Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55,
56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104,
105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 65, 66, 67, 68, 72, 73, 74, 75, 79, 80, 81, 82, 86, 87, 88, 89, 93, 94, 95, 96, 100, 101,
102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 123
}
B grade: { 2, 3, 4, 5, 6, 7, 107, 108 }
C grade: { 8, 13, 14, 62, 63, 64, 69, 70, 71, 76, 77, 78, 83, 84, 85, 90, 91, 92, 97, 98, 99, 121
}
F grade: { }
2.1.3 Maple
A grade: { 1, 8, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
60, 61, 65, 66, 67, 68, 72, 73, 74, 75, 79, 80, 81, 82, 86, 87, 88, 89, 93, 96, 111, 120, 122, 123
}
B grade: { 2, 3, 4, 5, 6, 7, 14, 62, 63, 64, 69, 70, 71, 76, 77, 78, 83, 84, 85, 90, 91, 92, 94, 95, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 121
}
C grade: { 11 }
F grade: { 9, 10 }
2.1.4 Maxima
A grade: { 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 65, 66, 67, 68, 72, 73, 74, 75,
79, 80, 81, 82, 86, 87, 88, 89, 96
B grade: { 93, 94, 95 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 62, 63, 64, 69, 70, 71, 76, 77, 78, 83, 84, 85, 90, 91, 92,
97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118,
119, 120, 121, 122, 123 }
2.1.5 FriCAS
A grade: { 1, 8, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 65, 66,
67, 68, 72, 73, 74, 75, 79, 80, 81, 82, 86, 87, 88, 93, 94, 96, 100, 101, 105, 109, 110, 111, 119
}
B grade: { 2, 3, 4, 5, 7, 62, 63, 64, 69, 70, 71, 76, 77, 78, 83, 84, 85, 89, 90, 91, 92, 95, 97, 98, 99, 104, 112,
114, 115, 116, 118, 120, 121 }
C grade: { }
F grade: { 6, 9, 10, 13, 102, 103, 106, 107, 108, 113, 117, 122, 123 }
2.1.6 Sympy
A grade: { 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122,
123 }
2.1.7 Giac
A grade: { 1, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 65, 66, 67, 68, 72, 73,
74, 75, 79, 80, 81, 82, 86, 87, 88, 89, 93, 94, 95, 96, 100, 101, 105, 109, 110, 111, 114, 115, 116, 118, 119
}
B grade: { 3, 8, 12, 14, 104, 120, 121 }
C grade: { }
F grade: { 2, 4, 5, 6, 7, 9, 10, 13, 62, 63, 64, 69, 70, 71, 76, 77, 78, 83, 84, 85, 90, 91, 92, 97, 98, 99, 102,
103, 106, 107, 108, 112, 113, 117, 122, 123 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 87 | 136 | 0 | 494 | 0 | 113 |
normalized size |
1 |
1. |
0.85 |
1.33 |
0. |
4.84 |
0. |
1.11 |
time (sec) |
N/A |
0.094 |
0.191 |
0.052 |
0. |
1.157 |
0. |
1.302 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F(-2) |
B |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 178 | 491 | 0 | 2226 | 0 | 0 |
normalized size |
1 |
1. |
2.17 |
5.99 |
0. |
27.15 |
0. |
0. |
time (sec) |
N/A |
0.111 |
0.388 |
0.388 |
0. |
2.14 |
0. |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F(-2) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 161 | 307 | 0 | 1755 | 0 | 620 |
normalized size |
1 |
1. |
2.44 |
4.65 |
0. |
26.59 |
0. |
9.39 |
time (sec) |
N/A |
0.079 |
0.226 |
0.327 |
0. |
1.458 |
0. |
14.668 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 296 | 829 | 0 | 3297 | 0 | 0 |
normalized size |
1 |
1. |
2.29 |
6.43 |
0. |
25.56 |
0. |
0. |
time (sec) |
N/A |
0.169 |
0.91 |
0.301 |
0. |
3.384 |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F |
B |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 1748 | 1884 | 0 | 8058 | 0 | 0 |
normalized size |
1 |
1. |
7.8 |
8.41 |
0. |
35.97 |
0. |
0. |
time (sec) |
N/A |
0.427 |
6.376 |
0.242 |
0. |
19.058 |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 3386 | 3695 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
10.32 |
11.27 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.97 |
6.58 |
0.259 |
0. |
0. |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 490 | 1377 | 0 | 4059 | 0 | 0 |
normalized size |
1 |
1. |
3.02 |
8.5 |
0. |
25.06 |
0. |
0. |
time (sec) |
N/A |
0.306 |
2.127 |
0.352 |
0. |
8.127 |
0. |
0. |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
F |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 84 | 27 | 0 | 123 | 0 | 70 |
normalized size | 1 | 1. | 3. | 0.96 | 0. | 4.39 | 0. | 2.5 |
time (sec) |
N/A |
0.017 |
0.068 |
0.048 |
0. |
1.034 |
0. |
1.142 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 142 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.103 |
0.138 |
2.905 |
0. |
0. |
0. |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 172 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.134 |
0.238 |
3.482 |
0. |
0. |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 27 | 16 | 0 | 55 | 0 | 66 |
normalized size | 1 | 1. | 0.56 | 0.33 | 0. | 1.15 | 0. | 1.38 |
time (sec) |
N/A |
0.015 |
0.018 |
0.168 |
0. |
0.866 |
0. |
1.182 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 66 | 84 | 0 | 235 | 0 | 193 |
