) * (x * (z * w))
x = x * ((y * z) * (w * x))
false
evaluation_extra_hard_0016
16
extra_hard
318
4,367
x * x = y * (z * x)
x * (y * z) = y * (w * z)
true
evaluation_extra_hard_0017
17
extra_hard
1,487
1,034
x = (y * x) * (x * (z * w))
x = x * ((x * (y * z)) * w)
false
evaluation_extra_hard_0018
18
extra_hard
339
3,654
x * y = y * (z * y)
x * y = z * ((w * u) * y)
true
evaluation_extra_hard_0019
19
extra_hard
1,487
1,044
x = (y * x) * (x * (z * w))
x = x * ((y * (x * z)) * w)
false
evaluation_extra_hard_0020
20
extra_hard
340
3,287
x * y = y * (z * z)
x * x = y * (y * (z * w))
true
evaluation_extra_hard_0021
21
extra_hard
1,487
1,058
x = (y * x) * (x * (z * w))
x = x * ((y * (z * x)) * w)
false
evaluation_extra_hard_0022
22
extra_hard
340
3,410
x * y = y * (z * z)
x * y = z * (y * (w * z))
true
evaluation_extra_hard_0023
23
extra_hard
1,487
1,067
x = (y * x) * (x * (z * w))
x = x * ((y * (z * w)) * x)
false
evaluation_extra_hard_0024
24
extra_hard
366
4,674
x * x = (y * x) * z
(x * y) * z = (x * z) * w
true
evaluation_extra_hard_0025
25
extra_hard
1,487
1,158
x = (y * x) * (x * (z * w))
x = y * ((z * (x * w)) * x)
false
evaluation_extra_hard_0026
26
extra_hard
368
4,341
x * x = (y * y) * y
x * (y * y) = x * (z * z)
true
evaluation_extra_hard_0027
27
extra_hard
1,487
1,237
x = (y * x) * (x * (z * w))
x = x * (((x * y) * z) * w)
false
evaluation_extra_hard_0028
28
extra_hard
382
3,730
x * y = (x * z) * z
x * y = (x * y) * (z * w)
true
evaluation_extra_hard_0029
29
extra_hard
1,487
1,247
x = (y * x) * (x * (z * w))
x = x * (((y * x) * z) * w)
false
evaluation_extra_hard_0030
30
extra_hard
382
4,150
x * y = (x * z) * z
x * y = ((x * z) * w) * y
true
evaluation_extra_hard_0031
31
extra_hard
1,487
1,261
x = (y * x) * (x * (z * w))
x = x * (((y * z) * x) * w)
false
evaluation_extra_hard_0032
32
extra_hard
387
4,358
x * y = (y * y) * x
x * (y * z) = x * (z * y)
true
evaluation_extra_hard_0033
33
extra_hard
1,487
1,270
x = (y * x) * (x * (z * w))
x = x * (((y * z) * w) * x)
false
evaluation_extra_hard_0034
34
extra_hard
387
4,544
x * y = (y * y) * x
x * (y * z) = (z * y) * x
true
evaluation_extra_hard_0035
35
extra_hard
1,487
1,307
x = (y * x) * (x * (z * w))
x = y * (((x * z) * w) * x)
false
evaluation_extra_hard_0036
36
extra_hard
387
4,677
x * y = (y * y) * x
(x * y) * z = (y * x) * z
true
evaluation_extra_hard_0037
37
extra_hard
1,487
1,464
x = (y * x) * (x * (z * w))
x = (x * y) * (z * (x * w))
false
evaluation_extra_hard_0038
38
extra_hard
3,327
3,332
x * y = x * (z * (x * z))
x * y = x * (z * (y * w))
true
evaluation_extra_hard_0039
39
extra_hard
1,487
1,473
x = (y * x) * (x * (z * w))
x = (x * y) * (z * (w * x))
false
evaluation_extra_hard_0040
40
extra_hard
322
3,260
x * y = x * (x * x)
x * x = x * (y * (x * z))
true
evaluation_extra_hard_0041
41
extra_hard
1,487
1,667
x = (y * x) * (x * (z * w))
x = (x * y) * ((z * x) * w)
false
evaluation_extra_hard_0042
42
extra_hard
322
3,263
x * y = x * (x * x)
x * x = x * (y * (y * z))
true
evaluation_extra_hard_0043
43
extra_hard
1,487
1,676
x = (y * x) * (x * (z * w))
x = (x * y) * ((z * w) * x)
