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 }
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, 112, 113 }
F grade: { }
2.1.3 Maple
A grade: { 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 22, 23, 24, 25, 30, 31, 32, 36, 37, 38, 39, 43,
44, 45, 46, 47, 48, 53, 54, 55, 56, 61, 62, 63, 64, 69, 70, 71, 75, 76, 78, 83, 84, 85, 86, 91, 92, 93
}
B grade: { 1, 2, 10, 11, 12, 18, 19, 20, 21, 26, 27, 28, 29, 33, 34, 35, 40, 41, 42, 49, 50, 51, 52, 57, 58, 59,
60, 65, 66, 67, 68, 72, 73, 74, 77, 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, 112, 113
}
F grade: { }
2.1.4 Maxima
A grade: { 3, 4, 11, 43 }
B grade: { 1, 2, 10, 12, 40, 41, 42, 49, 50, 51, 79, 80, 81, 82, 87, 88 }
C grade: { 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 21, 22, 30, 36, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 83, 84, 85, 86,
89, 90, 91, 92, 93 }
F grade: { 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 31, 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, 112, 113 }
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,
30, 31, 32, 33, 34, 35, 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: { 36, 37, 38, 39 }
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, 112, 113 }
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, 112, 113 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 10, 11, 12, 40, 41, 42, 43, 49, 50, 51, 79, 80, 81, 82, 87, 88 }
B grade: { 26, 27, 28, 29, 30, 31, 32 }
C grade: { 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 36, 44, 45, 46, 47, 48, 52, 53, 54, 55,
56, 83, 84, 85, 86, 89, 90, 91, 92, 93 }
F grade: { 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, 112, 113
}
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, 112, 113 }
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 |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 82 | 359 | 306 | 85 | 151 | 86 | 122 |
normalized size | 1 | 1.00 | 0.65 | 2.85 | 2.43 | 0.67 | 1.20 | 0.68 | 0.97 |
time (sec) |
N/A |
0.312 |
0.169 |
0.023 |
0.538 |
0.554 |
2.341 |
0.358 |
0.279 |
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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 | 96 | 96 | 65 | 225 | 201 | 67 | 117 | 68 | 92 |
normalized size | 1 | 1.00 | 0.68 | 2.34 | 2.09 | 0.70 | 1.22 | 0.71 | 0.96 |
time (sec) |
N/A |
0.208 |
0.147 |
0.024 |
0.472 |
0.527 |
1.145 |
0.417 |
4.619 |
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Problem 3 |
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 | 65 | 65 | 45 | 121 | 117 | 48 | 82 | 49 | 62 |
normalized size | 1 | 1.00 | 0.69 | 1.86 | 1.80 | 0.74 | 1.26 | 0.75 | 0.95 |
time (sec) |
N/A |
0.105 |
0.104 |
0.021 |
0.382 |
0.732 |
0.591 |
0.512 |
4.499 |
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Problem 4 |
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 | 28 | 28 | 27 | 52 | 53 | 30 | 46 | 31 | 35 |
normalized size | 1 | 1.00 | 0.96 | 1.86 | 1.89 | 1.07 | 1.64 | 1.11 | 1.25 |
time (sec) |
N/A |
0.017 |
0.077 |
0.023 |
0.434 |
0.701 |
0.239 |
1.055 |
4.485 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 40 | 31 | 522 | 44 | 37 | 339 | -1 |
normalized size | 1 | 1.00 | 1.38 | 1.07 | 18.00 | 1.52 | 1.28 | 11.69 | -0.03 |
time (sec) |
N/A |
0.148 |
0.038 |
0.027 |
0.644 |
0.494 |
6.401 |
0.481 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 60 | 56 | 108 | 75 | 0 | 569 | -1 |
normalized size | 1 | 1.00 | 1.25 | 1.17 | 2.25 | 1.56 | 0.00 | 11.85 | -0.02 |
time (sec) |
N/A |
0.221 |
0.143 |
0.033 |
1.246 |
0.599 |
0.000 |
0.488 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 76 | 88 | 111 | 111 | 0 | 796 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.99 | 1.25 | 1.25 | 0.00 | 8.94 | -0.01 |
time (sec) |
N/A |
0.270 |
0.269 |
0.039 |
1.604 |
0.712 |
0.000 |
0.539 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 110 | 117 | 110 | 137 | 0 | 961 | -1 |
normalized size | 1 | 1.00 | 0.83 | 0.89 | 0.83 | 1.04 | 0.00 | 7.28 | -0.01 |
time (sec) |
N/A |
0.325 |
0.342 |
0.035 |
2.141 |
0.491 |
0.000 |
0.537 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 138 | 145 | 112 | 154 | 0 | 1108 | -1 |