normalized size | 1 | 1. | 0.94 | 1.2 | 0. | 3.36 | 0. | 2.76 |
time (sec) |
N/A |
0.051 |
0.083 |
0.059 |
0. |
0.808 |
0. |
1.168 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1077 | 1077 | 600 | 661 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.56 | 0.61 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.099 |
1.528 |
0.618 |
0. |
0. |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 159 | 341 | 0 | 441 | 0 | 231 |
normalized size | 1 | 1. | 1.62 | 3.48 | 0. | 4.5 | 0. | 2.36 |
time (sec) |
N/A |
0.21 |
0.401 |
0.112 |
0. |
0.975 |
0. |
1.177 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 68 | 55 | 73 | 176 | 65 | 73 |
normalized size | 1 | 1. | 1. | 0.81 | 1.07 | 2.59 | 0.96 | 1.07 |
time (sec) |
N/A |
0.049 |
0.003 |
0.044 |
0.972 |
0.847 |
0.084 |
1.154 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 56 | 45 | 59 | 131 | 53 | 59 |
normalized size | 1 | 1. | 1. | 0.8 | 1.05 | 2.34 | 0.95 | 1.05 |
time (sec) |
N/A |
0.038 |
0.002 |
0.044 |
0.983 |
0.717 |
0.084 |
1.175 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 44 | 35 | 46 | 96 | 41 | 46 |
normalized size | 1 | 1. | 1. | 0.8 | 1.05 | 2.18 | 0.93 | 1.05 |
time (sec) |
N/A |
0.029 |
0.001 |
0.042 |
0.961 |
0.712 |
0.079 |
1.185 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 25 | 32 | 59 | 26 | 32 |
normalized size | 1 | 1. | 1. | 0.83 | 1.07 | 1.97 | 0.87 | 1.07 |
time (sec) |
N/A |
0.016 |
0.001 |
0.043 |
0.993 |
0.711 |
0.063 |
1.174 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 34 | 45 | 119 | 49 | 45 |
normalized size | 1 | 1. | 1. | 0.81 | 1.07 | 2.83 | 1.17 | 1.07 |
time (sec) |
N/A |
0.04 |
0.015 |
0.049 |
1.484 |
0.834 |
0.154 |
1.168 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 43 | 34 | 49 | 146 | 42 | 49 |
normalized size | 1 | 1. | 1. | 0.79 | 1.14 | 3.4 | 0.98 | 1.14 |
time (sec) |
N/A |
0.027 |
0.015 |
0.046 |
1.466 |
0.851 |
0.213 |
1.223 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 53 | 47 | 76 | 242 | 63 | 62 |
normalized size | 1 | 1. | 0.83 | 0.73 | 1.19 | 3.78 | 0.98 | 0.97 |
time (sec) |
N/A |
0.037 |
0.025 |
0.044 |
1.472 |
0.801 |
0.281 |
1.251 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 80 | 65 | 86 | 221 | 76 | 86 |
normalized size | 1 | 1. | 1. | 0.81 | 1.08 | 2.76 | 0.95 | 1.08 |
time (sec) |
N/A |
0.06 |
0.003 |
0.043 |
0.957 |
0.622 |
0.133 |
1.199 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 66 | 55 | 73 | 167 | 63 | 73 |
normalized size | 1 | 1. | 1. | 0.83 | 1.11 | 2.53 | 0.95 | 1.11 |
time (sec) |
N/A |
0.048 |
0.002 |
0.042 |
0.964 |
0.734 |
0.137 |
1.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 59 | 122 | 51 | 59 |
normalized size | 1 | 1. | 1. | 0.83 | 1.09 | 2.26 | 0.94 | 1.09 |
time (sec) |
N/A |
0.042 |
0.002 |
0.044 |
0.967 |
0.904 |
0.108 |
1.195 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 46 | 35 | 46 | 95 | 41 | 46 |
normalized size | 1 | 1. | 1. | 0.76 | 1. | 2.07 | 0.89 | 1. |
time (sec) |
N/A |
0.03 |
0.001 |
0.045 |
0.964 |
0.829 |
0.097 |
1.171 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 53 | 44 | 58 | 165 | 63 | 58 |
normalized size | 1 | 1. | 0.95 | 0.79 | 1.04 | 2.95 | 1.12 | 1.04 |
time (sec) |
N/A |
0.051 |
0.019 |
0.044 |
1.488 |
0.993 |
0.189 |
1.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 59 | 51 | 70 | 252 | 65 | 70 |
normalized size | 1 | 1. | 0.94 | 0.81 | 1.11 | 4. | 1.03 | 1.11 |
time (sec) |
N/A |
0.061 |
0.031 |
0.046 |
1.46 |
0.998 |
0.214 |
1.185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 53 | 47 | 76 | 258 | 63 | 62 |
normalized size | 1 | 1. | 0.83 | 0.73 | 1.19 | 4.03 | 0.98 | 0.97 |
time (sec) |
N/A |
0.052 |
0.023 |
0.046 |
1.488 |
0.948 |
0.298 |
1.239 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 63 | 57 | 103 | 371 | 83 | 76 |
normalized size | 1 | 1. | 0.74 | 0.67 | 1.21 | 4.36 | 0.98 | 0.89 |
time (sec) |
N/A |
0.063 |
0.045 |
0.05 |
1.446 |
0.963 |
0.251 |
1.182 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 96 | 75 | 100 | 274 | 92 | 100 |
normalized size | 1 | 1. | 1. | 0.78 | 1.04 | 2.85 | 0.96 | 1.04 |
time (sec) |
N/A |
0.071 |
0.003 |
0.044 |
0.983 |
0.823 |
0.126 |
1.177 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 82 | 65 | 86 | 217 | 78 | 86 |
normalized size | 1 | 1. | 1. | 0.79 | 1.05 | 2.65 | 0.95 | 1.05 |
time (sec) |
N/A |
0.056 |
0.002 |
0.045 |
0.97 |
0.832 |
0.085 |
1.14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 68 | 55 | 73 | 166 | 65 | 73 |
normalized size | 1 | 1. | 1. | 0.81 | 1.07 | 2.44 | 0.96 | 1.07 |
time (sec) |
N/A |
0.051 |
0.002 |
0.043 |
0.957 |
0.85 |
0.086 |
