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, 6, 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: { 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,
120 }
B grade: { 2, 3, 4, 5, 8, 12, 14, 104, 121 }
C grade: { }
F grade: { 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 }
2.1.8 Mupad
A grade: { }
B 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, 89, 96, 100, 101, 116, 120
}
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 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, 90, 91, 92, 93, 94, 95, 97, 98, 99, 102,
103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 121, 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 |
Mupad |
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grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 87 | 136 | 0 | 205 | 0 | 84 | -1 |
normalized size | 1 | 1.00 | 0.85 | 1.33 | 0.00 | 2.01 | 0.00 | 0.82 | -0.01 |
time (sec) |
N/A |
0.094 |
0.195 |
0.028 |
0.000 |
1.207 |
0.000 |
0.256 |
0.000 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F(-2) |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 178 | 491 | 0 | 1079 | 0 | 847 | -1 |
normalized size | 1 | 1.00 | 2.17 | 5.99 | 0.00 | 13.16 | 0.00 | 10.33 | -0.01 |
time (sec) |
N/A |
0.111 |
0.394 |
0.060 |
0.000 |
1.713 |
0.000 |
3.037 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F(-2) |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 161 | 307 | 0 | 813 | 0 | 703 | -1 |
normalized size | 1 | 1.00 | 2.44 | 4.65 | 0.00 | 12.32 | 0.00 | 10.65 | -0.02 |
time (sec) |
N/A |
0.079 |
0.228 |
0.029 |
0.000 |
1.428 |
0.000 |
1.898 |
0.000 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 296 | 829 | 0 | 1544 | 0 | 1166 | -1 |
normalized size | 1 | 1.00 | 2.29 | 6.43 | 0.00 | 11.97 | 0.00 | 9.04 | -0.01 |
time (sec) |
N/A |
0.169 |
0.923 |
0.033 |
0.000 |
1.865 |
0.000 |
2.265 |
0.000 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F |
B |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 1746 | 1884 | 0 | 3818 | 0 | 2986 | -1 |
normalized size | 1 | 1.00 | 7.79 | 8.41 | 0.00 | 17.04 | 0.00 | 13.33 | -0.00 |
time (sec) |
N/A |
0.427 |
6.382 |
0.032 |
0.000 |
9.944 |
0.000 |
4.870 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F |
B |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 3382 | 3695 | 0 | 8134 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 10.31 | 11.27 | 0.00 | 24.80 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.970 |
6.607 |
0.038 |
0.000 |
40.657 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
F |
B |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 490 | 1377 | 0 | 2005 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.02 | 8.50 | 0.00 | 12.38 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.306 |
1.965 |
0.033 |
0.000 |
3.066 |
0.000 |
0.000 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 84 | 27 | 0 | 38 | 0 | 52 | -1 |
normalized size | 1 | 1.00 | 3.00 | 0.96 | 0.00 | 1.36 | 0.00 | 1.86 | -0.04 |
time (sec) |
N/A |
0.017 |
0.074 |
0.022 |
0.000 |
0.844 |
0.000 |
0.219 |
0.000 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 142 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.103 |
0.143 |
0.253 |
0.000 |
0.908 |
0.000 |
0.000 |
0.000 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 172 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.134 |
0.243 |
0.302 |
0.000 |
0.905 |
0.000 |
0.000 |
0.000 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 27 | 16 | 0 | 22 | 0 | 49 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.33 | 0.00 | 0.46 | 0.00 | 1.02 | -0.02 |
time (sec) |
N/A |
0.015 |
0.020 |
0.046 |
0.000 |
0.862 |
0.000 |
0.229 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 66 | 84 | 0 | 82 | 0 | 143 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.20 | 0.00 | 1.17 | 0.00 | 2.04 | -0.01 |
time (sec) |
N/A |
0.051 |
0.088 |
0.021 |
0.000 |
0.912 |
0.000 |
0.260 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1077 | 1077 | 600 | 661 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.099 |
1.639 |
0.248 |
0.000 |
0.861 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
B |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 159 | 341 | 0 | 161 | 0 | 171 | -1 |
normalized size | 1 | 1.00 | 1.62 | 3.48 | 0.00 | 1.64 | 0.00 | 1.74 | -0.01 |
time (sec) |
N/A |
0.210 |
0.395 |
0.030 |
0.000 |
0.955 |
0.000 |
0.215 |
0.000 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 68 | 55 | 54 | 54 | 65 | 54 | 54 |
normalized size | 1 | 1.00 | 1.00 | 0.81 | 0.79 | 0.79 | 0.96 | 0.79 | 0.79 |
time (sec) |
N/A |
0.049 |
0.003 |
0.001 |
0.460 |
0.722 |
0.086 |
0.206 |
0.062 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 56 | 45 | 44 | 44 | 53 | 44 | 44 |
normalized size | 1 | 1.00 | 1.00 | 0.80 | 0.79 | 0.79 | 0.95 | 0.79 | 0.79 |
time (sec) |
N/A |
0.038 |
0.002 |
0.001 |
0.447 |
0.720 |
0.081 |
0.181 |
0.034 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 44 | 35 | 34 | 34 | 41 | 34 | 34 |
