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
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
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, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93 }
B grade: { }
C grade: { 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 94, 95, 96, 97,
98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111 }
F grade: { }
2.1.3 Maple
A grade: { 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 37,
43, 44, 45, 46, 47, 48, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76,
77, 83, 84, 85, 86, 91, 92, 93 }
B grade: { 1, 2, 10, 11, 12, 33, 34, 35, 36, 38, 39, 40, 41, 42, 49, 50, 51, 52, 72, 78, 79, 80, 81, 82, 87, 88,
89, 90 }
C grade: { 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111
}
F grade: { }
2.1.4 Maxima
A grade: { 1, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 22, 24, 25, 26, 27, 28, 29, 30, 31, 36, 40, 41, 43, 45, 46, 47,
48, 49, 50, 51, 53, 54, 55, 56, 79, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93 }
B grade: { 2, 3, 4, 5, 11, 12, 13, 19, 20, 21, 23, 42, 44, 52, 80, 81, 83 }
C grade: { }
F grade: { 32, 33, 34, 35, 37, 38, 39, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
75, 76, 77, 78, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111
}
2.1.5 FriCAS
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,
31, 32, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 60, 62, 79, 80, 81, 82, 83, 84, 85,
86, 87, 88, 89, 90, 91, 92, 93 }
B grade: { 30, 33, 35, 36, 37, 38, 39, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
75, 76, 77, 78, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111
}
C grade: { }
F grade: { }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 10, 11, 12, 13, 40, 41, 42, 43, 44, 49, 50, 51, 52, 79, 80, 81, 82, 83, 87, 88, 89
}
B grade: { }
C grade: { }
F grade: { 6, 7, 8, 9, 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, 45, 46, 47, 48, 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, 84, 85, 86, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110, 111 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 40, 41, 42, 43, 44,
45, 46, 47, 48, 49, 50, 51, 54, 55, 56, 79, 80, 81, 82, 83, 85, 86, 87, 88, 92 }
B grade: { 12, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 52, 53, 84, 89, 90, 91, 93
}
C grade: { }
F grade: { 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 94, 95, 96, 97,
98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111 }
2.1.8 Mupad
A grade: { }
B grade: { 1, 2, 3, 4, 10, 11, 12, 40, 41, 42, 43, 49, 50, 51, 79, 80, 81, 82, 87, 88 }
C grade: { }
F grade: { 5, 6, 7, 8, 9, 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, 44, 45, 46, 47, 48, 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, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104,
105, 106, 107, 108, 109, 110, 111 }
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 |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 82 | 356 | 232 | 85 | 151 | 152 | 122 |
normalized size | 1 | 1.00 | 0.66 | 2.87 | 1.87 | 0.69 | 1.22 | 1.23 | 0.98 |
time (sec) |
N/A |
0.321 |
0.161 |
0.043 |
0.369 |
0.431 |
1.881 |
0.136 |
0.958 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 65 | 224 | 196 | 67 | 117 | 116 | 92 |
normalized size | 1 | 1.00 | 0.69 | 2.38 | 2.09 | 0.71 | 1.24 | 1.23 | 0.98 |
time (sec) |
N/A |
0.217 |
0.137 |
0.041 |
0.409 |
0.999 |
0.938 |
0.113 |
0.962 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 45 | 122 | 160 | 48 | 82 | 79 | 62 |
normalized size | 1 | 1.00 | 0.70 | 1.91 | 2.50 | 0.75 | 1.28 | 1.23 | 0.97 |
time (sec) |
N/A |
0.114 |
0.097 |
0.050 |
0.395 |
0.654 |
0.487 |
0.118 |
0.922 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 27 | 53 | 68 | 30 | 46 | 46 | 35 |
normalized size | 1 | 1.00 | 0.96 | 1.89 | 2.43 | 1.07 | 1.64 | 1.64 | 1.25 |
time (sec) |
N/A |
0.021 |
0.055 |
0.045 |
0.316 |
0.440 |
0.210 |
0.115 |
0.062 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 39 | 52 | 97 | 54 | 34 | 47 | -1 |
normalized size | 1 | 1.00 | 1.39 | 1.86 | 3.46 | 1.93 | 1.21 | 1.68 | -0.04 |
time (sec) |
N/A |
0.149 |
0.029 |
0.088 |
0.532 |
0.762 |
3.192 |
0.138 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 59 | 77 | 82 | 76 | 0 | 72 | -1 |
normalized size | 1 | 1.00 | 1.26 | 1.64 | 1.74 | 1.62 | 0.00 | 1.53 | -0.02 |
time (sec) |
N/A |
0.228 |
0.136 |
0.097 |
0.410 |
0.544 |
0.000 |
0.118 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 78 | 139 | 66 | 116 | 0 | 134 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.58 | 0.75 | 1.32 | 0.00 | 1.52 | -0.01 |
time (sec) |
N/A |
0.281 |
0.166 |
0.098 |
0.429 |
0.521 |
0.000 |
0.123 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 110 | 205 | 78 | 143 | 0 | 199 | -1 |
normalized size | 1 | 1.00 | 0.83 | 1.55 | 0.59 | 1.08 | 0.00 | 1.51 | -0.01 |
time (sec) |
N/A |
0.340 |
0.292 |
0.116 |
0.414 |
0.493 |
0.000 |
0.146 |
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 |
A |
A |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 140 | 271 | 82 | 161 | 0 | 266 | -1 |
normalized size | 1 | 1.00 | 0.84 | 1.63 | 0.49 | 0.97 | 0.00 | 1.60 | -0.01 |