1.194 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 56 | 45 | 59 | 122 | 53 | 59 |
normalized size | 1 | 1. | 1. | 0.8 | 1.05 | 2.18 | 0.95 | 1.05 |
time (sec) |
N/A |
0.032 |
0.001 |
0.043 |
0.967 |
0.882 |
0.108 |
1.204 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 63 | 54 | 72 | 219 | 76 | 72 |
normalized size | 1 | 1. | 0.9 | 0.77 | 1.03 | 3.13 | 1.09 | 1.03 |
time (sec) |
N/A |
0.053 |
0.022 |
0.046 |
1.466 |
0.991 |
0.149 |
1.187 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 77 | 61 | 84 | 321 | 78 | 84 |
normalized size | 1 | 1. | 1. | 0.79 | 1.09 | 4.17 | 1.01 | 1.09 |
time (sec) |
N/A |
0.072 |
0.027 |
0.046 |
1.479 |
1.03 |
0.172 |
1.208 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 78 | 63 | 97 | 406 | 85 | 84 |
normalized size | 1 | 1. | 0.93 | 0.75 | 1.15 | 4.83 | 1.01 | 1. |
time (sec) |
N/A |
0.087 |
0.037 |
0.048 |
1.442 |
1.012 |
0.216 |
1.212 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 72 | 64 | 85 | 252 | 87 | 85 |
normalized size | 1 | 1. | 0.86 | 0.76 | 1.01 | 3. | 1.04 | 1.01 |
time (sec) |
N/A |
0.057 |
0.027 |
0.046 |
1.435 |
0.975 |
0.156 |
1.25 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 63 | 54 | 72 | 196 | 73 | 72 |
normalized size | 1 | 1. | 0.9 | 0.77 | 1.03 | 2.8 | 1.04 | 1.03 |
time (sec) |
N/A |
0.056 |
0.021 |
0.047 |
1.472 |
0.935 |
0.144 |
1.167 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 52 | 44 | 58 | 147 | 60 | 58 |
normalized size | 1 | 1. | 0.93 | 0.79 | 1.04 | 2.62 | 1.07 | 1.04 |
time (sec) |
N/A |
0.05 |
0.017 |
0.049 |
1.44 |
0.994 |
0.197 |
1.126 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 34 | 45 | 112 | 46 | 45 |
normalized size | 1 | 1. | 1. | 0.81 | 1.07 | 2.67 | 1.1 | 1.07 |
time (sec) |
N/A |
0.035 |
0.01 |
0.044 |
1.431 |
1.051 |
0.124 |
1.198 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 73 | 60 | 80 | 207 | 83 | 80 |
normalized size | 1 | 1. | 1. | 0.82 | 1.1 | 2.84 | 1.14 | 1.1 |
time (sec) |
N/A |
0.053 |
0.031 |
0.048 |
1.427 |
1. |
0.268 |
1.265 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 94 | 77 | 105 | 377 | 102 | 105 |
normalized size | 1 | 1. | 1. | 0.82 | 1.12 | 4.01 | 1.09 | 1.12 |
time (sec) |
N/A |
0.089 |
0.078 |
0.049 |
1.483 |
0.985 |
0.298 |
1.223 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 104 | 89 | 132 | 578 | 119 | 119 |
normalized size | 1 | 1. | 0.9 | 0.77 | 1.15 | 5.03 | 1.03 | 1.03 |
time (sec) |
N/A |
0.124 |
0.144 |
0.049 |
1.439 |
1.027 |
0.4 |
1.26 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 91 | 71 | 97 | 348 | 88 | 97 |
normalized size | 1 | 1. | 1. | 0.78 | 1.07 | 3.82 | 0.97 | 1.07 |
time (sec) |
N/A |
0.086 |
0.05 |
0.048 |
1.425 |
0.974 |
0.245 |
1.154 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 77 | 61 | 84 | 292 | 75 | 84 |
normalized size | 1 | 1. | 1. | 0.79 | 1.09 | 3.79 | 0.97 | 1.09 |
time (sec) |
N/A |
0.073 |
0.027 |
0.047 |
1.435 |
1.033 |
0.254 |
1.183 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 63 | 51 | 70 | 234 | 61 | 70 |
normalized size | 1 | 1. | 1. | 0.81 | 1.11 | 3.71 | 0.97 | 1.11 |
time (sec) |
N/A |
0.063 |
0.03 |
0.045 |
1.424 |
1.026 |
0.171 |
1.19 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 43 | 34 | 49 | 138 | 41 | 49 |
normalized size | 1 | 1. | 1. | 0.79 | 1.14 | 3.21 | 0.95 | 1.14 |
time (sec) |
N/A |
0.026 |
0.014 |
0.047 |
1.432 |
0.988 |
0.206 |
1.139 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 94 | 77 | 105 | 363 | 102 | 105 |
normalized size | 1 | 1. | 1. | 0.82 | 1.12 | 3.86 | 1.09 | 1.12 |
time (sec) |
N/A |
0.088 |
0.055 |
0.049 |
1.445 |
1.002 |
0.307 |
1.133 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 106 | 94 | 130 | 548 | 122 | 130 |
normalized size | 1 | 1. | 0.83 | 0.74 | 1.02 | 4.31 | 0.96 | 1.02 |
time (sec) |
N/A |
0.123 |
0.058 |
0.052 |
1.447 |
0.991 |
0.449 |
1.185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 136 | 106 | 159 | 802 | 143 | 149 |
normalized size | 1 | 1. | 0.92 | 0.72 | 1.07 | 5.42 | 0.97 | 1.01 |
time (sec) |
N/A |
0.161 |
0.064 |
0.053 |
1.491 |
1.041 |
0.466 |
1.132 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 98 | 73 | 111 | 447 | 95 | 97 |
normalized size | 1 | 1. | 1. | 0.74 | 1.13 | 4.56 | 0.97 | 0.99 |
time (sec) |
N/A |
0.113 |
0.037 |
0.054 |
1.454 |
0.905 |
0.278 |
1.148 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 84 | 63 | 97 | 377 | 82 | 84 |
normalized size | 1 | 1. | 1. | 0.75 | 1.15 | 4.49 | 0.98 | 1. |
time (sec) |
N/A |
0.087 |
0.036 |
0.05 |
1.454 |
0.985 |
0.3 |
1.131 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 51 | 47 | 76 | 239 | 61 | 62 |
normalized size | 1 | 1. | 0.8 | 0.73 | 1.19 | 3.73 | 0.95 | 0.97 |
time (sec) |
N/A |
0.053 |
0.029 |