false
evaluation_extra_hard_0044
44
extra_hard
322
3,264
x * y = x * (x * x)
x * x = x * (y * (z * x))
true
evaluation_extra_hard_0045
45
extra_hard
1,487
1,704
x = (y * x) * (x * (z * w))
x = (y * x) * ((z * x) * w)
false
evaluation_extra_hard_0046
46
extra_hard
322
3,463
x * y = x * (x * x)
x * x = x * ((y * x) * z)
true
evaluation_extra_hard_0047
47
extra_hard
1,487
1,713
x = (y * x) * (x * (z * w))
x = (y * x) * ((z * w) * x)
false
evaluation_extra_hard_0048
48
extra_hard
322
3,466
x * y = x * (x * x)
x * x = x * ((y * y) * z)
true
evaluation_extra_hard_0049
49
extra_hard
1,487
1,879
x = (y * x) * (x * (z * w))
x = (x * (y * z)) * (w * x)
false
evaluation_extra_hard_0050
50
extra_hard
322
3,467
x * y = x * (x * x)
x * x = x * ((y * z) * x)
true
evaluation_extra_hard_0051
51
extra_hard
1,487
1,961
x = (y * x) * (x * (z * w))
x = (y * (z * x)) * (x * w)
false
evaluation_extra_hard_0052
52
extra_hard
322
4,601
x * y = x * (x * x)
(x * x) * y = (x * z) * x
true
evaluation_extra_hard_0053
53
extra_hard
1,487
2,322
x = (y * x) * (x * (z * w))
x = (y * (x * (z * w))) * x
false
evaluation_extra_hard_0054
54
extra_hard
322
4,603
x * y = x * (x * x)
(x * x) * y = (x * z) * z
true
evaluation_extra_hard_0055
55
extra_hard
1,487
2,376
x = (y * x) * (x * (z * w))
x = (y * (z * (x * w))) * x
false
evaluation_extra_hard_0056
56
extra_hard
322
4,633
x * y = x * (x * x)
(x * y) * x = (x * z) * z
true
evaluation_extra_hard_0057
57
extra_hard
1,487
2,488
x = (y * x) * (x * (z * w))
x = (x * ((y * z) * w)) * x
false
evaluation_extra_hard_0058
58
extra_hard
336
391
x * y = y * (y * y)
x * y = (y * z) * y
true
evaluation_extra_hard_0059
59
extra_hard
1,487
2,618
x = (y * x) * (x * (z * w))
x = (y * ((z * w) * x)) * x
false
evaluation_extra_hard_0060
60
extra_hard
336
3,264
x * y = y * (y * y)
x * x = x * (y * (z * x))
true
evaluation_extra_hard_0061
61
extra_hard
1,487
2,894
x = (y * x) * (x * (z * w))
x = ((x * (y * z)) * w) * x
false
evaluation_extra_hard_0062
62
extra_hard
336
3,292
x * y = y * (y * y)
x * x = y * (z * (y * x))
true
evaluation_extra_hard_0063
63
extra_hard
1,487
2,931
x = (y * x) * (x * (z * w))
x = ((y * (x * z)) * w) * x
false
evaluation_extra_hard_0064
64
extra_hard
336
3,349
x * y = y * (y * y)
x * y = y * (x * (z * y))
true
evaluation_extra_hard_0065
65
extra_hard
1,487
3,024
x = (y * x) * (x * (z * w))
x = ((y * (z * w)) * x) * x
false
evaluation_extra_hard_0066
66
extra_hard
336
3,363
x * y = y * (y * y)
x * y = y * (z * (x * y))
true
evaluation_extra_hard_0067
67
extra_hard
1,487
3,097
x = (y * x) * (x * (z * w))
x = (((x * y) * z) * w) * x
false
evaluation_extra_hard_0068
68
extra_hard
336
3,367
x * y = y * (y * y)
x * y = y * (z * (y * y))
true
evaluation_extra_hard_0069
69
extra_hard
1,487
4,358
x = (y * x) * (x * (z * w))
x * (y * z) = x * (z * y)
false
evaluation_extra_hard_0070
70
extra_hard
336
3,397
x * y = y * (y * y)
x * y = z * (y * (x * y))
true
evaluation_extra_hard_0071
71
extra_hard
1,487
4,362
x = (y * x) * (x * (z * w))
x * (y * z) = y * (x * z)
false
evaluation_extra_hard_0072
72