time (sec) |
N/A |
0.406 |
0.350 |
0.117 |
0.408 |
0.554 |
0.000 |
0.144 |
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 |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 100 | 463 | 329 | 127 | 228 | 236 | 168 |
normalized size | 1 | 1.00 | 0.54 | 2.52 | 1.79 | 0.69 | 1.24 | 1.28 | 0.91 |
time (sec) |
N/A |
0.346 |
0.277 |
0.043 |
0.339 |
0.493 |
2.238 |
0.136 |
0.161 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 87 | 283 | 275 | 95 | 172 | 171 | 125 |
normalized size | 1 | 1.00 | 0.65 | 2.11 | 2.05 | 0.71 | 1.28 | 1.28 | 0.93 |
time (sec) |
N/A |
0.214 |
0.217 |
0.041 |
0.333 |
0.535 |
1.154 |
0.117 |
0.923 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 56 | 147 | 135 | 64 | 112 | 112 | 82 |
normalized size | 1 | 1.00 | 1.14 | 3.00 | 2.76 | 1.31 | 2.29 | 2.29 | 1.67 |
time (sec) |
N/A |
0.048 |
0.154 |
0.041 |
0.339 |
0.396 |
0.552 |
0.133 |
0.903 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 51 | 121 | 175 | 94 | 73 | 113 | -1 |
normalized size | 1 | 1.00 | 0.82 | 1.95 | 2.82 | 1.52 | 1.18 | 1.82 | -0.02 |
time (sec) |
N/A |
0.185 |
0.250 |
0.108 |
0.400 |
0.622 |
3.700 |
0.143 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 62 | 118 | 136 | 122 | 0 | 119 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.69 | 1.94 | 1.74 | 0.00 | 1.70 | -0.01 |
time (sec) |
N/A |
0.247 |
0.245 |
0.117 |
0.417 |
0.537 |
0.000 |
0.135 |
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 |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 93 | 181 | 126 | 153 | 0 | 181 | -1 |
normalized size | 1 | 1.00 | 0.77 | 1.50 | 1.04 | 1.26 | 0.00 | 1.50 | -0.01 |
time (sec) |
N/A |
0.339 |
0.399 |
0.113 |
0.442 |
0.627 |
0.000 |
0.119 |
0.000 |
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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 |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 154 | 287 | 117 | 194 | 0 | 285 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.67 | 0.68 | 1.13 | 0.00 | 1.66 | -0.01 |
time (sec) |
N/A |
0.426 |
0.487 |
0.129 |
0.438 |
0.475 |
0.000 |
0.138 |
0.000 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 206 | 396 | 128 | 231 | 0 | 395 | -1 |
normalized size | 1 | 1.00 | 0.83 | 1.60 | 0.52 | 0.93 | 0.00 | 1.59 | -0.00 |
time (sec) |
N/A |
0.521 |
0.586 |
0.135 |
0.438 |
0.471 |
0.000 |
0.143 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
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 | 219 | 219 | 159 | 442 | 437 | 236 | 0 | 407 | -1 |
normalized size | 1 | 1.00 | 0.73 | 2.02 | 2.00 | 1.08 | 0.00 | 1.86 | -0.00 |
time (sec) |
N/A |
0.484 |
0.652 |
0.194 |
0.405 |
0.446 |
0.000 |
0.124 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 19 |
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 | 150 | 150 | 118 | 292 | 328 | 190 | 0 | 256 | -1 |
normalized size | 1 | 1.00 | 0.79 | 1.95 | 2.19 | 1.27 | 0.00 | 1.71 | -0.01 |
time (sec) |
N/A |
0.329 |
0.451 |
0.139 |
0.413 |
0.911 |
0.000 |
0.146 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
Problem 20 |
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 | 100 | 100 | 89 | 184 | 233 | 156 | 0 | 148 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.84 | 2.33 | 1.56 | 0.00 | 1.48 | -0.01 |
time (sec) |
N/A |
0.262 |
0.308 |
0.110 |
0.392 |
0.564 |
0.000 |
0.142 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 21 |
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 | 68 | 68 | 64 | 114 | 156 | 118 | 0 | 83 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.68 | 2.29 | 1.74 | 0.00 | 1.22 | -0.01 |
time (sec) |
N/A |
0.176 |
0.147 |
0.089 |
0.380 |
0.451 |
0.000 |
0.143 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
Problem 22 |
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 | 51 | 51 | 49 | 81 | 57 | 95 | 0 | 56 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.59 | 1.12 | 1.86 | 0.00 | 1.10 | -0.02 |
time (sec) |
N/A |
0.080 |
0.065 |
0.066 |
0.362 |
0.508 |
0.000 |
0.139 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
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 | 73 | 73 | 63 | 108 | 155 | 123 | 0 | 75 | -1 |
normalized size | 1 | 1.00 | 0.86 | 1.48 | 2.12 | 1.68 | 0.00 | 1.03 | -0.01 |
time (sec) |
N/A |
0.259 |
0.150 |
0.082 |
0.413 |
0.638 |
0.000 |
0.141 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
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 | 113 | 113 | 101 | 172 | 192 | 179 | 0 | 129 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.52 | 1.70 | 1.58 | 0.00 | 1.14 | -0.01 |
time (sec) |
N/A |
0.369 |
0.401 |
0.098 |
0.455 |
0.484 |
0.000 |
0.153 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
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 | 190 | 190 | 178 | 281 | 242 | 275 | 0 | 248 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.48 | 1.27 | 1.45 | 0.00 | 1.31 | -0.01 |
time (sec) |
N/A |
0.485 |
0.499 |
0.104 |
0.485 |
0.516 |
0.000 |
0.141 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 231 | 231 | 173 | 431 | 406 | 371 | 0 | 2979 | -1 |
normalized size | 1 | 1.00 | 0.75 | 1.87 | 1.76 | 1.61 | 0.00 | 12.90 | -0.00 |