0.047 |
1.439 |
1.007 |
0.276 |
1.291 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 51 | 47 | 76 | 225 | 61 | 62 |
normalized size | 1 | 1. | 0.8 | 0.73 | 1.19 | 3.52 | 0.95 | 0.97 |
time (sec) |
N/A |
0.033 |
0.028 |
0.046 |
1.452 |
1.05 |
0.192 |
1.202 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 99 | 89 | 132 | 556 | 122 | 119 |
normalized size | 1 | 1. | 0.86 | 0.77 | 1.15 | 4.83 | 1.06 | 1.03 |
time (sec) |
N/A |
0.124 |
0.155 |
0.053 |
1.432 |
1.025 |
0.397 |
1.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 136 | 106 | 157 | 763 | 143 | 149 |
normalized size | 1 | 1. | 0.85 | 0.66 | 0.98 | 4.77 | 0.89 | 0.93 |
time (sec) |
N/A |
0.16 |
0.102 |
0.056 |
1.466 |
1.03 |
0.535 |
1.156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 181 | 181 | 151 | 118 | 186 | 1035 | 163 | 157 |
normalized size | 1 | 1. | 0.83 | 0.65 | 1.03 | 5.72 | 0.9 | 0.87 |
time (sec) |
N/A |
0.204 |
0.085 |
0.053 |
1.447 |
1.172 |
0.539 |
1.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 85 | 166 | 239 | 439 | 0 | 126 |
normalized size | 1 | 1. | 0.41 | 0.8 | 1.15 | 2.11 | 0. | 0.61 |
time (sec) |
N/A |
0.309 |
0.291 |
0.069 |
1.484 |
1.408 |
0. |
1.137 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 75 | 132 | 193 | 352 | 0 | 112 |
normalized size | 1 | 1. | 0.45 | 0.8 | 1.16 | 2.12 | 0. | 0.67 |
time (sec) |
N/A |
0.181 |
0.172 |
0.059 |
1.472 |
1.523 |
0. |
1.327 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 65 | 98 | 147 | 257 | 0 | 99 |
normalized size | 1 | 1. | 0.52 | 0.79 | 1.19 | 2.07 | 0. | 0.8 |
time (sec) |
N/A |
0.099 |
0.106 |
0.053 |
1.534 |
1.529 |
0. |
1.196 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 55 | 64 | 101 | 207 | 0 | 85 |
normalized size | 1 | 1. | 0.67 | 0.78 | 1.23 | 2.52 | 0. | 1.04 |
time (sec) |
N/A |
0.04 |
0.053 |
0.048 |
1.504 |
1.649 |
0. |
1.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 185 | 2065 | 0 | 7056 | 0 | 0 |
normalized size |
1 |
1. |
1.06 |
11.87 |
0. |
40.55 |
0. |
0. |
time (sec) |
N/A |
0.441 |
0.463 |
0.276 |
0. |
4.393 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 214 | 16357 | 0 | 8142 | 0 | 0 |
normalized size |
1 |
1. |
1.14 |
87.01 |
0. |
43.31 |
0. |
0. |
time (sec) |
N/A |
0.393 |
1.083 |
0.292 |
0. |
5.824 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 299 | 44343 | 0 | 10298 | 0 | 0 |
normalized size |
1 |
1. |
1.34 |
198.85 |
0. |
46.18 |
0. |
0. |
time (sec) |
N/A |
0.459 |
2.069 |
0.428 |
0. |
6.156 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 231 | 231 | 95 | 185 | 278 | 532 | 0 | 139 |
normalized size | 1 | 1. | 0.41 | 0.8 | 1.2 | 2.3 | 0. | 0.6 |
time (sec) |
N/A |
0.342 |
0.367 |
0.072 |
1.546 |
1.585 |
0. |
1.174 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 85 | 151 | 232 | 423 | 0 | 126 |
normalized size | 1 | 1. | 0.45 | 0.8 | 1.23 | 2.24 | 0. | 0.67 |
time (sec) |
N/A |
0.19 |
0.234 |
0.059 |
1.503 |
1.593 |
0. |
1.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 75 | 117 | 186 | 342 | 0 | 112 |
normalized size | 1 | 1. | 0.51 | 0.8 | 1.27 | 2.33 | 0. | 0.76 |
time (sec) |
N/A |
0.122 |
0.144 |
0.055 |
1.5 |
1.517 |
0. |
1.154 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 65 | 83 | 140 | 257 | 0 | 99 |
normalized size | 1 | 1. | 0.62 | 0.79 | 1.33 | 2.45 | 0. | 0.94 |
time (sec) |
N/A |
0.05 |
0.084 |
0.058 |
1.499 |
1.602 |
0. |
1.248 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 310 | 3460 | 0 | 7468 | 0 | 0 |
normalized size |
1 |
1. |
1.57 |
17.56 |
0. |
37.91 |
0. |
0. |
time (sec) |
N/A |
0.488 |
0.695 |
0.19 |
0. |
4.324 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 232 | 530 | 28185 | 0 | 8892 | 0 | 0 |
normalized size |
1 |
1. |
2.28 |
121.49 |
0. |
38.33 |
0. |
0. |
time (sec) |
N/A |
0.575 |
2.584 |
0.355 |
0. |
5.108 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 1262 | 81552 | 0 | 9586 | 0 | 0 |
normalized size |
1 |
1. |
5.66 |
365.7 |
0. |
42.99 |
0. |
0. |
time (sec) |
N/A |
0.433 |
5.388 |
0.607 |
0. |
4.943 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 254 | 254 | 105 | 204 | 317 | 657 | 0 | 153 |
normalized size | 1 | 1. | 0.41 | 0.8 | 1.25 | 2.59 | 0. | 0.6 |
time (sec) |
N/A |
0.373 |
0.454 |
0.08 |
1.534 |
1.407 |
0. |
1.155 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 212 | 212 | 95 | 170 | 271 | 512 | 0 | 139 |
normalized size | 1 | 1. | 0.45 | 0.8 | 1.28 | 2.42 | 0. | 0.66 |
time (sec) |
N/A |
0.22 |
0.288 |
0.061 |
1.48 |
1.358 |
0. |
1.152 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 85 | 136 | 225 | 409 | 0 | 126 |
normalized size | 1 | 1. | 0.5 | 0.8 | 1.32 | 2.41 | 0. | 0.74 |
time (sec) |
N/A |
0.13 |
0.19 |
0.053 |
1.474 |
1.377 |
0. |