normalized size | 1 | 1.00 | 1.00 | 0.80 | 0.77 | 0.77 | 0.93 | 0.77 | 0.77 |
time (sec) |
N/A |
0.029 |
0.001 |
0.001 |
0.434 |
0.691 |
0.075 |
0.209 |
0.025 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 24 |
normalized size | 1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.80 |
time (sec) |
N/A |
0.016 |
0.001 |
0.001 |
0.432 |
0.692 |
0.062 |
0.182 |
0.023 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 34 | 33 | 33 | 49 | 33 | 35 |
normalized size | 1 | 1.00 | 1.00 | 0.81 | 0.79 | 0.79 | 1.17 | 0.79 | 0.83 |
time (sec) |
N/A |
0.040 |
0.016 |
0.005 |
0.975 |
0.647 |
0.141 |
0.176 |
3.393 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 43 | 34 | 36 | 45 | 42 | 36 | 35 |
normalized size | 1 | 1.00 | 1.00 | 0.79 | 0.84 | 1.05 | 0.98 | 0.84 | 0.81 |
time (sec) |
N/A |
0.027 |
0.015 |
0.005 |
0.969 |
0.734 |
0.157 |
0.209 |
0.038 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 53 | 47 | 56 | 75 | 63 | 46 | 55 |
normalized size | 1 | 1.00 | 0.83 | 0.73 | 0.88 | 1.17 | 0.98 | 0.72 | 0.86 |
time (sec) |
N/A |
0.037 |
0.026 |
0.005 |
0.958 |
0.796 |
0.182 |
0.175 |
0.049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 80 | 65 | 64 | 64 | 76 | 64 | 64 |
normalized size | 1 | 1.00 | 1.00 | 0.81 | 0.80 | 0.80 | 0.95 | 0.80 | 0.80 |
time (sec) |
N/A |
0.060 |
0.003 |
0.002 |
0.452 |
0.772 |
0.102 |
0.201 |
0.085 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 66 | 55 | 54 | 54 | 63 | 54 | 54 |
normalized size | 1 | 1.00 | 1.00 | 0.83 | 0.82 | 0.82 | 0.95 | 0.82 | 0.82 |
time (sec) |
N/A |
0.048 |
0.002 |
0.001 |
0.438 |
0.507 |
0.086 |
0.215 |
0.054 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 45 | 44 | 44 | 51 | 44 | 44 |
normalized size | 1 | 1.00 | 1.00 | 0.83 | 0.81 | 0.81 | 0.94 | 0.81 | 0.81 |
time (sec) |
N/A |
0.042 |
0.002 |
0.001 |
0.437 |
0.980 |
0.082 |
0.202 |
0.034 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 46 | 35 | 34 | 34 | 41 | 34 | 34 |
normalized size | 1 | 1.00 | 1.00 | 0.76 | 0.74 | 0.74 | 0.89 | 0.74 | 0.74 |
time (sec) |
N/A |
0.030 |
0.001 |
0.001 |
0.435 |
1.108 |
0.072 |
0.192 |
0.025 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 53 | 44 | 43 | 43 | 63 | 43 | 45 |
normalized size | 1 | 1.00 | 0.95 | 0.79 | 0.77 | 0.77 | 1.12 | 0.77 | 0.80 |
time (sec) |
N/A |
0.051 |
0.020 |
0.004 |
0.968 |
0.715 |
0.150 |
0.210 |
3.449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 59 | 51 | 52 | 78 | 65 | 52 | 51 |
normalized size | 1 | 1.00 | 0.94 | 0.81 | 0.83 | 1.24 | 1.03 | 0.83 | 0.81 |
time (sec) |
N/A |
0.061 |
0.032 |
0.006 |
0.961 |
0.871 |
0.198 |
0.172 |
0.050 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 53 | 47 | 56 | 75 | 63 | 46 | 55 |
normalized size | 1 | 1.00 | 0.83 | 0.73 | 0.88 | 1.17 | 0.98 | 0.72 | 0.86 |
time (sec) |
N/A |
0.052 |
0.024 |
0.006 |
0.968 |
0.844 |
0.199 |
0.185 |
3.442 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 63 | 57 | 76 | 105 | 83 | 56 | 75 |
normalized size | 1 | 1.00 | 0.74 | 0.67 | 0.89 | 1.24 | 0.98 | 0.66 | 0.88 |
time (sec) |
N/A |
0.063 |
0.044 |
0.007 |
0.962 |
0.841 |
0.229 |
0.183 |
3.468 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 96 | 75 | 74 | 74 | 92 | 74 | 74 |
normalized size | 1 | 1.00 | 1.00 | 0.78 | 0.77 | 0.77 | 0.96 | 0.77 | 0.77 |
time (sec) |
N/A |
0.071 |
0.004 |
0.000 |
0.432 |
0.779 |
0.097 |
0.176 |
0.121 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 82 | 65 | 64 | 64 | 78 | 64 | 64 |
normalized size | 1 | 1.00 | 1.00 | 0.79 | 0.78 | 0.78 | 0.95 | 0.78 | 0.78 |
time (sec) |
N/A |
0.056 |
0.002 |
0.001 |
0.426 |
0.803 |
0.090 |
0.205 |
0.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 68 | 55 | 54 | 54 | 65 | 54 | 54 |
normalized size | 1 | 1.00 | 1.00 | 0.81 | 0.79 | 0.79 | 0.96 | 0.79 | 0.79 |
time (sec) |
N/A |
0.051 |
0.002 |
0.002 |
0.429 |
0.769 |
0.084 |
0.202 |
0.054 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 56 | 45 | 44 | 44 | 53 | 44 | 44 |
normalized size | 1 | 1.00 | 1.00 | 0.80 | 0.79 | 0.79 | 0.95 | 0.79 | 0.79 |
time (sec) |
N/A |
0.032 |
0.001 |
0.001 |
0.434 |
0.826 |
0.077 |
0.201 |
0.033 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 63 | 54 | 53 | 53 | 76 | 53 | 55 |
normalized size | 1 | 1.00 | 0.90 | 0.77 | 0.76 | 0.76 | 1.09 | 0.76 | 0.79 |
time (sec) |
N/A |
0.053 |
0.023 |
0.004 |
0.963 |
0.875 |
0.159 |
0.211 |
0.043 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 77 | 61 | 62 | 88 | 78 | 62 | 61 |
normalized size | 1 | 1.00 | 1.00 | 0.79 | 0.81 | 1.14 | 1.01 | 0.81 | 0.79 |
time (sec) |
N/A |
0.072 |
0.027 |
0.008 |
0.961 |
0.845 |
0.188 |
0.206 |
3.431 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 78 | 63 | 72 | 118 | 85 | 62 | 71 |
normalized size | 1 | 1.00 | 0.93 | 0.75 | 0.86 | 1.40 | 1.01 | 0.74 | 0.85 |
time (sec) |
N/A |
0.087 |
0.037 |
0.009 |
0.970 |
0.882 |
0.235 |
0.189 |
3.426 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 72 | 64 | 63 | 63 | 87 | 63 | 65 |