time (sec) |
N/A |
0.536 |
1.263 |
0.210 |
0.421 |
0.468 |
0.000 |
0.241 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 156 | 325 | 312 | 333 | 0 | 1991 | -1 |
normalized size | 1 | 1.00 | 0.86 | 1.79 | 1.71 | 1.83 | 0.00 | 10.94 | -0.01 |
time (sec) |
N/A |
0.423 |
0.956 |
0.149 |
0.421 |
0.536 |
0.000 |
0.212 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 115 | 254 | 236 | 274 | 0 | 1308 | -1 |
normalized size | 1 | 1.00 | 0.78 | 1.73 | 1.61 | 1.86 | 0.00 | 8.90 | -0.01 |
time (sec) |
N/A |
0.375 |
0.713 |
0.120 |
0.412 |
0.473 |
0.000 |
0.179 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 97 | 215 | 178 | 200 | 0 | 994 | -1 |
normalized size | 1 | 1.00 | 0.78 | 1.72 | 1.42 | 1.60 | 0.00 | 7.95 | -0.01 |
time (sec) |
N/A |
0.297 |
0.443 |
0.102 |
0.406 |
0.385 |
0.000 |
0.189 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 65 | 132 | 81 | 149 | 0 | 615 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.86 | 1.14 | 2.10 | 0.00 | 8.66 | -0.01 |
time (sec) |
N/A |
0.110 |
0.211 |
0.079 |
0.361 |
0.566 |
0.000 |
0.171 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 139 | 254 | 227 | 270 | 0 | 1329 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.69 | 1.51 | 1.80 | 0.00 | 8.86 | -0.01 |
time (sec) |
N/A |
0.400 |
1.212 |
0.098 |
0.465 |
0.612 |
0.000 |
0.196 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 183 | 312 | 0 | 377 | 0 | 3353 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.68 | 0.00 | 2.03 | 0.00 | 18.03 | -0.01 |
time (sec) |
N/A |
0.501 |
1.420 |
0.106 |
0.000 |
0.503 |
0.000 |
0.223 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 264 | 264 | 236 | 571 | 0 | 566 | 0 | 879 | -1 |
normalized size | 1 | 1.00 | 0.89 | 2.16 | 0.00 | 2.14 | 0.00 | 3.33 | -0.00 |
time (sec) |
N/A |
0.618 |
1.047 |
0.195 |
0.000 |
0.870 |
0.000 |
0.145 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 241 | 241 | 153 | 527 | 0 | 475 | 0 | 741 | -1 |
normalized size | 1 | 1.00 | 0.63 | 2.19 | 0.00 | 1.97 | 0.00 | 3.07 | -0.00 |
time (sec) |
N/A |
0.530 |
0.973 |
0.132 |
0.000 |
0.615 |
0.000 |
0.131 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 158 | 435 | 0 | 373 | 0 | 529 | -1 |
normalized size | 1 | 1.00 | 0.89 | 2.44 | 0.00 | 2.10 | 0.00 | 2.97 | -0.01 |
time (sec) |
N/A |
0.370 |
0.597 |
0.107 |
0.000 |
0.533 |
0.000 |
0.138 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 88 | 276 | 95 | 253 | 0 | 298 | -1 |
normalized size | 1 | 1.00 | 0.85 | 2.65 | 0.91 | 2.43 | 0.00 | 2.87 | -0.01 |
time (sec) |
N/A |
0.146 |
0.511 |
0.087 |
0.363 |
0.484 |
0.000 |
0.125 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 451 | 488 | 0 | 601 | 0 | 837 | -1 |
normalized size | 1 | 1.00 | 1.72 | 1.86 | 0.00 | 2.29 | 0.00 | 3.19 | -0.00 |
time (sec) |
N/A |
0.561 |
1.376 |
0.110 |
0.000 |
0.479 |
0.000 |
0.143 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 541 | 643 | 0 | 762 | 0 | 1006 | -1 |
normalized size | 1 | 1.00 | 1.82 | 2.16 | 0.00 | 2.56 | 0.00 | 3.38 | -0.00 |
time (sec) |
N/A |
0.690 |
1.572 |
0.131 |
0.000 |
0.537 |
0.000 |
0.146 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 627 | 760 | 0 | 892 | 0 | 1169 | -1 |
normalized size | 1 | 1.00 | 1.66 | 2.02 | 0.00 | 2.37 | 0.00 | 3.10 | -0.00 |
time (sec) |
N/A |
0.821 |
1.869 |
0.143 |
0.000 |
0.561 |
0.000 |
0.139 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 92 | 447 | 250 | 95 | 168 | 174 | 116 |
normalized size | 1 | 1.00 | 0.66 | 3.22 | 1.80 | 0.68 | 1.21 | 1.25 | 0.83 |
time (sec) |
N/A |
0.255 |
0.170 |
0.042 |
0.324 |
0.528 |
3.424 |
0.123 |
0.991 |
|
|
|
|
|
|
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|
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|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 74 | 298 | 214 | 78 | 134 | 138 | 93 |
normalized size | 1 | 1.00 | 0.68 | 2.73 | 1.96 | 0.72 | 1.23 | 1.27 | 0.85 |
time (sec) |
N/A |
0.187 |
0.138 |
0.044 |
0.329 |
0.466 |
1.963 |
0.120 |
0.934 |
|
|
|
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|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 57 | 183 | 213 | 60 | 99 | 101 | 70 |
normalized size | 1 | 1.00 | 0.72 | 2.32 | 2.70 | 0.76 | 1.25 | 1.28 | 0.89 |
time (sec) |
N/A |
0.121 |
0.122 |
0.041 |
0.325 |
0.423 |
0.993 |
0.114 |
0.975 |
|
|
|
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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 | 51 | 51 | 40 | 97 | 86 | 42 | 65 | 70 | 47 |
normalized size | 1 | 1.00 | 0.78 | 1.90 | 1.69 | 0.82 | 1.27 | 1.37 | 0.92 |
time (sec) |
N/A |
0.067 |
0.074 |
0.044 |
0.326 |
0.441 |
0.485 |
0.146 |
0.925 |
|
|
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Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 55 | 81 | 122 | 73 | 49 | 76 | -1 |
normalized size | 1 | 1.00 | 1.34 | 1.98 | 2.98 | 1.78 | 1.20 | 1.85 | -0.02 |
time (sec) |
N/A |
0.098 |
0.119 |
0.101 |
0.391 |
0.540 |
3.414 |
0.121 |
0.000 |
|
|
|
|
|
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|
Problem 45 |
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 | 42 | 42 | 42 | 81 | 80 | 82 | 0 | 80 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.93 | 1.90 | 1.95 | 0.00 | 1.90 | -0.02 |