normalized size | 1 | 1.00 | 0.83 | 0.87 | 0.67 | 0.93 | 0.00 | 6.67 | -0.01 |
time (sec) |
N/A |
0.368 |
0.289 |
0.033 |
1.920 |
0.751 |
0.000 |
0.846 |
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 |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 101 | 468 | 406 | 126 | 228 | 128 | 172 |
normalized size | 1 | 1.00 | 0.54 | 2.52 | 2.18 | 0.68 | 1.23 | 0.69 | 0.92 |
time (sec) |
N/A |
0.320 |
0.293 |
0.025 |
0.929 |
0.670 |
2.690 |
0.498 |
0.295 |
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Problem 11 |
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 | 135 | 135 | 87 | 281 | 259 | 95 | 172 | 95 | 128 |
normalized size | 1 | 1.00 | 0.64 | 2.08 | 1.92 | 0.70 | 1.27 | 0.70 | 0.95 |
time (sec) |
N/A |
0.186 |
0.224 |
0.026 |
0.754 |
0.714 |
1.368 |
0.752 |
4.763 |
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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 |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 57 | 148 | 141 | 63 | 112 | 65 | 84 |
normalized size | 1 | 1.00 | 1.14 | 2.96 | 2.82 | 1.26 | 2.24 | 1.30 | 1.68 |
time (sec) |
N/A |
0.042 |
0.183 |
0.024 |
0.950 |
0.608 |
0.722 |
0.569 |
4.700 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 51 | 79 | 80 | 78 | 90 | 551 | -1 |
normalized size | 1 | 1.00 | 0.82 | 1.27 | 1.29 | 1.26 | 1.45 | 8.89 | -0.02 |
time (sec) |
N/A |
0.183 |
0.310 |
0.030 |
1.743 |
0.773 |
4.906 |
0.744 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 64 | 74 | 123 | 111 | 0 | 743 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.03 | 1.71 | 1.54 | 0.00 | 10.32 | -0.01 |
time (sec) |
N/A |
0.242 |
0.264 |
0.038 |
2.534 |
0.751 |
0.000 |
1.582 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 95 | 114 | 187 | 147 | 0 | 1182 | -1 |
normalized size | 1 | 1.00 | 0.79 | 0.94 | 1.55 | 1.21 | 0.00 | 9.77 | -0.01 |
time (sec) |
N/A |
0.340 |
0.438 |
0.037 |
4.287 |
0.582 |
0.000 |
0.993 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 154 | 158 | 188 | 186 | 0 | 1400 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.90 | 1.07 | 1.06 | 0.00 | 8.00 | -0.01 |
time (sec) |
N/A |
0.410 |
0.565 |
0.042 |
5.666 |
0.582 |
0.000 |
0.793 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 204 | 201 | 188 | 222 | 0 | 1712 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.81 | 0.76 | 0.90 | 0.00 | 6.90 | -0.00 |
time (sec) |
N/A |
0.480 |
0.485 |
0.039 |
5.998 |
0.640 |
0.000 |
0.429 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 158 | 777 | 0 | 213 | 0 | 3337 | -1 |
normalized size | 1 | 1.00 | 0.72 | 3.56 | 0.00 | 0.98 | 0.00 | 15.31 | -0.00 |
time (sec) |
N/A |
0.464 |
0.687 |
0.033 |
0.000 |
0.918 |
0.000 |
2.514 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 152 | 152 | 117 | 514 | 0 | 167 | 0 | 2709 | -1 |
normalized size | 1 | 1.00 | 0.77 | 3.38 | 0.00 | 1.10 | 0.00 | 17.82 | -0.01 |
time (sec) |
N/A |
0.306 |
0.577 |
0.028 |
0.000 |
0.573 |
0.000 |
2.122 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 87 | 315 | 0 | 133 | 0 | 2205 | -1 |
normalized size | 1 | 1.00 | 0.88 | 3.18 | 0.00 | 1.34 | 0.00 | 22.27 | -0.01 |
time (sec) |
N/A |
0.262 |
0.318 |
0.026 |
0.000 |
0.650 |
0.000 |
0.929 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 63 | 180 | 776 | 99 | 0 | 1647 | -1 |
normalized size | 1 | 1.00 | 0.91 | 2.61 | 11.25 | 1.43 | 0.00 | 23.87 | -0.01 |
time (sec) |
N/A |
0.166 |
0.199 |
0.025 |
0.528 |
0.640 |
0.000 |
0.838 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 49 | 73 | 141 | 78 | 0 | 597 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.43 | 2.76 | 1.53 | 0.00 | 11.71 | -0.02 |
time (sec) |
N/A |
0.078 |
0.072 |
0.023 |
0.721 |
0.629 |
0.000 |
1.534 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 63 | 99 | 0 | 99 | 0 | 838 | -1 |
normalized size | 1 | 1.00 | 0.86 | 1.36 | 0.00 | 1.36 | 0.00 | 11.48 | -0.01 |
time (sec) |
N/A |
0.261 |
0.167 |
0.031 |
0.000 |
0.782 |
0.000 |
2.055 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 101 | 144 | 0 | 157 | 0 | 2897 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.26 | 0.00 | 1.38 | 0.00 | 25.41 | -0.01 |
time (sec) |
N/A |
0.350 |