normalized size | 1 | 1.00 | 0.86 | 0.76 | 0.75 | 0.75 | 1.04 | 0.75 | 0.77 |
time (sec) |
N/A |
0.057 |
0.028 |
0.006 |
0.976 |
0.802 |
0.167 |
0.211 |
3.441 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 63 | 54 | 53 | 53 | 73 | 53 | 55 |
normalized size | 1 | 1.00 | 0.90 | 0.77 | 0.76 | 0.76 | 1.04 | 0.76 | 0.79 |
time (sec) |
N/A |
0.056 |
0.021 |
0.004 |
0.968 |
1.024 |
0.152 |
0.213 |
0.042 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 52 | 44 | 43 | 43 | 60 | 43 | 45 |
normalized size | 1 | 1.00 | 0.93 | 0.79 | 0.77 | 0.77 | 1.07 | 0.77 | 0.80 |
time (sec) |
N/A |
0.050 |
0.017 |
0.004 |
0.958 |
0.852 |
0.155 |
0.182 |
3.445 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 34 | 33 | 33 | 46 | 33 | 35 |
normalized size | 1 | 1.00 | 1.00 | 0.81 | 0.79 | 0.79 | 1.10 | 0.79 | 0.83 |
time (sec) |
N/A |
0.035 |
0.010 |
0.004 |
0.950 |
0.863 |
0.141 |
0.207 |
0.039 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 73 | 60 | 59 | 59 | 83 | 59 | 79 |
normalized size | 1 | 1.00 | 1.00 | 0.82 | 0.81 | 0.81 | 1.14 | 0.81 | 1.08 |
time (sec) |
N/A |
0.053 |
0.032 |
0.006 |
0.963 |
0.807 |
0.244 |
0.191 |
0.187 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 94 | 77 | 78 | 117 | 102 | 78 | 95 |
normalized size | 1 | 1.00 | 1.00 | 0.82 | 0.83 | 1.24 | 1.09 | 0.83 | 1.01 |
time (sec) |
N/A |
0.089 |
0.083 |
0.007 |
0.960 |
0.962 |
0.322 |
0.198 |
3.567 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 104 | 89 | 98 | 177 | 119 | 88 | 115 |
normalized size | 1 | 1.00 | 0.90 | 0.77 | 0.85 | 1.54 | 1.03 | 0.77 | 1.00 |
time (sec) |
N/A |
0.124 |
0.155 |
0.008 |
0.959 |
1.019 |
0.363 |
0.180 |
0.179 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 91 | 71 | 72 | 98 | 90 | 72 | 72 |
normalized size | 1 | 1.00 | 1.00 | 0.78 | 0.79 | 1.08 | 0.99 | 0.79 | 0.79 |
time (sec) |
N/A |
0.086 |
0.052 |
0.010 |
0.964 |
1.168 |
0.198 |
0.183 |
3.462 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 77 | 61 | 62 | 88 | 75 | 62 | 61 |
normalized size | 1 | 1.00 | 1.00 | 0.79 | 0.81 | 1.14 | 0.97 | 0.81 | 0.79 |
time (sec) |
N/A |
0.073 |
0.028 |
0.008 |
0.960 |
0.732 |
0.191 |
0.195 |
3.424 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 63 | 51 | 52 | 78 | 61 | 52 | 52 |
normalized size | 1 | 1.00 | 1.00 | 0.81 | 0.83 | 1.24 | 0.97 | 0.83 | 0.83 |
time (sec) |
N/A |
0.063 |
0.031 |
0.007 |
0.966 |
0.970 |
0.189 |
0.173 |
3.404 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 43 | 34 | 36 | 45 | 42 | 36 | 36 |
normalized size | 1 | 1.00 | 1.00 | 0.79 | 0.84 | 1.05 | 0.98 | 0.84 | 0.84 |
time (sec) |
N/A |
0.026 |
0.015 |
0.004 |
0.964 |
0.949 |
0.154 |
0.189 |
0.040 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 94 | 77 | 78 | 117 | 102 | 78 | 96 |
normalized size | 1 | 1.00 | 1.00 | 0.82 | 0.83 | 1.24 | 1.09 | 0.83 | 1.02 |
time (sec) |
N/A |
0.088 |
0.061 |
0.007 |
0.963 |
0.926 |
0.319 |
0.192 |
3.578 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 106 | 94 | 96 | 167 | 122 | 96 | 115 |
normalized size | 1 | 1.00 | 0.83 | 0.74 | 0.76 | 1.31 | 0.96 | 0.76 | 0.91 |
time (sec) |
N/A |
0.123 |
0.057 |
0.010 |
0.961 |
0.862 |
0.359 |
0.193 |
0.177 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 136 | 106 | 118 | 237 | 143 | 110 | 135 |
normalized size | 1 | 1.00 | 0.92 | 0.72 | 0.80 | 1.60 | 0.97 | 0.74 | 0.91 |
time (sec) |
N/A |
0.161 |
0.076 |
0.011 |
0.968 |
1.070 |
0.400 |
0.202 |
3.586 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 98 | 73 | 82 | 128 | 95 | 72 | 81 |
normalized size | 1 | 1.00 | 1.00 | 0.74 | 0.84 | 1.31 | 0.97 | 0.73 | 0.83 |
time (sec) |
N/A |
0.113 |
0.038 |
0.008 |
0.951 |
0.818 |
0.241 |
0.207 |
0.045 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 84 | 63 | 72 | 118 | 82 | 62 | 72 |
normalized size | 1 | 1.00 | 1.00 | 0.75 | 0.86 | 1.40 | 0.98 | 0.74 | 0.86 |
time (sec) |
N/A |
0.087 |
0.037 |
0.007 |
0.958 |
0.820 |
0.229 |
0.183 |
0.049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 51 | 47 | 56 | 75 | 63 | 46 | 56 |
normalized size | 1 | 1.00 | 0.80 | 0.73 | 0.88 | 1.17 | 0.98 | 0.72 | 0.88 |
time (sec) |
N/A |
0.053 |
0.029 |
0.006 |
0.961 |
0.873 |
0.201 |
0.186 |
3.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 51 | 47 | 56 | 75 | 61 | 46 | 55 |
normalized size | 1 | 1.00 | 0.80 | 0.73 | 0.88 | 1.17 | 0.95 | 0.72 | 0.86 |
time (sec) |
N/A |
0.033 |
0.028 |
0.007 |
0.960 |
0.917 |
0.183 |
0.205 |
0.044 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 99 | 89 | 98 | 177 | 122 | 88 | 116 |
normalized size | 1 | 1.00 | 0.86 | 0.77 | 0.85 | 1.54 | 1.06 | 0.77 | 1.01 |
time (sec) |
N/A |
0.124 |
0.161 |
0.008 |
0.973 |
0.833 |
0.357 |
0.211 |
3.580 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 136 | 106 | 116 | 227 | 143 | 110 | 136 |
normalized size | 1 | 1.00 | 0.85 | 0.66 | 0.72 | 1.42 | 0.89 | 0.69 | 0.85 |
time (sec) |
N/A |
0.160 |
0.124 |
0.011 |
0.974 |
0.868 |
0.427 |
0.217 |
3.597 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 181 | 181 | 151 | 118 | 138 | 297 | 163 | 116 | 155 |
