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 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 23, 25, 29, 31, 33, 36, 38, 42, 45, 47, 49,
50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 72, 73, 74, 79, 80, 81, 83, 85, 86, 87,
88, 89, 90, 91 }
B grade: { 7, 9, 22, 24, 26, 27, 28, 30, 32, 34, 35, 37, 39, 40, 41, 43, 44, 46, 48, 66, 70, 71, 75, 76, 77, 84
}
C grade: { 18, 20, 78 }
F grade: { 82}
2.1.3 Maple
A grade: { 1, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32,
34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60, 64, 65, 66, 70, 71,
72, 75, 76, 77, 78, 83, 88, 89, 90, 91 }
B grade: { 2, 4, 7, 24, 33, 42, 52, 54, 61, 62, 63, 67, 68, 69, 73, 74 }
C grade: { }
F grade: { 79, 80, 81, 82, 84, 85, 86, 87 }
2.1.4 Maxima
A grade: { 6, 8, 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, 52, 54, 57, 59, 60, 64, 65, 66, 70, 71, 72, 75,
76, 77, 83, 88, 89, 90, 91
B grade: { 5, 7, 9, 61, 62, 63, 67, 68, 69, 73, 74, 78 }
C grade: { }
F grade: { 1, 2, 3, 4, 51, 53, 55, 56, 58, 79, 80, 81, 82, 84, 85, 86, 87 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 6, 11, 12, 13, 14, 15, 22, 23, 24, 25, 32, 33, 34, 35, 41, 42, 43, 44, 45, 47, 50, 51, 52,
53, 54, 57, 83, 88, 89, 90, 91 }
B grade: { 5, 7, 8, 9, 10, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 36, 37, 38, 39, 40, 46, 48, 49, 55, 56,
58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78 }
C grade: { }
F grade: { 79, 80, 81, 82, 84, 85, 86, 87 }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 89 }
B grade: { }
C grade: { }
F grade: { 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, 90, 91
}
2.1.7 Giac
A grade: { 1, 3, 5, 6, 8, 10, 16, 17, 19, 20, 21, 26, 27, 28, 29, 30, 31, 35, 36, 38, 39, 40, 44, 45, 46, 47,
48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 70, 71, 72, 75, 76, 77, 78, 88, 89, 90, 91
}
B grade: { 2, 4, 7, 9, 12, 13, 14, 15, 18, 22, 24, 25, 33, 37, 42, 52, 54, 61, 62, 67, 68, 69, 73, 74
}
C grade: { }
F grade: { 11, 23, 32, 34, 41, 43, 79, 80, 81, 82, 83, 84, 85, 86, 87 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 67 | 66 | 0 | 136 | 51 | 72 |
normalized size |
1 |
1. |
0.86 |
0.85 |
0. |
1.74 |
0.65 |
0.92 |
time (sec) |
N/A |
0.066 |
0.08 |
0.075 |
0. |
2.065 |
0.395 |
1.306 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 51 | 81 | 0 | 101 | 37 | 96 |
normalized size |
1 |
1. |
1.76 |
2.79 |
0. |
3.48 |
1.28 |
3.31 |
time (sec) |
N/A |
0.137 |
0.019 |
0.051 |
0. |
2.061 |
0.289 |
1.298 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 39 | 47 | 0 | 89 | 31 | 55 |
normalized size |
1 |
1. |
0.78 |
0.94 |
0. |
1.78 |
0.62 |
1.1 |
time (sec) |
N/A |
0.054 |
0.091 |
0.041 |
0. |
2.125 |
0.425 |
1.341 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 33 | 47 | 0 | 47 | 17 | 45 |
normalized size |
1 |
1. |
1.74 |
2.47 |
0. |
2.47 |
0.89 |
2.37 |
time (sec) |
N/A |
0.089 |
0.012 |
0.035 |
0. |
1.994 |
0.174 |
1.34 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 31 | 21 | 38 | 73 | 0 | 30 |
normalized size | 1 | 1. | 1.94 | 1.31 | 2.38 | 4.56 | 0. | 1.88 |
time (sec) |
N/A |
0.086 |
0.016 |
0.033 |
1.478 |
2.205 |
0. |
1.333 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 15 | 20 | 23 | 78 | 0 | 24 |