extra_hard
336
3,467
x * y = y * (y * y)
x * x = x * ((y * z) * x)
true
evaluation_extra_hard_0073
73
extra_hard
1,487
4,364
x = (y * x) * (x * (z * w))
x * (y * z) = y * (z * x)
false
evaluation_extra_hard_0074
74
extra_hard
336
3,477
x * y = y * (y * y)
x * x = y * ((x * z) * x)
true
evaluation_extra_hard_0075
75
extra_hard
1,487
4,396
x = (y * x) * (x * (z * w))
x * (x * y) = (x * x) * y
false
evaluation_extra_hard_0076
76
extra_hard
336
3,487
x * y = y * (y * y)
x * x = y * ((y * z) * x)
true
evaluation_extra_hard_0077
77
extra_hard
1,487
4,398
x = (y * x) * (x * (z * w))
x * (x * y) = (x * y) * x
false
evaluation_extra_hard_0078
78
extra_hard
336
3,552
x * y = y * (y * y)
x * y = y * ((x * z) * y)
true
evaluation_extra_hard_0079
79
extra_hard
1,487
4,473
x = (y * x) * (x * (z * w))
x * (y * y) = (x * y) * y
false
evaluation_extra_hard_0080
80
extra_hard
336
3,566
x * y = y * (y * y)
x * y = y * ((z * x) * y)
true
evaluation_extra_hard_0081
81
extra_hard
1,487
4,515
x = (y * x) * (x * (z * w))
x * (y * z) = (x * z) * y
false
evaluation_extra_hard_0082
82
extra_hard
336
3,600
x * y = y * (y * y)
x * y = z * ((y * x) * y)
true
evaluation_extra_hard_0083
83
extra_hard
1,487
4,531
x = (y * x) * (x * (z * w))
x * (y * z) = (y * z) * x
false
evaluation_extra_hard_0084
84
extra_hard
336
3,608
x * y = y * (y * y)
x * y = z * ((y * z) * y)
true
evaluation_extra_hard_0085
85
extra_hard
1,487
4,541
x = (y * x) * (x * (z * w))
x * (y * z) = (z * x) * y
false
evaluation_extra_hard_0086
86
extra_hard
336
3,621
x * y = y * (y * y)
x * y = z * ((z * y) * y)
true
evaluation_extra_hard_0087
87
extra_hard
1,487
4,598
x = (y * x) * (x * (z * w))
(x * x) * y = (x * y) * x
false
evaluation_extra_hard_0088
88
extra_hard
336
3,629
x * y = y * (y * y)
x * y = z * ((z * w) * y)
true
evaluation_extra_hard_0089
89
extra_hard
1,487
4,673
x = (y * x) * (x * (z * w))
(x * y) * z = (x * z) * y
false
evaluation_extra_hard_0090
90
extra_hard
336
3,644
x * y = y * (y * y)
x * y = z * ((w * z) * y)
true
evaluation_extra_hard_0091
91
extra_hard
1,487
4,677
x = (y * x) * (x * (z * w))
(x * y) * z = (y * x) * z
false
evaluation_extra_hard_0092
92
extra_hard
336
3,670
x * y = y * (y * y)
x * x = (x * y) * (z * x)
true
evaluation_extra_hard_0093
93
extra_hard
1,487
4,679
x = (y * x) * (x * (z * w))
(x * y) * z = (y * z) * x
false
evaluation_extra_hard_0094
94
extra_hard
336
3,680
x * y = y * (y * y)
x * x = (y * x) * (z * x)
true
evaluation_extra_hard_0095
95
extra_hard
2,126
634
x = ((y * y) * x) * (x * z)
x = x * (y * ((x * y) * z))
false
evaluation_extra_hard_0096
96
extra_hard
336
3,694
x * y = y * (y * y)
x * x = (y * z) * (x * x)
true
evaluation_extra_hard_0097
97
extra_hard
2,126
641
x = ((y * y) * x) * (x * z)
x = x * (y * ((y * x) * z))
false
evaluation_extra_hard_0098
98
extra_hard
336
3,698
x * y = y * (y * y)
x * x = (y * z) * (y * x)
true
evaluation_extra_hard_0099
99
extra_hard
2,126
653
x = ((y * y) * x) * (x * z)
x = x * (y * ((z * y) * x))
false
evaluation_extra_hard_0100
100
extra_hard
336
3,702
x * y = y * (y * y)
x * x = (y * z) * (z * x)
true