0.417 |
0.030 |
0.000 |
0.689 |
0.000 |
0.680 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 176 | 202 | 0 | 245 | 0 | 4565 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.07 | 0.00 | 1.30 | 0.00 | 24.15 | -0.01 |
time (sec) |
N/A |
0.491 |
0.673 |
0.029 |
0.000 |
0.588 |
0.000 |
0.715 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 233 | 233 | 177 | 1214 | 0 | 357 | 0 | 1973 | -1 |
normalized size | 1 | 1.00 | 0.76 | 5.21 | 0.00 | 1.53 | 0.00 | 8.47 | -0.00 |
time (sec) |
N/A |
0.509 |
1.064 |
0.038 |
0.000 |
0.824 |
0.000 |
1.714 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 181 | 181 | 153 | 848 | 0 | 316 | 0 | 1474 | -1 |
normalized size | 1 | 1.00 | 0.85 | 4.69 | 0.00 | 1.75 | 0.00 | 8.14 | -0.01 |
time (sec) |
N/A |
0.408 |
0.913 |
0.036 |
0.000 |
0.722 |
0.000 |
0.791 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 117 | 553 | 0 | 264 | 0 | 1120 | -1 |
normalized size | 1 | 1.00 | 0.79 | 3.71 | 0.00 | 1.77 | 0.00 | 7.52 | -0.01 |
time (sec) |
N/A |
0.363 |
0.836 |
0.033 |
0.000 |
0.699 |
0.000 |
0.748 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 96 | 315 | 0 | 208 | 0 | 951 | -1 |
normalized size | 1 | 1.00 | 0.77 | 2.54 | 0.00 | 1.68 | 0.00 | 7.67 | -0.01 |
time (sec) |
N/A |
0.285 |
0.481 |
0.031 |
0.000 |
0.631 |
0.000 |
0.809 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 66 | 107 | 164 | 123 | 0 | 518 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.49 | 2.28 | 1.71 | 0.00 | 7.19 | -0.01 |
time (sec) |
N/A |
0.097 |
0.225 |
0.026 |
1.076 |
0.600 |
0.000 |
0.385 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 138 | 210 | 0 | 260 | 0 | 1281 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.41 | 0.00 | 1.74 | 0.00 | 8.60 | -0.01 |
time (sec) |
N/A |
0.410 |
1.069 |
0.032 |
0.000 |
0.701 |
0.000 |
0.793 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 184 | 256 | 0 | 355 | 0 | 3180 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.36 | 0.00 | 1.89 | 0.00 | 16.91 | -0.01 |
time (sec) |
N/A |
0.514 |
2.049 |
0.031 |
0.000 |
0.771 |
0.000 |
1.737 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 265 | 265 | 235 | 1208 | 0 | 515 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 4.56 | 0.00 | 1.94 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.610 |
1.118 |
0.037 |
0.000 |
0.704 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 241 | 241 | 154 | 779 | 0 | 438 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.64 | 3.23 | 0.00 | 1.82 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.535 |
1.248 |
0.033 |
0.000 |
0.875 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 157 | 419 | 0 | 346 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 2.34 | 0.00 | 1.93 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.350 |
0.606 |
0.029 |
0.000 |
0.726 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
B |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 87 | 145 | 199 | 210 | 0 | 5727 | -1 |
normalized size | 1 | 1.00 | 0.84 | 1.39 | 1.91 | 2.02 | 0.00 | 55.07 | -0.01 |
time (sec) |
N/A |
0.127 |
0.735 |
0.027 |
0.461 |
0.623 |
0.000 |
1.154 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 449 | 359 | 0 | 532 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.72 | 1.38 | 0.00 | 2.04 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.542 |
1.049 |
0.030 |
0.000 |
0.771 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 299 | 299 | 540 | 405 | 0 | 689 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.81 | 1.35 | 0.00 | 2.30 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.668 |
2.074 |
0.032 |
0.000 |
0.730 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 630 | 466 | 0 | 816 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.67 | 1.24 | 0.00 | 2.16 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.804 |
2.075 |
0.031 |
0.000 |
0.858 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
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 | 141 | 141 | 92 | 449 | 372 | 95 | 168 | 97 | 121 |
normalized size | 1 | 1.00 | 0.65 | 3.18 | 2.64 | 0.67 | 1.19 | 0.69 | 0.86 |
time (sec) |
N/A |
0.208 |