time (sec) |
N/A |
0.107 |
0.091 |
0.110 |
0.383 |
0.575 |
0.000 |
0.121 |
0.000 |
|
|
|
|
|
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|
Problem 46 |
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 | 74 | 74 | 80 | 110 | 90 | 107 | 0 | 109 | -1 |
normalized size | 1 | 1.00 | 1.08 | 1.49 | 1.22 | 1.45 | 0.00 | 1.47 | -0.01 |
time (sec) |
N/A |
0.178 |
0.160 |
0.112 |
0.410 |
0.499 |
0.000 |
0.119 |
0.000 |
|
|
|
|
|
|
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|
|
Problem 47 |
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 | 95 | 172 | 73 | 127 | 0 | 170 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.64 | 0.70 | 1.21 | 0.00 | 1.62 | -0.01 |
time (sec) |
N/A |
0.234 |
0.237 |
0.120 |
0.410 |
0.507 |
0.000 |
0.120 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 127 | 238 | 76 | 152 | 0 | 237 | -1 |
normalized size | 1 | 1.00 | 0.85 | 1.60 | 0.51 | 1.02 | 0.00 | 1.59 | -0.01 |
time (sec) |
N/A |
0.290 |
0.286 |
0.122 |
0.414 |
0.483 |
0.000 |
0.144 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 234 | 138 | 738 | 383 | 155 | 286 | 304 | 182 |
normalized size | 1 | 1.00 | 0.59 | 3.15 | 1.64 | 0.66 | 1.22 | 1.30 | 0.78 |
time (sec) |
N/A |
0.388 |
0.349 |
0.046 |
0.339 |
0.623 |
6.018 |
0.143 |
1.031 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 113 | 513 | 353 | 126 | 226 | 239 | 148 |
normalized size | 1 | 1.00 | 0.61 | 2.79 | 1.92 | 0.68 | 1.23 | 1.30 | 0.80 |
time (sec) |
N/A |
0.277 |
0.248 |
0.045 |
0.332 |
0.615 |
3.577 |
0.144 |
0.982 |
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 85 | 332 | 189 | 98 | 172 | 180 | 114 |
normalized size | 1 | 1.00 | 0.62 | 2.44 | 1.39 | 0.72 | 1.26 | 1.32 | 0.84 |
time (sec) |
N/A |
0.181 |
0.197 |
0.046 |
0.336 |
0.437 |
2.105 |
0.137 |
0.118 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 82 | 226 | 235 | 130 | 121 | 222 | -1 |
normalized size | 1 | 1.00 | 0.75 | 2.05 | 2.14 | 1.18 | 1.10 | 2.02 | -0.01 |
time (sec) |
N/A |
0.189 |
0.390 |
0.147 |
0.400 |
0.588 |
4.773 |
0.127 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 95 | 190 | 179 | 127 | 0 | 197 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.00 | 1.88 | 1.34 | 0.00 | 2.07 | -0.01 |
time (sec) |
N/A |
0.177 |
0.281 |
0.164 |
0.502 |
0.763 |
0.000 |
0.125 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
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 | 114 | 114 | 97 | 188 | 165 | 164 | 0 | 206 | -1 |
normalized size | 1 | 1.00 | 0.85 | 1.65 | 1.45 | 1.44 | 0.00 | 1.81 | -0.01 |
time (sec) |
N/A |
0.225 |
0.396 |
0.171 |
0.427 |
0.895 |
0.000 |
0.127 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
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 | 133 | 133 | 114 | 222 | 135 | 171 | 0 | 236 | -1 |
normalized size | 1 | 1.00 | 0.86 | 1.67 | 1.02 | 1.29 | 0.00 | 1.77 | -0.01 |
time (sec) |
N/A |
0.259 |
0.436 |
0.183 |
0.421 |
0.482 |
0.000 |
0.124 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
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 | 175 | 175 | 124 | 291 | 139 | 194 | 0 | 294 | -1 |
normalized size | 1 | 1.00 | 0.71 | 1.66 | 0.79 | 1.11 | 0.00 | 1.68 | -0.01 |
time (sec) |
N/A |
0.360 |
0.488 |
0.196 |
0.452 |
0.546 |
0.000 |
0.142 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 273 | 273 | 274 | 369 | 0 | 605 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.35 | 0.00 | 2.22 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.729 |
0.454 |
0.293 |
0.000 |
0.800 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 210 | 268 | 0 | 502 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.28 | 0.00 | 2.40 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.358 |
0.390 |
0.214 |
0.000 |
1.114 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 213 | 259 | 0 | 496 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.15 | 0.00 | 2.19 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.376 |
0.270 |
0.148 |
0.000 |
0.743 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 171 | 200 | 0 | 219 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 1.13 | 0.00 | 1.24 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.254 |
0.186 |
0.110 |
0.000 |
0.659 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 180 | 212 | 0 | 316 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 1.00 | 0.00 | 1.48 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.259 |
0.205 |
0.102 |
0.000 |
0.728 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 187 | 227 | 0 | 249 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 1.15 | 0.00 | 1.26 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.372 |
0.334 |
0.103 |
0.000 |
0.689 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 243 | 288 | 0 | 599 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.16 | 0.00 | 2.41 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.496 |
0.380 |
0.122 |
0.000 |
0.511 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 257 | 330 | 0 | 583 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 1.22 | 0.00 | 2.16 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.504 |