normalized size | 1 | 1. | 0.83 | 1.11 | 1.28 | 4.33 | 0. | 1.33 |
time (sec) |
N/A |
0.033 |
0.019 |
0.033 |
1.404 |
2.02 |
0. |
1.32 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 75 | 42 | 80 | 232 | 0 | 63 |
normalized size | 1 | 1. | 3.12 | 1.75 | 3.33 | 9.67 | 0. | 2.62 |
time (sec) |
N/A |
0.132 |
0.022 |
0.039 |
1.246 |
2.133 |
0. |
1.385 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 29 | 15 | 16 | 109 | 0 | 16 |
normalized size |
1 |
1. |
1.53 |
0.79 |
0.84 |
5.74 |
0. |
0.84 |
time (sec) |
N/A |
0.039 |
0.018 |
0.038 |
1.366 |
1.996 |
0. |
1.417 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
A |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 139 | 58 | 112 | 424 | 0 | 85 |
normalized size |
1 |
1. |
3.48 |
1.45 |
2.8 |
10.6 |
0. |
2.12 |
time (sec) |
N/A |
0.151 |
0.023 |
0.043 |
1.301 |
2.139 |
0. |
1.402 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 41 | 28 | 32 | 176 | 0 | 32 |
normalized size |
1 |
1. |
1.11 |
0.76 |
0.86 |
4.76 |
0. |
0.86 |
time (sec) |
N/A |
0.047 |
0.019 |
0.041 |
1.363 |
1.987 |
0. |
1.388 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 103 | 113 | 123 | 267 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
1.12 |
1.22 |
2.64 |
0. |
0. |
time (sec) |
N/A |
0.076 |
0.032 |
0.041 |
1.389 |
2.277 |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 82 | 92 | 117 | 189 | 0 | 1439 |
normalized size | 1 | 1. | 0.99 | 1.11 | 1.41 | 2.28 | 0. | 17.34 |
time (sec) |
N/A |
0.168 |
0.079 |
0.033 |
2.159 |
2.359 |
0. |
1.7 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 71 | 79 | 95 | 197 | 0 | 7223 |
normalized size | 1 | 1. | 1.03 | 1.14 | 1.38 | 2.86 | 0. | 104.68 |
time (sec) |
N/A |
0.068 |
0.027 |
0.035 |
1.361 |
2.303 |
0. |
2.784 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 56 | 58 | 70 | 120 | 0 | 558 |
normalized size | 1 | 1. | 1.14 | 1.18 | 1.43 | 2.45 | 0. | 11.39 |
time (sec) |
N/A |
0.084 |
0.048 |
0.035 |
2.511 |
2.255 |
0. |
1.437 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 48 | 45 | 62 | 134 | 0 | 1669 |
normalized size | 1 | 1. | 1.3 | 1.22 | 1.68 | 3.62 | 0. | 45.11 |
time (sec) |
N/A |
0.036 |
0.02 |
0.027 |
1.521 |
2.3 |
0. |
1.658 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 52 | 42 | 62 | 170 | 0 | 66 |
normalized size | 1 | 1. | 2. | 1.62 | 2.38 | 6.54 | 0. | 2.54 |
time (sec) |
N/A |
0.029 |
0.024 |
0.036 |
1.535 |
2.351 |
0. |
1.413 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 36 | 26 | 34 | 171 | 0 | 47 |
normalized size | 1 | 1. | 1.44 | 1.04 | 1.36 | 6.84 | 0. | 1.88 |
time (sec) |
N/A |
0.078 |
0.059 |
0.077 |
1.388 |
2.495 |
0. |
1.364 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 107 | 75 | 112 | 367 | 0 | 159 |
normalized size | 1 | 1. | 1.78 | 1.25 | 1.87 | 6.12 | 0. | 2.65 |
time (sec) |
N/A |
0.068 |
0.027 |
0.082 |
1.142 |
2.89 |
0. |
1.512 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 72 | 60 | 68 | 316 | 0 | 84 |
normalized size | 1 | 1. | 1.26 | 1.05 | 1.19 | 5.54 | 0. | 1.47 |
time (sec) |
N/A |
0.088 |
0.245 |
0.081 |
1.128 |
2.795 |
0. |
1.362 |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 151 | 109 | 166 | 585 | 0 | 239 |
normalized size |
1 |
1. |
1.54 |
1.11 |
1.69 |
5.97 |
0. |