0.183 |
0.023 |
0.344 |
0.641 |
4.127 |
1.875 |
0.344 |
|
|
|
|
|
|
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|
Problem 41 |
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 | 111 | 111 | 75 | 302 | 258 | 77 | 134 | 79 | 97 |
normalized size | 1 | 1.00 | 0.68 | 2.72 | 2.32 | 0.69 | 1.21 | 0.71 | 0.87 |
time (sec) |
N/A |
0.163 |
0.145 |
0.022 |
0.325 |
0.710 |
2.345 |
0.623 |
4.733 |
|
|
|
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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 | 80 | 80 | 57 | 181 | 165 | 60 | 99 | 60 | 73 |
normalized size | 1 | 1.00 | 0.71 | 2.26 | 2.06 | 0.75 | 1.24 | 0.75 | 0.91 |
time (sec) |
N/A |
0.102 |
0.126 |
0.023 |
0.331 |
0.711 |
1.181 |
0.454 |
0.144 |
|
|
|
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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 | 53 | 53 | 41 | 99 | 91 | 41 | 65 | 42 | 49 |
normalized size | 1 | 1.00 | 0.77 | 1.87 | 1.72 | 0.77 | 1.23 | 0.79 | 0.92 |
time (sec) |
N/A |
0.057 |
0.088 |
0.023 |
0.315 |
0.510 |
0.587 |
0.351 |
4.692 |
|
|
|
|
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Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 54 | 60 | 66 | 61 | 63 | 432 | -1 |
normalized size | 1 | 1.00 | 1.32 | 1.46 | 1.61 | 1.49 | 1.54 | 10.54 | -0.02 |
time (sec) |
N/A |
0.091 |
0.137 |
0.026 |
0.636 |
0.764 |
4.904 |
0.769 |
0.000 |
|
|
|
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Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 44 | 48 | 937 | 68 | 0 | 411 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.09 | 21.30 | 1.55 | 0.00 | 9.34 | -0.02 |
time (sec) |
N/A |
0.107 |
0.097 |
0.033 |
0.595 |
0.612 |
0.000 |
0.348 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 82 | 73 | 122 | 85 | 0 | 766 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.99 | 1.65 | 1.15 | 0.00 | 10.35 | -0.01 |
time (sec) |
N/A |
0.161 |
0.194 |
0.034 |
1.033 |
0.729 |
0.000 |
0.317 |
0.000 |
|
|
|
|
|
|
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|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 95 | 102 | 123 | 105 | 0 | 834 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.96 | 1.16 | 0.99 | 0.00 | 7.87 | -0.01 |
time (sec) |
N/A |
0.207 |
0.201 |
0.033 |
1.128 |
0.583 |
0.000 |
0.422 |
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 |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 125 | 131 | 121 | 127 | 0 | 1086 | -1 |
normalized size | 1 | 1.00 | 0.84 | 0.88 | 0.81 | 0.85 | 0.00 | 7.29 | -0.01 |
time (sec) |
N/A |
0.258 |
0.249 |
0.033 |
1.235 |
0.872 |
0.000 |
0.482 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 236 | 236 | 139 | 746 | 612 | 154 | 286 | 162 | 186 |
normalized size | 1 | 1.00 | 0.59 | 3.16 | 2.59 | 0.65 | 1.21 | 0.69 | 0.79 |
time (sec) |
N/A |
0.327 |
0.416 |
0.023 |
0.384 |
0.751 |
7.534 |
0.558 |
0.581 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
|
Problem 50 |
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 | 185 | 185 | 113 | 514 | 438 | 126 | 226 | 129 | 151 |
normalized size | 1 | 1.00 | 0.61 | 2.78 | 2.37 | 0.68 | 1.22 | 0.70 | 0.82 |
time (sec) |
N/A |
0.235 |
0.275 |
0.024 |
0.345 |
0.726 |
4.552 |
1.005 |
4.928 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
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 | 138 | 138 | 86 | 336 | 292 | 97 | 172 | 99 | 118 |
normalized size | 1 | 1.00 | 0.62 | 2.43 | 2.12 | 0.70 | 1.25 | 0.72 | 0.86 |
time (sec) |
N/A |
0.163 |
0.206 |
0.023 |
0.336 |
0.770 |
2.715 |
0.414 |
4.834 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 82 | 236 | 116 | 114 | 160 | 725 | -1 |
normalized size | 1 | 1.00 | 0.74 | 2.13 | 1.05 | 1.03 | 1.44 | 6.53 | -0.01 |
time (sec) |
N/A |
0.172 |
0.417 |
0.031 |
2.092 |
0.826 |
6.925 |
1.030 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 97 | 156 | 97 | 113 | 0 | 1638 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.61 | 1.00 | 1.16 | 0.00 | 16.89 | -0.01 |
time (sec) |
N/A |
0.163 |
0.284 |
0.047 |
1.683 |
0.818 |
0.000 |
0.551 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 99 | 124 | 150 | 136 | 0 | 1058 | -1 |