1.163 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 75 | 102 | 180 | 327 | 0 | 112 |
normalized size | 1 | 1. | 0.59 | 0.8 | 1.41 | 2.55 | 0. | 0.88 |
time (sec) |
N/A |
0.062 |
0.108 |
0.049 |
1.438 |
1.386 |
0. |
1.145 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 229 | 4860 | 0 | 7899 | 0 | 0 |
normalized size |
1 |
1. |
1.03 |
21.89 |
0. |
35.58 |
0. |
0. |
time (sec) |
N/A |
0.539 |
1.07 |
0.179 |
0. |
3.907 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 255 | 255 | 685 | 40028 | 0 | 9335 | 0 | 0 |
normalized size |
1 |
1. |
2.69 |
156.97 |
0. |
36.61 |
0. |
0. |
time (sec) |
N/A |
0.66 |
1.699 |
0.414 |
0. |
5.257 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 1009 | 119458 | 0 | 10927 | 0 | 0 |
normalized size |
1 |
1. |
3.59 |
425.12 |
0. |
38.89 |
0. |
0. |
time (sec) |
N/A |
0.655 |
2.116 |
0.69 |
0. |
5.495 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 185 | 185 | 75 | 147 | 200 | 355 | 0 | 112 |
normalized size | 1 | 1. | 0.41 | 0.79 | 1.08 | 1.92 | 0. | 0.61 |
time (sec) |
N/A |
0.312 |
0.246 |
0.065 |
1.532 |
1.36 |
0. |
1.18 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 65 | 113 | 154 | 266 | 0 | 99 |
normalized size | 1 | 1. | 0.45 | 0.79 | 1.08 | 1.86 | 0. | 0.69 |
time (sec) |
N/A |
0.168 |
0.132 |
0.054 |
1.449 |
1.34 |
0. |
1.195 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 55 | 79 | 108 | 211 | 0 | 85 |
normalized size | 1 | 1. | 0.54 | 0.78 | 1.07 | 2.09 | 0. | 0.84 |
time (sec) |
N/A |
0.088 |
0.076 |
0.051 |
1.489 |
1.377 |
0. |
1.165 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 45 | 45 | 62 | 163 | 0 | 72 |
normalized size | 1 | 1. | 0.76 | 0.76 | 1.05 | 2.76 | 0. | 1.22 |
time (sec) |
N/A |
0.033 |
0.038 |
0.051 |
1.532 |
1.321 |
0. |
1.156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 176 | 684 | 0 | 7101 | 0 | 0 |
normalized size |
1 |
1. |
1.19 |
4.62 |
0. |
47.98 |
0. |
0. |
time (sec) |
N/A |
0.314 |
0.347 |
0.108 |
0. |
4.685 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 287 | 5225 | 0 | 8625 | 0 | 0 |
normalized size |
1 |
1. |
1.53 |
27.79 |
0. |
45.88 |
0. |
0. |
time (sec) |
N/A |
0.429 |
1.007 |
0.153 |
0. |
5.141 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 1279 | 13040 | 0 | 9927 | 0 | 0 |
normalized size |
1 |
1. |
5.74 |
58.48 |
0. |
44.52 |
0. |
0. |
time (sec) |
N/A |
0.469 |
6.238 |
0.191 |
0. |
5.178 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 95 | 166 | 200 | 385 | 0 | 111 |
normalized size | 1 | 1. | 0.57 | 1. | 1.2 | 2.32 | 0. | 0.67 |
time (sec) |
N/A |
0.204 |
0.377 |
0.066 |
1.495 |
1.416 |
0. |
1.198 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 65 | 132 | 154 | 311 | 0 | 97 |
normalized size | 1 | 1. | 0.52 | 1.06 | 1.24 | 2.51 | 0. | 0.78 |
time (sec) |
N/A |
0.127 |
0.229 |
0.059 |
1.526 |
1.327 |
0. |
1.206 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 55 | 98 | 108 | 251 | 0 | 84 |
normalized size | 1 | 1. | 0.67 | 1.2 | 1.32 | 3.06 | 0. | 1.02 |
time (sec) |
N/A |
0.071 |
0.141 |
0.052 |
1.484 |
1.3 |
0. |
1.181 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 64 | 62 | 209 | 0 | 72 |
normalized size | 1 | 1. | 1. | 1.42 | 1.38 | 4.64 | 0. | 1.6 |
time (sec) |
N/A |
0.029 |
0.077 |
0.049 |
1.509 |
1.301 |
0. |
1.229 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 176 | 202 | 718 | 0 | 7618 | 0 | 0 |
normalized size |
1 |
1. |
1.15 |
4.08 |
0. |
43.28 |
0. |
0. |
time (sec) |
N/A |
0.408 |
1.364 |
0.124 |
0. |
4.791 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 740 | 5942 | 0 | 9287 | 0 | 0 |
normalized size |
1 |
1. |
3.51 |
28.16 |
0. |
44.01 |
0. |
0. |
time (sec) |
N/A |
0.473 |
1.488 |
0.179 |
0. |
5.232 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 231 | 18981 | 0 | 11105 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
77.16 |
0. |
45.14 |
0. |
0. |
time (sec) |
N/A |
0.525 |
2.25 |
0.266 |
0. |
5.473 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 75 | 214 | 342 | 441 | 0 | 109 |
normalized size | 1 | 1. | 0.51 | 1.46 | 2.33 | 3. | 0. | 0.74 |
time (sec) |
N/A |
0.167 |
0.518 |
0.071 |
1.92 |
1.373 |
0. |
1.15 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 65 | 180 | 296 | 370 | 0 | 97 |
normalized size | 1 | 1. | 0.62 | 1.71 | 2.82 | 3.52 | 0. | 0.92 |
time (sec) |
N/A |
0.105 |
0.335 |
0.057 |
1.501 |
1.371 |
0. |
1.224 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 55 | 146 | 250 | 302 | 0 | 82 |
normalized size | 1 | 1. | 0.81 | 2.15 | 3.68 | 4.44 | 0. | 1.21 |
time (sec) |
N/A |
0.061 |
0.241 |
0.052 |
1.776 |
1.371 |
0. |
1.269 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 33 | 30 | 80 | 132 | 0 | 39 |