0.569 |
0.115 |
0.000 |
0.491 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 449 | 449 | 621 | 532 | 0 | 1179 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.38 | 1.18 | 0.00 | 2.63 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.859 |
1.626 |
0.406 |
0.000 |
0.639 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 582 | 495 | 0 | 931 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 1.15 | 0.00 | 2.16 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.701 |
0.794 |
0.278 |
0.000 |
0.521 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 364 | 491 | 0 | 1162 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 1.18 | 0.00 | 2.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.611 |
1.064 |
0.226 |
0.000 |
0.580 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 239 | 239 | 239 | 291 | 0 | 641 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.22 | 0.00 | 2.68 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.325 |
0.534 |
0.182 |
0.000 |
0.573 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 590 | 503 | 0 | 1162 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 1.06 | 0.00 | 2.44 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.818 |
0.740 |
0.111 |
0.000 |
0.508 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 435 | 435 | 501 | 546 | 0 | 992 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 1.26 | 0.00 | 2.28 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.839 |
1.333 |
0.157 |
0.000 |
0.673 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 500 | 500 | 675 | 595 | 0 | 1310 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 1.19 | 0.00 | 2.62 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.253 |
1.091 |
0.174 |
0.000 |
0.640 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 648 | 820 | 0 | 1620 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.36 | 1.72 | 0.00 | 3.40 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.062 |
1.967 |
0.477 |
0.000 |
0.509 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 746 | 746 | 932 | 1064 | 0 | 2047 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.25 | 1.43 | 0.00 | 2.74 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.100 |
2.671 |
0.327 |
0.000 |
0.476 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 512 | 512 | 637 | 743 | 0 | 1607 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 1.45 | 0.00 | 3.14 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.831 |
1.847 |
0.227 |
0.000 |
0.587 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 856 | 856 | 933 | 1064 | 0 | 2116 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 1.24 | 0.00 | 2.47 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.255 |
2.601 |
0.146 |
0.000 |
0.665 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 730 | 730 | 1046 | 1090 | 0 | 2076 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.43 | 1.49 | 0.00 | 2.84 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.682 |
2.614 |
0.178 |
0.000 |
0.553 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 874 | 874 | 1009 | 1178 | 0 | 2346 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 1.35 | 0.00 | 2.68 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.689 |
2.945 |
0.201 |
0.000 |
0.609 |
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(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 998 | 1294 | 0 | 2363 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 1.64 | 0.00 | 2.99 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.868 |
4.020 |
0.233 |
0.000 |
0.529 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 100 | 551 | 268 | 105 | 185 | 192 | 152 |
normalized size | 1 | 1.00 | 0.65 | 3.58 | 1.74 | 0.68 | 1.20 | 1.25 | 0.99 |
time (sec) |
N/A |
0.297 |
0.185 |
0.042 |
1.090 |
0.466 |
5.708 |
0.119 |
1.046 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 84 | 389 | 267 | 87 | 151 | 156 | 122 |
normalized size | 1 | 1.00 | 0.68 | 3.14 | 2.15 | 0.70 | 1.22 | 1.26 | 0.98 |
time (sec) |
N/A |
0.228 |
0.147 |
0.046 |
0.340 |
0.514 |
3.252 |
0.125 |
0.960 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 66 | 257 | 196 | 68 | 116 | 119 | 92 |
normalized size | 1 | 1.00 | 0.70 | 2.73 | 2.09 | 0.72 | 1.23 | 1.27 | 0.98 |
time (sec) |
N/A |
0.159 |
0.124 |
0.041 |
0.346 |
0.595 |
1.920 |
0.132 |
0.924 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 49 | 158 | 104 | 53 | 82 | 88 | 65 |
normalized size | 1 | 1.00 | 0.74 | 2.39 | 1.58 | 0.80 | 1.24 | 1.33 | 0.98 |
time (sec) |
N/A |
0.103 |
0.097 |
0.043 |
0.341 |
0.572 |
0.940 |
0.124 |
0.098 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 49 | 113 | 140 | 86 | 66 | 109 | -1 |
normalized size | 1 | 1.00 | 0.88 | 2.02 | 2.50 | 1.54 | 1.18 | 1.95 | -0.02 |
time (sec) |
N/A |
0.128 |
0.182 |
0.116 |
0.397 |
0.549 |
3.906 |
0.146 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 55 | 110 | 102 | 90 | 0 | 111 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.00 | 1.85 | 1.64 | 0.00 | 2.02 | -0.02 |