normalized size | 1 | 1.00 | 0.87 | 1.09 | 1.32 | 1.19 | 0.00 | 9.28 | -0.01 |
time (sec) |
N/A |
0.203 |
0.443 |
0.043 |
2.810 |
0.600 |
0.000 |
0.315 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 114 | 120 | 142 | 145 | 0 | 1032 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.90 | 1.06 | 1.08 | 0.00 | 7.70 | -0.01 |
time (sec) |
N/A |
0.238 |
0.448 |
0.046 |
2.278 |
0.804 |
0.000 |
0.504 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 122 | 157 | 221 | 162 | 0 | 1497 | -1 |
normalized size | 1 | 1.00 | 0.69 | 0.89 | 1.25 | 0.92 | 0.00 | 8.46 | -0.01 |
time (sec) |
N/A |
0.333 |
0.470 |
0.045 |
10.622 |
0.658 |
0.000 |
0.697 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 273 | 273 | 275 | 1656 | 0 | 240 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 6.07 | 0.00 | 0.88 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.730 |
0.498 |
0.075 |
0.000 |
0.787 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 202 | 1184 | 0 | 185 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 5.67 | 0.00 | 0.89 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.348 |
0.427 |
0.056 |
0.000 |
0.739 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 216 | 798 | 0 | 195 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 3.52 | 0.00 | 0.86 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.365 |
0.356 |
0.048 |
0.000 |
0.647 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 163 | 494 | 0 | 146 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 2.79 | 0.00 | 0.82 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.248 |
0.216 |
0.038 |
0.000 |
0.647 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 172 | 229 | 0 | 187 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 1.08 | 0.00 | 0.88 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.239 |
0.210 |
0.032 |
0.000 |
0.853 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 179 | 200 | 0 | 168 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 1.02 | 0.00 | 0.85 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.382 |
0.372 |
0.040 |
0.000 |
0.753 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 238 | 270 | 0 | 240 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 1.08 | 0.00 | 0.96 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.487 |
0.517 |
0.037 |
0.000 |
0.686 |
0.000 |
0.000 |
0.000 |
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 247 | 259 | 0 | 231 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.96 | 0.00 | 0.86 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.508 |
0.693 |
0.056 |
0.000 |
0.910 |
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 |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 450 | 450 | 632 | 3453 | 0 | 351 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.40 | 7.67 | 0.00 | 0.78 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.783 |
1.184 |
0.141 |
0.000 |
0.865 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 583 | 2563 | 0 | 291 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 5.95 | 0.00 | 0.68 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.661 |
0.892 |
0.108 |
0.000 |
0.759 |
0.000 |
0.000 |
0.000 |
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 583 | 1804 | 0 | 333 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.40 | 4.34 | 0.00 | 0.80 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.573 |
0.863 |
0.088 |
0.000 |
0.774 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 239 | 239 | 309 | 1109 | 0 | 244 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.29 | 4.64 | 0.00 | 1.02 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.315 |
0.399 |
0.066 |
0.000 |
0.729 |
0.000 |
0.000 |
0.000 |
|
|
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 585 | 495 | 0 | 333 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 1.04 | 0.00 | 0.70 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.806 |
0.648 |
0.049 |
0.000 |
0.678 |
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 |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 435 | 435 | 650 | 482 | 0 | 330 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.49 | 1.11 | 0.00 | 0.76 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.832 |