normalized size | 1 | 1.00 | 0.83 | 0.65 | 0.76 | 1.64 | 0.90 | 0.64 | 0.86 |
time (sec) |
N/A |
0.204 |
0.095 |
0.013 |
0.972 |
0.734 |
0.470 |
0.219 |
3.588 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 85 | 166 | 177 | 98 | 0 | 93 | 221 |
normalized size | 1 | 1.00 | 0.41 | 0.80 | 0.85 | 0.47 | 0.00 | 0.45 | 1.06 |
time (sec) |
N/A |
0.309 |
0.296 |
0.031 |
1.006 |
0.660 |
0.000 |
0.249 |
5.028 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 75 | 132 | 143 | 88 | 0 | 83 | 187 |
normalized size | 1 | 1.00 | 0.45 | 0.80 | 0.86 | 0.53 | 0.00 | 0.50 | 1.13 |
time (sec) |
N/A |
0.181 |
0.171 |
0.008 |
0.982 |
0.899 |
0.000 |
0.254 |
4.692 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 65 | 98 | 109 | 78 | 0 | 73 | 153 |
normalized size | 1 | 1.00 | 0.52 | 0.79 | 0.88 | 0.63 | 0.00 | 0.59 | 1.23 |
time (sec) |
N/A |
0.099 |
0.105 |
0.007 |
0.976 |
0.847 |
0.000 |
0.217 |
4.185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 55 | 64 | 75 | 68 | 0 | 63 | 119 |
normalized size | 1 | 1.00 | 0.67 | 0.78 | 0.91 | 0.83 | 0.00 | 0.77 | 1.45 |
time (sec) |
N/A |
0.040 |
0.052 |
0.006 |
0.961 |
1.012 |
0.000 |
0.238 |
3.835 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 185 | 2065 | 0 | 2016 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 11.87 | 0.00 | 11.59 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.441 |
0.457 |
0.149 |
0.000 |
2.105 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 214 | 16357 | 0 | 2102 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 87.01 | 0.00 | 11.18 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.393 |
1.036 |
0.232 |
0.000 |
2.365 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 299 | 44343 | 0 | 2182 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.34 | 198.85 | 0.00 | 9.78 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.459 |
2.075 |
0.372 |
0.000 |
2.816 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 231 | 231 | 95 | 185 | 206 | 108 | 0 | 103 | -1 |
normalized size | 1 | 1.00 | 0.41 | 0.80 | 0.89 | 0.47 | 0.00 | 0.45 | -0.00 |
time (sec) |
N/A |
0.342 |
0.367 |
0.035 |
1.022 |
0.668 |
0.000 |
0.255 |
0.000 |
|
|
|
|
|
|
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|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 85 | 151 | 172 | 98 | 0 | 93 | -1 |
normalized size | 1 | 1.00 | 0.45 | 0.80 | 0.91 | 0.52 | 0.00 | 0.49 | -0.01 |
time (sec) |
N/A |
0.190 |
0.231 |
0.007 |
0.991 |
0.988 |
0.000 |
0.256 |
0.000 |
|
|
|
|
|
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|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 75 | 117 | 138 | 88 | 0 | 83 | -1 |
normalized size | 1 | 1.00 | 0.51 | 0.80 | 0.94 | 0.60 | 0.00 | 0.56 | -0.01 |
time (sec) |
N/A |
0.122 |
0.141 |
0.009 |
0.983 |
0.805 |
0.000 |
0.257 |
0.000 |
|
|
|
|
|
|
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|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 65 | 83 | 104 | 78 | 0 | 73 | -1 |
normalized size | 1 | 1.00 | 0.62 | 0.79 | 0.99 | 0.74 | 0.00 | 0.70 | -0.01 |
time (sec) |
N/A |
0.050 |
0.080 |
0.006 |
0.963 |
0.739 |
0.000 |
0.230 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 310 | 3460 | 0 | 2027 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.57 | 17.56 | 0.00 | 10.29 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.488 |
0.693 |
0.053 |
0.000 |
1.975 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 232 | 530 | 28185 | 0 | 2150 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.28 | 121.49 | 0.00 | 9.27 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.575 |
2.562 |
0.158 |
0.000 |
2.643 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 1262 | 81552 | 0 | 2183 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.66 | 365.70 | 0.00 | 9.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.433 |
5.342 |
0.350 |
0.000 |
2.609 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 254 | 254 | 105 | 204 | 235 | 118 | 0 | 113 | -1 |
normalized size | 1 | 1.00 | 0.41 | 0.80 | 0.93 | 0.46 | 0.00 | 0.44 | -0.00 |
time (sec) |
N/A |
0.373 |
0.452 |
0.040 |
1.021 |
0.811 |
0.000 |
0.536 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 212 | 212 | 95 | 170 | 201 | 108 | 0 | 103 | -1 |
normalized size | 1 | 1.00 | 0.45 | 0.80 | 0.95 | 0.51 | 0.00 | 0.49 | -0.00 |
time (sec) |
N/A |
0.220 |
0.296 |
0.009 |
0.996 |
1.005 |
0.000 |
0.549 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 85 | 136 | 167 | 98 | 0 | 93 | -1 |
normalized size | 1 | 1.00 | 0.50 | 0.80 | 0.98 | 0.58 | 0.00 | 0.55 | -0.01 |
time (sec) |
N/A |
0.130 |
0.183 |
0.007 |
1.028 |
0.795 |
0.000 |
0.516 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 75 | 102 | 133 | 88 | 0 | 83 | -1 |
normalized size | 1 | 1.00 | 0.59 | 0.80 | 1.04 | 0.69 | 0.00 | 0.65 | -0.01 |
time (sec) |
N/A |
0.062 |
0.112 |
0.006 |
0.974 |
0.696 |
0.000 |