time (sec) |
N/A |
0.129 |
0.142 |
0.139 |
0.398 |
0.591 |
0.000 |
0.140 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
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 | 69 | 69 | 86 | 114 | 87 | 101 | 0 | 118 | -1 |
normalized size | 1 | 1.00 | 1.25 | 1.65 | 1.26 | 1.46 | 0.00 | 1.71 | -0.01 |
time (sec) |
N/A |
0.139 |
0.148 |
0.129 |
0.396 |
0.445 |
0.000 |
0.121 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
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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 | 91 | 91 | 73 | 143 | 95 | 118 | 0 | 141 | -1 |
normalized size | 1 | 1.00 | 0.80 | 1.57 | 1.04 | 1.30 | 0.00 | 1.55 | -0.01 |
time (sec) |
N/A |
0.215 |
0.263 |
0.132 |
0.419 |
0.483 |
0.000 |
0.117 |
0.000 |
|
|
|
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Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 234 | 139 | 818 | 383 | 161 | 284 | 303 | 301 |
normalized size | 1 | 1.00 | 0.59 | 3.50 | 1.64 | 0.69 | 1.21 | 1.29 | 1.29 |
time (sec) |
N/A |
0.395 |
0.320 |
0.045 |
0.346 |
0.470 |
9.632 |
0.118 |
0.354 |
|
|
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Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 111 | 592 | 243 | 130 | 226 | 244 | 182 |
normalized size | 1 | 1.00 | 0.60 | 3.18 | 1.31 | 0.70 | 1.22 | 1.31 | 0.98 |
time (sec) |
N/A |
0.287 |
0.244 |
0.042 |
0.345 |
0.654 |
5.855 |
0.136 |
0.241 |
|
|
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Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 108 | 335 | 289 | 161 | 168 | 331 | -1 |
normalized size | 1 | 1.00 | 0.68 | 2.09 | 1.81 | 1.01 | 1.05 | 2.07 | -0.01 |
time (sec) |
N/A |
0.282 |
0.515 |
0.188 |
0.410 |
0.576 |
8.103 |
0.152 |
0.000 |
|
|
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Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 143 | 296 | 235 | 160 | 0 | 308 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.07 | 1.64 | 1.12 | 0.00 | 2.15 | -0.01 |
time (sec) |
N/A |
0.252 |
0.377 |
0.207 |
0.403 |
0.553 |
0.000 |
0.124 |
0.000 |
|
|
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Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 136 | 265 | 203 | 161 | 0 | 280 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.88 | 1.44 | 1.14 | 0.00 | 1.99 | -0.01 |
time (sec) |
N/A |
0.233 |
0.376 |
0.219 |
0.394 |
0.440 |
0.000 |
0.127 |
0.000 |
|
|
|
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Problem 92 |
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 | 150 | 150 | 135 | 261 | 188 | 187 | 0 | 279 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.74 | 1.25 | 1.25 | 0.00 | 1.86 | -0.01 |
time (sec) |
N/A |
0.279 |
0.633 |
0.237 |
0.439 |
0.453 |
0.000 |
0.129 |
0.000 |
|
|
|
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|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 150 | 292 | 154 | 196 | 0 | 315 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.75 | 0.92 | 1.17 | 0.00 | 1.89 | -0.01 |
time (sec) |
N/A |
0.308 |
0.576 |
0.257 |
0.459 |
0.403 |
0.000 |
0.138 |
0.000 |
|
|
|
|
|
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Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 373 | 373 | 213 | 925 | 0 | 989 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.57 | 2.48 | 0.00 | 2.65 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.937 |
0.511 |
0.187 |
0.000 |
0.534 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 358 | 358 | 198 | 671 | 0 | 977 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.55 | 1.87 | 0.00 | 2.73 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.648 |
0.284 |
0.143 |
0.000 |
0.585 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
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|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 283 | 283 | 170 | 423 | 0 | 500 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.60 | 1.49 | 0.00 | 1.77 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.455 |
0.240 |
0.120 |
0.000 |
0.450 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 345 | 345 | 180 | 280 | 0 | 671 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.52 | 0.81 | 0.00 | 1.94 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.412 |
0.223 |
0.119 |
0.000 |
0.573 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 345 | 345 | 180 | 143 | 0 | 673 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.52 | 0.41 | 0.00 | 1.95 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.401 |
0.136 |
0.094 |
0.000 |
0.652 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 303 | 303 | 186 | 138 | 0 | 530 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.61 | 0.46 | 0.00 | 1.75 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.523 |
0.283 |
0.111 |
0.000 |
0.524 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 381 | 381 | 215 | 187 | 0 | 1154 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.49 | 0.00 | 3.03 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.600 |
0.435 |
0.132 |
0.000 |
0.690 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 237 | 240 | 0 | 1251 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.58 | 0.59 | 0.00 | 3.05 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.639 |