0.983 |
0.057 |
0.000 |
0.732 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 501 | 501 | 768 | 769 | 0 | 406 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.53 | 1.53 | 0.00 | 0.81 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.313 |
1.098 |
0.053 |
0.000 |
0.939 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 647 | 3391 | 0 | 492 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.36 | 7.12 | 0.00 | 1.03 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.008 |
1.994 |
0.153 |
0.000 |
0.683 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 746 | 746 | 927 | 2310 | 0 | 604 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 3.10 | 0.00 | 0.81 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.135 |
2.772 |
0.123 |
0.000 |
0.789 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 512 | 512 | 634 | 1374 | 0 | 487 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.24 | 2.68 | 0.00 | 0.95 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.769 |
1.824 |
0.081 |
0.000 |
0.675 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
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|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 856 | 856 | 932 | 602 | 0 | 611 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 0.70 | 0.00 | 0.71 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.181 |
2.521 |
0.060 |
0.000 |
0.787 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 730 | 730 | 924 | 584 | 0 | 645 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.27 | 0.80 | 0.00 | 0.88 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.830 |
2.869 |
0.066 |
0.000 |
0.970 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 875 | 875 | 1177 | 1375 | 0 | 720 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 1.57 | 0.00 | 0.82 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.846 |
3.038 |
0.078 |
0.000 |
0.851 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 995 | 701 | 0 | 766 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 0.89 | 0.00 | 0.97 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.877 |
2.871 |
0.080 |
0.000 |
0.861 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 79 |
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 | 156 | 156 | 101 | 556 | 449 | 104 | 185 | 106 | 151 |
normalized size | 1 | 1.00 | 0.65 | 3.56 | 2.88 | 0.67 | 1.19 | 0.68 | 0.97 |
time (sec) |
N/A |
0.249 |
0.199 |
0.023 |
0.991 |
0.516 |
7.523 |
0.522 |
0.586 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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 | 126 | 126 | 84 | 392 | 326 | 87 | 151 | 88 | 121 |
normalized size | 1 | 1.00 | 0.67 | 3.11 | 2.59 | 0.69 | 1.20 | 0.70 | 0.96 |
time (sec) |
N/A |
0.191 |
0.163 |
0.023 |
0.691 |
0.656 |
4.458 |
0.416 |
4.954 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
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 | 95 | 95 | 66 | 258 | 224 | 68 | 116 | 69 | 92 |
normalized size | 1 | 1.00 | 0.69 | 2.72 | 2.36 | 0.72 | 1.22 | 0.73 | 0.97 |
time (sec) |
N/A |
0.132 |
0.131 |
0.022 |
0.773 |
0.699 |
2.551 |
0.417 |
4.795 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
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 | 68 | 68 | 50 | 159 | 141 | 52 | 82 | 54 | 65 |
normalized size | 1 | 1.00 | 0.74 | 2.34 | 2.07 | 0.76 | 1.21 | 0.79 | 0.96 |
time (sec) |
N/A |
0.087 |
0.092 |
0.023 |
0.728 |
0.685 |
1.213 |
0.639 |
0.111 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 50 | 112 | 76 | 72 | 85 | 510 | -1 |
normalized size | 1 | 1.00 | 0.88 | 1.96 | 1.33 | 1.26 | 1.49 | 8.95 | -0.02 |
time (sec) |
N/A |
0.115 |
0.203 |
0.029 |
2.268 |
0.620 |
6.382 |
0.380 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 56 | 79 | 69 | 79 | 0 | 489 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.41 | 1.23 | 1.41 | 0.00 | 8.73 | -0.02 |
time (sec) |
N/A |
0.117 |
0.139 |
0.037 |
2.270 |
0.737 |
0.000 |
0.558 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 66 | 65 | 1151 | 84 | 0 | 564 | -1 |