2.44 |
time (sec) |
N/A |
0.092 |
0.029 |
0.084 |
1.26 |
2.723 |
0. |
1.427 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 104 | 94 | 97 | 473 | 0 | 113 |
normalized size |
1 |
1. |
1.2 |
1.08 |
1.11 |
5.44 |
0. |
1.3 |
time (sec) |
N/A |
0.108 |
0.545 |
0.085 |
1.132 |
2.1 |
0. |
1.384 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 240 | 204 | 173 | 333 | 0 | 7808 |
normalized size |
1 |
1. |
2.12 |
1.81 |
1.53 |
2.95 |
0. |
69.1 |
time (sec) |
N/A |
0.186 |
3.197 |
0.04 |
1.477 |
2.063 |
0. |
6.669 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 152 | 167 | 140 | 321 | 0 | 0 |
normalized size |
1 |
1. |
1.25 |
1.37 |
1.15 |
2.63 |
0. |
0. |
time (sec) |
N/A |
0.131 |
1.023 |
0.041 |
0.974 |
1.993 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 162 | 145 | 111 | 240 | 0 | 1432 |
normalized size | 1 | 1. | 2.13 | 1.91 | 1.46 | 3.16 | 0. | 18.84 |
time (sec) |
N/A |
0.113 |
2.362 |
0.039 |
1.476 |
2.016 |
0. |
1.879 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 111 | 108 | 90 | 230 | 0 | 3830 |
normalized size | 1 | 1. | 1.63 | 1.59 | 1.32 | 3.38 | 0. | 56.32 |
time (sec) |
N/A |
0.074 |
0.439 |
0.036 |
1.119 |
2.322 |
0. |
4.538 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 97 | 61 | 81 | 288 | 0 | 100 |
normalized size | 1 | 1. | 2.26 | 1.42 | 1.88 | 6.7 | 0. | 2.33 |
time (sec) |
N/A |
0.056 |
0.233 |
0.044 |
1.069 |
2.434 |
0. |
1.572 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 91 | 43 | 53 | 246 | 0 | 69 |
normalized size | 1 | 1. | 2.17 | 1.02 | 1.26 | 5.86 | 0. | 1.64 |
time (sec) |
N/A |
0.047 |
0.544 |
0.042 |
1.107 |
2.282 |
0. |
1.539 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 250 | 120 | 165 | 581 | 0 | 232 |
normalized size | 1 | 1. | 2.63 | 1.26 | 1.74 | 6.12 | 0. | 2.44 |
time (sec) |
N/A |
0.118 |
1.951 |
0.051 |
1.101 |
2.778 |
0. |
1.636 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 127 | 104 | 93 | 446 | 0 | 123 |
normalized size |
1 |
1. |
1.61 |
1.32 |
1.18 |
5.65 |
0. |
1.56 |
time (sec) |
N/A |
0.07 |
1.409 |
0.053 |
1.086 |
2.394 |
0. |
1.619 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 994 | 183 | 252 | 856 | 0 | 363 |
normalized size |
1 |
1. |
6.02 |
1.11 |
1.53 |
5.19 |
0. |
2.2 |
time (sec) |
N/A |
0.16 |
6.2 |
0.054 |
1.075 |
2.974 |
0. |
1.652 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 114 | 166 | 140 | 628 | 0 | 177 |
normalized size |
1 |
1. |
0.93 |
1.36 |
1.15 |
5.15 |
0. |
1.45 |
time (sec) |
N/A |
0.101 |
1.51 |
0.055 |
1.04 |
2.428 |
0. |
1.408 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 771 | 271 | 234 | 455 | 0 | 0 |
normalized size |
1 |
1. |
3.76 |
1.32 |
1.14 |
2.22 |
0. |
0. |
time (sec) |
N/A |
0.189 |
6.266 |
0.053 |
1.037 |
2.396 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 203 | 226 | 153 | 342 | 0 | 3497 |
normalized size | 1 | 1. | 1.97 | 2.19 | 1.49 | 3.32 | 0. | 33.95 |
time (sec) |
N/A |
0.145 |
4.227 |
0.052 |
1.515 |
2.168 |
0. |
3.227 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 637 | 193 | 173 | 346 | 0 | 0 |
normalized size |
1 |
1. |
4.79 |
1.45 |
1.3 |
2.6 |
0. |
0. |
time (sec) |
N/A |
0.116 |
6.156 |
0.043 |
1.118 |
2.124 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 241 | 125 | 150 | 383 | 0 | 194 |