0.407 |
0.135 |
0.000 |
0.566 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 718 | 718 | 363 | 877 | 0 | 2050 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.51 | 1.22 | 0.00 | 2.86 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.081 |
0.367 |
0.250 |
0.000 |
0.605 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 373 | 373 | 203 | 594 | 0 | 1276 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.54 | 1.59 | 0.00 | 3.42 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.601 |
0.178 |
0.194 |
0.000 |
0.469 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 695 | 695 | 387 | 395 | 0 | 2135 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.57 | 0.00 | 3.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.324 |
0.204 |
0.158 |
0.000 |
0.944 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 739 | 739 | 387 | 226 | 0 | 2048 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.52 | 0.31 | 0.00 | 2.77 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.323 |
0.210 |
0.124 |
0.000 |
0.721 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 697 | 697 | 411 | 338 | 0 | 1773 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.59 | 0.48 | 0.00 | 2.54 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.472 |
0.826 |
0.147 |
0.000 |
0.683 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 784 | 784 | 397 | 2448 | 0 | 2980 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.51 | 3.12 | 0.00 | 3.80 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.626 |
0.677 |
0.683 |
0.000 |
1.004 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1105 | 1105 | 675 | 1927 | 0 | 4691 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.61 | 1.74 | 0.00 | 4.25 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.853 |
0.577 |
0.479 |
0.000 |
0.589 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 776 | 776 | 429 | 1456 | 0 | 2962 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.55 | 1.88 | 0.00 | 3.82 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.659 |
0.705 |
0.405 |
0.000 |
0.648 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 781 | 781 | 423 | 994 | 0 | 2972 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.54 | 1.27 | 0.00 | 3.81 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.449 |
0.458 |
0.346 |
0.000 |
0.692 |
0.000 |
0.000 |
0.000 |
|
|
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|
|
|
|
|
|
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|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1147 | 1147 | 669 | 810 | 0 | 4691 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.58 | 0.71 | 0.00 | 4.09 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.198 |
0.502 |
0.258 |
0.000 |
0.683 |
0.000 |
0.000 |
0.000 |
|
|
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|
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 [111] had the largest ratio of
[.5294]
|
|
|
|
|
|
|
| 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 |
11 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
2 |
A |
9 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
3 |
A |
7 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
4 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
5 |
A |
6 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
6 |
A |
9 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
7 |
A |
11 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
8 |
A |
13 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
9 |
A |
15 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
10 |
A |
14 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
11 |
A |
11 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
12 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
13 |
A |
8 |
7 |
1.00 |
17 |
0.412 |
|
|
|
|
|
|
|
14 |
A |
10 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
15 |
A |
14 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
16 |
A |
17 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
17 |
A |
20 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
18 |
A |
15 |
7 |
1.00 |
17 |
0.412 |
|
|
|
|
|
|
|
19 |
A |
11 |
7 |
1.00 |
17 |
0.412 |
|
|
|
|
|
|
|
20 |
A |
8 |
7 |
1.00 |
17 |
0.412 |
|
|
|
|
|
|
|
21 |
A |
6 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
22 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
23 |
A |
8 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
24 |
A |
12 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
25 |
A |
17 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
26 |
A |
15 |
8 |
1.00 |
17 |
0.471 |
|
|
|
|
|
|
|
27 |
A |
12 |
8 |
1.00 |
17 |
0.471 |
|
|
|
|
|
|
|
28 |
A |
10 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
29 |
A |
9 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
30 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
31 |
A |
12 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
32 |
A |
16 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
33 |
A |