normalized size | 1 | 1.00 | 0.94 | 0.93 | 16.44 | 1.20 | 0.00 | 8.06 | -0.01 |
time (sec) |
N/A |
0.127 |
0.164 |
0.039 |
1.519 |
0.786 |
0.000 |
0.331 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 104 | 87 | 132 | 114 | 0 | 796 | -1 |
normalized size | 1 | 1.00 | 1.14 | 0.96 | 1.45 | 1.25 | 0.00 | 8.75 | -0.01 |
time (sec) |
N/A |
0.196 |
0.229 |
0.036 |
2.551 |
0.593 |
0.000 |
0.502 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
Problem 87 |
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 | 235 | 235 | 139 | 822 | 662 | 161 | 284 | 161 | 225 |
normalized size | 1 | 1.00 | 0.59 | 3.50 | 2.82 | 0.69 | 1.21 | 0.69 | 0.96 |
time (sec) |
N/A |
0.326 |
0.406 |
0.025 |
1.050 |
0.558 |
11.926 |
0.533 |
5.086 |
|
|
|
|
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|
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|
Problem 88 |
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 | 188 | 188 | 112 | 599 | 489 | 129 | 226 | 131 | 184 |
normalized size | 1 | 1.00 | 0.60 | 3.19 | 2.60 | 0.69 | 1.20 | 0.70 | 0.98 |
time (sec) |
N/A |
0.242 |
0.327 |
0.024 |
0.784 |
0.663 |
7.389 |
0.407 |
0.619 |
|
|
|
|
|
|
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|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 108 | 487 | 147 | 145 | 211 | 921 | -1 |
normalized size | 1 | 1.00 | 0.67 | 3.02 | 0.91 | 0.90 | 1.31 | 5.72 | -0.01 |
time (sec) |
N/A |
0.256 |
0.528 |
0.036 |
12.019 |
0.727 |
10.635 |
0.358 |
0.000 |
|
|
|
|
|
|
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|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 145 | 365 | 129 | 145 | 0 | 2038 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.52 | 0.89 | 1.00 | 0.00 | 14.06 | -0.01 |
time (sec) |
N/A |
0.233 |
0.394 |
0.056 |
14.760 |
0.768 |
0.000 |
1.341 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
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|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 142 | 142 | 138 | 251 | 110 | 142 | 0 | 2171 | -1 |
normalized size | 1 | 1.00 | 0.97 | 1.77 | 0.77 | 1.00 | 0.00 | 15.29 | -0.01 |
time (sec) |
N/A |
0.219 |
0.407 |
0.053 |
3.074 |
0.693 |
0.000 |
1.151 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 135 | 196 | 173 | 176 | 0 | 1181 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.30 | 1.15 | 1.17 | 0.00 | 7.82 | -0.01 |
time (sec) |
N/A |
0.252 |
0.626 |
0.057 |
10.004 |
0.842 |
0.000 |
0.952 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 148 | 167 | 166 | 186 | 0 | 1255 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.00 | 0.99 | 1.11 | 0.00 | 7.51 | -0.01 |
time (sec) |
N/A |
0.283 |
0.606 |
0.052 |
16.429 |
0.754 |
0.000 |
1.326 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 371 | 371 | 231 | 559 | 0 | 397 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.62 | 1.51 | 0.00 | 1.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.915 |
0.573 |
0.061 |
0.000 |
0.873 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 357 | 357 | 216 | 392 | 0 | 393 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.61 | 1.10 | 0.00 | 1.10 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.676 |
0.355 |
0.052 |
0.000 |
0.931 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 186 | 266 | 0 | 292 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.66 | 0.95 | 0.00 | 1.04 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.453 |
0.315 |
0.041 |
0.000 |
0.810 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 343 | 343 | 196 | 176 | 0 | 379 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.57 | 0.51 | 0.00 | 1.10 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.413 |
0.303 |
0.040 |
0.000 |
0.741 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 343 | 343 | 196 | 85 | 0 | 385 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.57 | 0.25 | 0.00 | 1.12 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.429 |
0.207 |
0.038 |
0.000 |
0.844 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 301 | 301 | 206 | 88 | 0 | 314 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.68 | 0.29 | 0.00 | 1.04 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.527 |