0.391 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 229 | 4860 | 0 | 2010 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 21.89 | 0.00 | 9.05 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.539 |
1.047 |
0.053 |
0.000 |
2.250 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 255 | 255 | 685 | 40028 | 0 | 2161 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.69 | 156.97 | 0.00 | 8.47 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.660 |
1.655 |
0.157 |
0.000 |
2.739 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 1009 | 119458 | 0 | 2240 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.59 | 425.12 | 0.00 | 7.97 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.655 |
1.996 |
0.384 |
0.000 |
2.978 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 185 | 185 | 75 | 147 | 148 | 88 | 0 | 83 | -1 |
normalized size | 1 | 1.00 | 0.41 | 0.79 | 0.80 | 0.48 | 0.00 | 0.45 | -0.01 |
time (sec) |
N/A |
0.312 |
0.241 |
0.019 |
0.999 |
0.769 |
0.000 |
0.503 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 65 | 113 | 114 | 78 | 0 | 73 | -1 |
normalized size | 1 | 1.00 | 0.45 | 0.79 | 0.80 | 0.55 | 0.00 | 0.51 | -0.01 |
time (sec) |
N/A |
0.168 |
0.134 |
0.008 |
0.977 |
0.682 |
0.000 |
0.524 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 55 | 79 | 80 | 68 | 0 | 63 | -1 |
normalized size | 1 | 1.00 | 0.54 | 0.78 | 0.79 | 0.67 | 0.00 | 0.62 | -0.01 |
time (sec) |
N/A |
0.088 |
0.075 |
0.008 |
0.965 |
0.731 |
0.000 |
0.487 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 45 | 45 | 46 | 58 | 0 | 53 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.76 | 0.78 | 0.98 | 0.00 | 0.90 | -0.02 |
time (sec) |
N/A |
0.033 |
0.039 |
0.006 |
0.956 |
0.812 |
0.000 |
0.530 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 176 | 684 | 0 | 2002 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.19 | 4.62 | 0.00 | 13.53 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.314 |
0.300 |
0.004 |
0.000 |
2.250 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 287 | 5225 | 0 | 2102 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.53 | 27.79 | 0.00 | 11.18 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.429 |
0.996 |
0.006 |
0.000 |
2.601 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 1277 | 13040 | 0 | 2183 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.73 | 58.48 | 0.00 | 9.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.469 |
6.230 |
0.007 |
0.000 |
2.372 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 95 | 166 | 148 | 112 | 0 | 82 | -1 |
normalized size | 1 | 1.00 | 0.57 | 1.00 | 0.89 | 0.67 | 0.00 | 0.49 | -0.01 |
time (sec) |
N/A |
0.204 |
0.373 |
0.029 |
0.985 |
0.914 |
0.000 |
0.251 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 65 | 132 | 114 | 102 | 0 | 72 | -1 |
normalized size | 1 | 1.00 | 0.52 | 1.06 | 0.92 | 0.82 | 0.00 | 0.58 | -0.01 |
time (sec) |
N/A |
0.127 |
0.232 |
0.008 |
0.973 |
0.945 |
0.000 |
0.281 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
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|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 55 | 98 | 80 | 92 | 0 | 62 | -1 |
normalized size | 1 | 1.00 | 0.67 | 1.20 | 0.98 | 1.12 | 0.00 | 0.76 | -0.01 |
time (sec) |
N/A |
0.071 |
0.143 |
0.008 |
0.959 |
0.884 |
0.000 |
0.237 |
0.000 |
|
|
|
|
|
|
|
|
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|
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|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 64 | 46 | 82 | 0 | 53 | 87 |
normalized size | 1 | 1.00 | 1.00 | 1.42 | 1.02 | 1.82 | 0.00 | 1.18 | 1.93 |
time (sec) |
N/A |
0.029 |
0.076 |
0.006 |
0.955 |
0.804 |
0.000 |
0.234 |
0.227 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 176 | 202 | 718 | 0 | 2083 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 4.08 | 0.00 | 11.84 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.408 |
1.287 |
0.034 |
0.000 |
2.341 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 740 | 5942 | 0 | 2173 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.51 | 28.16 | 0.00 | 10.30 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.473 |
1.525 |
0.099 |
0.000 |
2.526 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 231 | 18981 | 0 | 2263 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 77.16 | 0.00 | 9.20 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.525 |
2.206 |
0.208 |
0.000 |
3.041 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 75 | 214 | 253 | 132 | 0 | 81 | -1 |
normalized size | 1 | 1.00 | 0.51 | 1.46 | 1.72 | 0.90 | 0.00 | 0.55 | -0.01 |
time (sec) |
N/A |
0.167 |
0.513 |
0.031 |
1.002 |
0.647 |
0.000 |
0.252 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 65 | 180 | 219 | 122 | 0 | 72 | -1 |
normalized size | 1 | 1.00 | 0.62 | 1.71 | 2.09 | 1.16 | 0.00 | 0.69 | -0.01 |
time (sec) |
N/A |
0.105 |
0.338 |
0.008 |
1.020 |
0.602 |
0.000 |
0.268 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 55 | 146 | 185 | 112 | 0 | 61 | -1 |
normalized size | 1 | 1.00 | 0.81 | 2.15 | 2.72 | 1.65 | 0.00 | 0.90 | -0.01 |