normalized size | 1 | 1. | 0.7 | 0.64 | 1.7 | 2.81 | 0. | 0.83 |
time (sec) |
N/A |
0.022 |
0.104 |
0.045 |
1.077 |
1.341 |
0. |
1.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 199 | 199 | 218 | 751 | 0 | 8280 | 0 | 0 |
normalized size |
1 |
1. |
1.1 |
3.77 |
0. |
41.61 |
0. |
0. |
time (sec) |
N/A |
0.456 |
0.91 |
0.121 |
0. |
4.947 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 234 | 296 | 5975 | 0 | 8498 | 0 | 0 |
normalized size |
1 |
1. |
1.26 |
25.53 |
0. |
36.32 |
0. |
0. |
time (sec) |
N/A |
0.543 |
1.162 |
0.175 |
0. |
4.836 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 242 | 19014 | 0 | 11142 | 0 | 0 |
normalized size |
1 |
1. |
0.9 |
70.68 |
0. |
41.42 |
0. |
0. |
time (sec) |
N/A |
0.589 |
1.971 |
0.277 |
0. |
5.318 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 436 | 436 | 657 | 1429 | 0 | 2866 | 0 | 861 |
normalized size |
1 |
1. |
1.51 |
3.28 |
0. |
6.57 |
0. |
1.97 |
time (sec) |
N/A |
0.789 |
0.965 |
0.063 |
0. |
2.833 |
0. |
1.302 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 173 | 453 | 0 | 1061 | 0 | 286 |
normalized size |
1 |
1. |
0.99 |
2.59 |
0. |
6.06 |
0. |
1.63 |
time (sec) |
N/A |
0.164 |
0.293 |
0.052 |
0. |
1.495 |
0. |
1.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 417 | 6019 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
13.97 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.051 |
1.255 |
0.433 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 488 | 488 | 555 | 22287 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.14 |
45.67 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.929 |
5.449 |
0.371 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 564 | 564 | 829 | 2458 | 0 | 5115 | 0 | 1553 |
normalized size |
1 |
1. |
1.47 |
4.36 |
0. |
9.07 |
0. |
2.75 |
time (sec) |
N/A |
0.935 |
1.828 |
0.063 |
0. |
9.817 |
0. |
1.339 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 236 | 236 | 392 | 862 | 0 | 1947 | 0 | 563 |
normalized size |
1 |
1. |
1.66 |
3.65 |
0. |
8.25 |
0. |
2.39 |
time (sec) |
N/A |
0.23 |
0.703 |
0.053 |
0. |
2.634 |
0. |
1.294 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 679 | 678 | 1232 | 22523 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.81 |
33.17 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
11.033 |
4.857 |
0.329 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 704 | 704 | 2843 | 72576 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
4.04 |
103.09 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
11.95 |
6.82 |
0.369 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 671 | 669 | 4727 | 178044 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
7.04 |
265.34 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
11.597 |
7.296 |
0.36 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 717 | 717 | 615 | 1930 | 0 | 3661 | 0 | 1112 |
normalized size |
1 |
1. |
0.86 |
2.69 |
0. |
5.11 |
0. |
1.55 |
time (sec) |
N/A |
2.71 |
1.405 |
0.073 |
0. |
7.39 |
0. |
1.369 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 316 | 316 | 251 | 706 | 0 | 1457 | 0 | 410 |
normalized size |
1 |
1. |
0.79 |
2.23 |
0. |
4.61 |
0. |
1.3 |
time (sec) |
N/A |
0.626 |
0.537 |
0.062 |
0. |
2.845 |
0. |
1.396 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 96 | 185 | 0 | 549 | 0 | 132 |
normalized size |
1 |
1. |
0.83 |
1.59 |
0. |
4.73 |
0. |
1.14 |
time (sec) |
N/A |
0.111 |
0.151 |
0.062 |
0. |
1.929 |
0. |
1.291 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 376 | 761 | 0 | 22873 | 0 | 0 |
normalized size |
1 |
1. |
1.01 |
2.03 |
0. |
61.16 |
0. |
0. |
time (sec) |
N/A |
0.579 |
1.508 |
0.359 |
0. |
45.018 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 789 | 787 | 1377 | 3858 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.75 |
4.89 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
8.21 |
6.734 |
0.329 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 649 | 649 | 745 | 2827 | 0 | 6743 | 0 | 1484 |
normalized size |
1 |
1. |
1.15 |
4.36 |
0. |
10.39 |
0. |
2.29 |
time (sec) |
N/A |
2.106 |
1.685 |
0.069 |
0. |
15.911 |
0. |
1.382 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 309 | 309 | 288 | 1011 | 0 | 2750 | 0 | 549 |
normalized size |
1 |
1. |
0.93 |
3.27 |
0. |
8.9 |
0. |
1.78 |
time (sec) |
N/A |
0.447 |
0.757 |
0.067 |
0. |
9.595 |
0. |
1.658 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 113 | 249 | 0 | 941 | 0 | 165 |
normalized size |
1 |
1. |
1.02 |
2.24 |
0. |
8.48 |
0. |
1.49 |
time (sec) |
N/A |
0.08 |
0.328 |
0.052 |
0. |
4.45 |
0. |
1.502 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 666 | 666 | 700 | 4099 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