0.382 |
0.048 |
0.000 |
0.842 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 380 | 380 | 233 | 116 | 0 | 454 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.61 | 0.31 | 0.00 | 1.19 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.609 |
0.497 |
0.055 |
0.000 |
0.723 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 408 | 408 | 253 | 136 | 0 | 491 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.62 | 0.33 | 0.00 | 1.20 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.681 |
0.503 |
0.041 |
0.000 |
0.828 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 714 | 714 | 383 | 1185 | 0 | 670 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.54 | 1.66 | 0.00 | 0.94 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.073 |
0.484 |
0.110 |
0.000 |
0.803 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 371 | 371 | 214 | 823 | 0 | 480 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.58 | 2.22 | 0.00 | 1.29 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.619 |
0.188 |
0.087 |
0.000 |
0.944 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 691 | 691 | 408 | 508 | 0 | 661 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.59 | 0.74 | 0.00 | 0.96 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.297 |
0.222 |
0.069 |
0.000 |
0.714 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 735 | 735 | 406 | 248 | 0 | 673 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.55 | 0.34 | 0.00 | 0.92 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.341 |
0.227 |
0.053 |
0.000 |
0.911 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 693 | 693 | 446 | 233 | 0 | 584 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.34 | 0.00 | 0.84 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.485 |
0.891 |
0.064 |
0.000 |
0.900 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 712 | 712 | 445 | 283 | 0 | 722 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.62 | 0.40 | 0.00 | 1.01 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.602 |
1.162 |
0.068 |
0.000 |
0.710 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 800 | 800 | 470 | 388 | 0 | 916 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.59 | 0.48 | 0.00 | 1.14 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.788 |
1.195 |
0.058 |
0.000 |
0.962 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 772 | 772 | 457 | 2032 | 0 | 890 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.59 | 2.63 | 0.00 | 1.15 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.766 |
0.665 |
0.189 |
0.000 |
0.791 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 777 | 777 | 449 | 1394 | 0 | 929 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.58 | 1.79 | 0.00 | 1.20 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.528 |
0.437 |
0.137 |
0.000 |
0.958 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1141 | 1141 | 698 | 845 | 0 | 1321 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.61 | 0.74 | 0.00 | 1.16 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.116 |
0.586 |
0.103 |
0.000 |
1.116 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1161 | 1161 | 675 | 392 | 0 | 1223 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.58 | 0.34 | 0.00 | 1.05 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.368 |
0.432 |
0.065 |
0.000 |
0.964 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1163 | 1163 | 2109 | 363 | 0 | 1117 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.81 | 0.31 | 0.00 | 0.96 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.893 |
1.148 |
0.091 |
0.000 |
1.140 |
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 [112] had the largest ratio of
[.6250]
|
|
|
|
|
|
|
| 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 |
47 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
108 |
A |
51 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
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 |
|
|
|
|
|
|
|
112 |
A |
99 |
10 |
1.00 |
16 |
0.625 |
|
|
|
|
|
|
|
113 |
A |
110 |
9 |
1.00 |
19 |
0.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|