time (sec) |
N/A |
0.061 |
0.236 |
0.007 |
0.978 |
0.684 |
0.000 |
0.267 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 33 | 30 | 59 | 51 | 0 | 29 | 29 |
normalized size | 1 | 1.00 | 0.70 | 0.64 | 1.26 | 1.09 | 0.00 | 0.62 | 0.62 |
time (sec) |
N/A |
0.022 |
0.103 |
0.005 |
0.432 |
0.569 |
0.000 |
0.232 |
0.090 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 199 | 199 | 218 | 751 | 0 | 2133 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 3.77 | 0.00 | 10.72 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.456 |
0.868 |
0.039 |
0.000 |
2.042 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 234 | 296 | 5975 | 0 | 2253 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 25.53 | 0.00 | 9.63 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.543 |
1.153 |
0.104 |
0.000 |
1.992 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 242 | 19014 | 0 | 2343 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 70.68 | 0.00 | 8.71 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.589 |
1.958 |
0.209 |
0.000 |
1.994 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 436 | 436 | 657 | 1429 | 0 | 1269 | 0 | 638 | 1299 |
normalized size | 1 | 1.00 | 1.51 | 3.28 | 0.00 | 2.91 | 0.00 | 1.46 | 2.98 |
time (sec) |
N/A |
0.789 |
0.935 |
0.023 |
0.000 |
1.322 |
0.000 |
0.365 |
5.312 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 173 | 453 | 0 | 465 | 0 | 212 | 320 |
normalized size | 1 | 1.00 | 0.99 | 2.59 | 0.00 | 2.66 | 0.00 | 1.21 | 1.83 |
time (sec) |
N/A |
0.164 |
0.273 |
0.007 |
0.000 |
0.770 |
0.000 |
0.299 |
3.906 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 417 | 6019 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 13.97 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.051 |
1.219 |
0.052 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 488 | 488 | 555 | 22287 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 45.67 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.929 |
5.093 |
0.037 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 564 | 564 | 829 | 2458 | 0 | 2179 | 0 | 1150 | -1 |
normalized size | 1 | 1.00 | 1.47 | 4.36 | 0.00 | 3.86 | 0.00 | 2.04 | -0.00 |
time (sec) |
N/A |
0.935 |
1.762 |
0.025 |
0.000 |
3.790 |
0.000 |
0.598 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 236 | 236 | 392 | 862 | 0 | 839 | 0 | 417 | -1 |
normalized size | 1 | 1.00 | 1.66 | 3.65 | 0.00 | 3.56 | 0.00 | 1.77 | -0.00 |
time (sec) |
N/A |
0.230 |
0.606 |
0.009 |
0.000 |
1.268 |
0.000 |
0.612 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 679 | 678 | 1232 | 22523 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.81 | 33.17 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
11.033 |
4.576 |
0.029 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 704 | 704 | 2843 | 72576 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.04 | 103.09 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
11.950 |
6.831 |
0.039 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 671 | 669 | 4727 | 178044 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 7.04 | 265.34 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
11.597 |
7.229 |
0.066 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 717 | 717 | 615 | 1930 | 0 | 1583 | 0 | 824 | -1 |
normalized size | 1 | 1.00 | 0.86 | 2.69 | 0.00 | 2.21 | 0.00 | 1.15 | -0.00 |
time (sec) |
N/A |
2.710 |
1.346 |
0.028 |
0.000 |
3.195 |
0.000 |
0.528 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
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|
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|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 316 | 316 | 251 | 706 | 0 | 637 | 0 | 304 | -1 |
normalized size | 1 | 1.00 | 0.79 | 2.23 | 0.00 | 2.02 | 0.00 | 0.96 | -0.00 |
time (sec) |
N/A |
0.626 |
0.503 |
0.014 |
0.000 |
1.435 |
0.000 |
0.632 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 96 | 185 | 0 | 227 | 0 | 98 | -1 |
normalized size | 1 | 1.00 | 0.83 | 1.59 | 0.00 | 1.96 | 0.00 | 0.84 | -0.01 |
time (sec) |
N/A |
0.111 |
0.146 |
0.008 |
0.000 |
1.455 |
0.000 |
0.499 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 376 | 761 | 0 | 11287 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 2.03 | 0.00 | 30.18 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.579 |
1.454 |
0.025 |
0.000 |
14.925 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
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|
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|
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|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 789 | 787 | 1377 | 3858 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.75 | 4.89 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
8.210 |
6.689 |
0.031 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 649 | 649 | 745 | 2827 | 0 | 3143 | 0 | 1099 | -1 |
normalized size | 1 | 1.00 | 1.15 | 4.36 | 0.00 | 4.84 | 0.00 | 1.69 | -0.00 |