6.15 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.829 |
6.792 |
0.355 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 891 | 891 | 872 | 4635 | 0 | 8338 | 0 | 1891 |
normalized size |
1 |
1. |
0.98 |
5.2 |
0. |
9.36 |
0. |
2.12 |
time (sec) |
N/A |
1.768 |
2.376 |
0.071 |
0. |
48.355 |
0. |
1.541 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 444 | 444 | 387 | 1786 | 0 | 3252 | 0 | 792 |
normalized size |
1 |
1. |
0.87 |
4.02 |
0. |
7.32 |
0. |
1.78 |
time (sec) |
N/A |
0.451 |
1.315 |
0.061 |
0. |
27.422 |
0. |
1.388 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 147 | 185 | 0 | 614 | 0 | 356 |
normalized size |
1 |
1. |
1.12 |
1.41 |
0. |
4.69 |
0. |
2.72 |
time (sec) |
N/A |
0.085 |
0.395 |
0.052 |
0. |
23.233 |
0. |
1.364 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 81 | 144 | 0 | 424 | 0 | 277 |
normalized size | 1 | 1. | 1.59 | 2.82 | 0. | 8.31 | 0. | 5.43 |
time (sec) |
N/A |
0.066 |
0.04 |
0.108 |
0. |
1.91 |
0. |
1.494 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1432 | 1432 | 670 | 929 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.47 | 0.65 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
6.219 |
2.487 |
0.836 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 652 | 652 | 390 | 420 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.6 | 0.64 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.677 |
0.62 |
3.535 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf size
of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the
integral was to solve. In this test, problem number [14] had the largest ratio of [ 0.4444
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
4 |
4 |
1. |
29 |
0.138 |
|
|
|
|
|
|
|
2 |
A |
2 |
2 |
1. |
31 |
0.065 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1. |
27 |
0.074 |
|
|
|
|
|
|
|
4 |
A |
4 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
5 |
A |
5 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
6 |
A |
6 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
7 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
8 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1. |
31 |
0.065 |
|
|
|
|
|
|
|
10 |
A |
2 |
2 |
1. |
34 |
0.059 |
|
|
|
|
|
|
|
11 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
12 |
A |
6 |
5 |
1. |
18 |
0.278 |
|
|
|
|
|
|
|
13 |
A |
3 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
14 |
A |
16 |
12 |
1. |
27 |
0.444 |
|
|
|
|
|
|
|
15 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
16 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
17 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
18 |
A |
2 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
19 |
A |
6 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
|
21 |
A |
5 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
22 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
23 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
24 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
25 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
26 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
27 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
28 |
A |
5 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
29 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
30 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
31 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
32 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
33 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
34 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
35 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
36 |
A |
8 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
37 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
38 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
39 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
40 |
A |
6 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
|
41 |
A |
9 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
42 |
A |
10 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
43 |
A |
11 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
44 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
45 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
46 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
48 |
A |
10 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
49 |
A |
11 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
50 |
A |
12 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
51 |
A |
8 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
52 |
A |
8 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
53 |
A |
5 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