15 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
34 |
A |
14 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
35 |
A |
11 |
5 |
1.00 |
15 |
0.333 |
|
|
|
|
|
|
|
36 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
37 |
A |
17 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
38 |
A |
21 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
39 |
A |
26 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
40 |
A |
12 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
41 |
A |
10 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
42 |
A |
8 |
3 |
1.00 |
15 |
0.200 |
|
|
|
|
|
|
|
43 |
A |
6 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
44 |
A |
7 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
45 |
A |
7 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
46 |
A |
10 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
47 |
A |
12 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
48 |
A |
14 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
49 |
A |
17 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
50 |
A |
14 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
51 |
A |
11 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
52 |
A |
11 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
53 |
A |
10 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
54 |
A |
12 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
55 |
A |
13 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
56 |
A |
17 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
57 |
A |
14 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
58 |
A |
12 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
59 |
A |
11 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
60 |
A |
8 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
61 |
A |
8 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
62 |
A |
13 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
63 |
A |
14 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
64 |
A |
18 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
65 |
A |
24 |
9 |
1.00 |
19 |
0.474 |
|
|
|
|
|
|
|
66 |
A |
20 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
67 |
A |
17 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
68 |
A |
9 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
69 |
A |
18 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
70 |
A |
22 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
71 |
A |
32 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
72 |
A |
27 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
73 |
A |
28 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
74 |
A |
19 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
75 |
A |
28 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
76 |
A |
41 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
77 |
A |
60 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
78 |
A |
46 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
79 |
A |
13 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
80 |
A |
11 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
81 |
A |
9 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
82 |
A |
7 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
83 |
A |
8 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
84 |
A |
8 |
7 |
1.00 |
17 |
0.412 |
|
|
|
|
|
|
|
85 |
A |
8 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
86 |
A |
11 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
87 |
A |
17 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
88 |
A |
14 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
89 |
A |
14 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
90 |
A |
13 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
91 |
A |
12 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
92 |
A |
14 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
93 |
A |
15 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
94 |
A |
15 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
95 |
A |
14 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
96 |
A |
11 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
97 |
A |
11 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
98 |
A |
11 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
99 |
A |
16 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
100 |
A |
17 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
101 |
A |
18 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
102 |
A |
23 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
103 |
A |
12 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
104 |
A |
34 |
7 |
1.00 |
17 |
0.412 |
|
|
|
|
|
|
|
105 |
A |
36 |
8 |
1.00 |
16 |
0.500 |
|
|
|
|
|
|
|
106 |
A |
41 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
107 |
A |
36 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
108 |
A |
47 |
9 |
1.00 |
19 |
0.474 |
|
|
|
|
|
|
|
109 |
A |
71 |
10 |
1.00 |
19 |
0.526 |
|
|
|
|
|
|
|
110 |
A |
37 |
9 |
1.00 |
19 |
0.474 |
|
|
|
|
|
|
|
111 |
A |
89 |
9 |
1.00 |
17 |
0.529 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|