time (sec) |
N/A |
2.106 |
1.664 |
0.030 |
0.000 |
5.599 |
0.000 |
0.423 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 309 | 309 | 288 | 1011 | 0 | 1305 | 0 | 407 | -1 |
normalized size | 1 | 1.00 | 0.93 | 3.27 | 0.00 | 4.22 | 0.00 | 1.32 | -0.00 |
time (sec) |
N/A |
0.447 |
0.733 |
0.015 |
0.000 |
3.263 |
0.000 |
0.352 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 113 | 249 | 0 | 429 | 0 | 122 | 143 |
normalized size | 1 | 1.00 | 1.02 | 2.24 | 0.00 | 3.86 | 0.00 | 1.10 | 1.29 |
time (sec) |
N/A |
0.080 |
0.311 |
0.006 |
0.000 |
1.744 |
0.000 |
0.312 |
3.734 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 666 | 666 | 700 | 4099 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 6.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.829 |
5.343 |
0.028 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 891 | 891 | 872 | 4635 | 0 | 3995 | 0 | 1401 | -1 |
normalized size | 1 | 1.00 | 0.98 | 5.20 | 0.00 | 4.48 | 0.00 | 1.57 | -0.00 |
time (sec) |
N/A |
1.768 |
2.191 |
0.031 |
0.000 |
12.868 |
0.000 |
0.455 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 444 | 444 | 387 | 1786 | 0 | 1581 | 0 | 587 | -1 |
normalized size | 1 | 1.00 | 0.87 | 4.02 | 0.00 | 3.56 | 0.00 | 1.32 | -0.00 |
time (sec) |
N/A |
0.451 |
1.257 |
0.014 |
0.000 |
6.519 |
0.000 |
0.338 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 147 | 185 | 0 | 286 | 0 | 240 | 175 |
normalized size | 1 | 1.00 | 1.12 | 1.41 | 0.00 | 2.18 | 0.00 | 1.83 | 1.34 |
time (sec) |
N/A |
0.085 |
0.378 |
0.007 |
0.000 |
4.021 |
0.000 |
0.322 |
3.708 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 81 | 144 | 0 | 154 | 0 | 205 | -1 |
normalized size | 1 | 1.00 | 1.59 | 2.82 | 0.00 | 3.02 | 0.00 | 4.02 | -0.02 |
time (sec) |
N/A |
0.066 |
0.041 |
0.024 |
0.000 |
0.755 |
0.000 |
0.276 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1432 | 1432 | 670 | 928 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.47 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
6.219 |
2.341 |
0.272 |
0.000 |
1.039 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 652 | 652 | 390 | 418 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.60 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.677 |
0.611 |
0.468 |
0.000 |
0.930 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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
[.4444]
|
|
|
|
|
|
|
| Table 2.1:Rubi 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 |
1.00 |
29 |
0.138 |
|
|
|
|
|
|
|
2 |
A |
2 |
2 |
1.00 |
31 |
0.065 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1.00 |
27 |
0.074 |
|
|
|
|
|
|
|
4 |
A |
4 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
5 |
A |
5 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
6 |
A |
6 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
7 |
A |
4 |
4 |
1.00 |
31 |
0.129 |
|
|
|
|
|
|
|
8 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1.00 |
31 |
0.065 |
|
|
|
|
|
|
|
10 |
A |
2 |
2 |
1.00 |
34 |
0.059 |
|
|
|
|
|
|
|
11 |
A |
3 |
3 |
1.00 |
22 |
0.136 |
|
|
|
|
|
|
|
12 |
A |
6 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
13 |
A |
3 |
3 |
1.00 |
26 |
0.115 |
|
|
|
|
|
|
|
14 |
A |
16 |
12 |
1.00 |
27 |
0.444 |
|
|
|
|
|
|
|
15 |
A |
2 |
1 |
1.00 |
23 |
0.043 |
|
|
|
|
|
|
|
16 |
A |
2 |
1 |
1.00 |
23 |
0.043 |
|
|
|
|
|
|
|
17 |
A |
2 |
1 |
1.00 |
23 |
0.043 |
|
|
|
|
|
|
|
18 |
A |
2 |
1 |
1.00 |
21 |
0.048 |
|
|
|
|
|
|
|
19 |
A |
6 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
21 |
A |
5 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
22 |
A |
2 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
23 |
A |
2 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
24 |
A |
2 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
25 |
A |
2 |
1 |
1.00 |
23 |
0.043 |
|
|
|
|
|
|
|
26 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
27 |
A |
7 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
28 |
A |
5 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
29 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
30 |
A |
2 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
31 |
A |
2 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
32 |
A |
2 |
1 |
1.00 |
25 |
0.040 |
|
|
|
|
|
|
|
33 |
A |
2 |
1 |
1.00 |
23 |
0.043 |
|
|
|
|
|
|
|
34 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
35 |
A |
7 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
36 |
A |
8 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
37 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
38 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
39 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
40 |
A |
6 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
41 |
A |
9 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
42 |
A |
10 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
43 |
A |
11 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
44 |
A |
7 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