54 |
A |
5 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
55 |
A |
11 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
56 |
A |
12 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
57 |
A |
13 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
58 |
A |
11 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
59 |
A |
9 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
60 |
A |
7 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
|
61 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
62 |
A |
8 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
63 |
A |
6 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
64 |
A |
7 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
65 |
A |
12 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
66 |
A |
10 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
67 |
A |
8 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
68 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
69 |
A |
9 |
8 |
1. |
27 |
0.296 |
|
|
|
|
|
|
|
70 |
A |
10 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
71 |
A |
7 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
72 |
A |
13 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
73 |
A |
11 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
74 |
A |
9 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
75 |
A |
7 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
76 |
A |
10 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
77 |
A |
11 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
78 |
A |
11 |
10 |
1. |
27 |
0.37 |
|
|
|
|
|
|
|
79 |
A |
10 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
80 |
A |
8 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
|
81 |
A |
6 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
82 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
83 |
A |
5 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
84 |
A |
6 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
85 |
A |
7 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
86 |
A |
9 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
87 |
A |
7 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
88 |
A |
5 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
89 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
90 |
A |
6 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
91 |
A |
7 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
92 |
A |
8 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
93 |
A |
8 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
94 |
A |
6 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
95 |
A |
5 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
96 |
A |
3 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
97 |
A |
7 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
98 |
A |
8 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
99 |
A |
9 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
100 |
A |
7 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
|
101 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
102 |
A |
8 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
103 |
A |
6 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
104 |
A |
8 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
105 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
106 |
A |
9 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
107 |
A |
10 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
108 |
A |
7 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
109 |
A |
8 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
110 |
A |
6 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
111 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
112 |
A |
5 |
3 |
1. |
27 |
0.111 |
|
|
|
|
|
|
|
113 |
A |
6 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
114 |
A |
7 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
115 |
A |
5 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
116 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
117 |
A |
6 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
118 |
A |
6 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
119 |
A |
5 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
120 |
A |
3 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
|
121 |
A |
5 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
122 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
123 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
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|
|
|
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|
|
|
|
|
|
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