45 |
A |
7 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
46 |
A |
7 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
48 |
A |
10 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
49 |
A |
11 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
50 |
A |
12 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
51 |
A |
8 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
52 |
A |
8 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
53 |
A |
5 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
54 |
A |
5 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
55 |
A |
11 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
56 |
A |
12 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
57 |
A |
13 |
7 |
1.00 |
25 |
0.280 |
|
|
|
|
|
|
|
58 |
A |
11 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
59 |
A |
9 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
60 |
A |
7 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
61 |
A |
5 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
62 |
A |
8 |
7 |
1.00 |
27 |
0.259 |
|
|
|
|
|
|
|
63 |
A |
6 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
64 |
A |
7 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
65 |
A |
12 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
66 |
A |
10 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
67 |
A |
8 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
68 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
69 |
A |
9 |
8 |
1.00 |
27 |
0.296 |
|
|
|
|
|
|
|
70 |
A |
10 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
71 |
A |
7 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
72 |
A |
13 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
73 |
A |
11 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
74 |
A |
9 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
75 |
A |
7 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
76 |
A |
10 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
77 |
A |
11 |
9 |
1.00 |
27 |
0.333 |
|
|
|
|
|
|
|
78 |
A |
11 |
10 |
1.00 |
27 |
0.370 |
|
|
|
|
|
|
|
79 |
A |
10 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
80 |
A |
8 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
81 |
A |
6 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
82 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
83 |
A |
5 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
84 |
A |
6 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
85 |
A |
7 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
86 |
A |
9 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
87 |
A |
7 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
88 |
A |
5 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
89 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
90 |
A |
6 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
91 |
A |
7 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
92 |
A |
8 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
93 |
A |
8 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
94 |
A |
6 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
95 |
A |
5 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
96 |
A |
3 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
97 |
A |
7 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
98 |
A |
8 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
99 |
A |
9 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
100 |
A |
7 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
101 |
A |
5 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
102 |
A |
8 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
103 |
A |
6 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
104 |
A |
8 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
105 |
A |
6 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
106 |
A |
9 |
6 |
1.00 |
27 |
0.222 |
|
|
|
|
|
|
|
107 |
A |
10 |
7 |
1.00 |
27 |
0.259 |
|
|
|
|
|
|
|
108 |
A |
7 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
109 |
A |
8 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
110 |
A |
6 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
111 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
112 |
A |
5 |
3 |
1.00 |
27 |
0.111 |
|
|
|
|
|
|
|
113 |
A |
6 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
114 |
A |
7 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
115 |
A |
5 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
116 |
A |
4 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
117 |
A |
6 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
118 |
A |
6 |
5 |
1.00 |
27 |
0.185 |
|
|
|
|
|
|
|
119 |
A |
5 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
120 |
A |
3 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
121 |
A |
5 |
4 |
1.00 |
27 |
0.148 |
|
|
|
|
|
|
|
122 |
A |
3 |
3 |
1.00 |
29 |
0.103 |
|
|
|
|
|
|
|
123 |
A |
3 |
3 |
1.00 |
29 |
0.103 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|