normalized size | 1 | 1. | 2.8 | 1.45 | 1.74 | 4.45 | 0. | 2.26 |
time (sec) |
N/A |
0.086 |
2.26 |
0.061 |
1.085 |
2.497 |
0. |
2.06 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 126 | 63 | 76 | 327 | 0 | 95 |
normalized size | 1 | 1. | 1.97 | 0.98 | 1.19 | 5.11 | 0. | 1.48 |
time (sec) |
N/A |
0.053 |
0.976 |
0.056 |
1.101 |
2.047 |
0. |
2.067 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 897 | 170 | 231 | 720 | 0 | 410 |
normalized size |
1 |
1. |
6.36 |
1.21 |
1.64 |
5.11 |
0. |
2.91 |
time (sec) |
N/A |
0.135 |
6.183 |
0.065 |
1.152 |
2.74 |
0. |
1.985 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 212 | 141 | 132 | 575 | 0 | 180 |
normalized size |
1 |
1. |
1.88 |
1.25 |
1.17 |
5.09 |
0. |
1.59 |
time (sec) |
N/A |
0.086 |
2.207 |
0.068 |
1.064 |
2.018 |
0. |
2.048 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 1229 | 254 | 338 | 1060 | 0 | 504 |
normalized size |
1 |
1. |
5.37 |
1.11 |
1.48 |
4.63 |
0. |
2.2 |
time (sec) |
N/A |
0.208 |
6.2 |
0.068 |
1.106 |
2.955 |
0. |
2.15 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 515 | 230 | 192 | 834 | 0 | 255 |
normalized size |
1 |
1. |
3.08 |
1.38 |
1.15 |
4.99 |
0. |
1.53 |
time (sec) |
N/A |
0.134 |
1.758 |
0.069 |
1.118 |
2.284 |
0. |
2.032 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 275 | 275 | 1017 | 412 | 294 | 528 | 0 | 0 |
normalized size |
1 |
1. |
3.7 |
1.5 |
1.07 |
1.92 |
0. |
0. |
time (sec) |
N/A |
0.248 |
6.275 |
0.059 |
1.148 |
2.133 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 263 | 368 | 208 | 431 | 0 | 5307 |
normalized size |
1 |
1. |
1.89 |
2.65 |
1.5 |
3.1 |
0. |
38.18 |
time (sec) |
N/A |
0.175 |
6.266 |
0.057 |
1.709 |
2.248 |
0. |
7.192 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 180 | 180 | 383 | 309 | 224 | 414 | 0 | 0 |
normalized size |
1 |
1. |
2.13 |
1.72 |
1.24 |
2.3 |
0. |
0. |
time (sec) |
N/A |
0.157 |
5.459 |
0.049 |
1.093 |
2.066 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 352 | 214 | 188 | 444 | 0 | 261 |
normalized size |
1 |
1. |
2.98 |
1.81 |
1.59 |
3.76 |
0. |
2.21 |
time (sec) |
N/A |
0.114 |
5.132 |
0.069 |
1.108 |
2.565 |
0. |
2.71 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 162 | 90 | 97 | 389 | 0 | 116 |
normalized size |
1 |
1. |
1.95 |
1.08 |
1.17 |
4.69 |
0. |
1.4 |
time (sec) |
N/A |
0.058 |
1.16 |
0.063 |
1.12 |
2.049 |
0. |
2.648 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 1128 | 192 | 254 | 818 | 0 | 405 |
normalized size |
1 |
1. |
7.01 |
1.19 |
1.58 |
5.08 |
0. |
2.52 |
time (sec) |
N/A |
0.157 |
6.193 |
0.075 |
1.174 |
3.035 |
0. |
2.77 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 188 | 184 | 162 | 633 | 0 | 217 |
normalized size |
1 |
1. |
1.37 |
1.34 |
1.18 |
4.62 |
0. |
1.58 |
time (sec) |
N/A |
0.104 |
3.677 |
0.077 |
1.07 |
2.199 |
0. |
2.645 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 1491 | 317 | 410 | 1289 | 0 | 647 |
normalized size |
1 |
1. |
5.44 |
1.16 |
1.5 |
4.7 |
0. |
2.36 |
time (sec) |
N/A |
0.241 |
6.287 |
0.082 |
1.173 |
3.983 |
0. |
2.684 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 233 | 301 | 231 | 922 | 0 | 317 |
normalized size |
1 |
1. |
1.2 |
1.55 |
1.19 |
4.75 |
0. |
1.63 |
time (sec) |
N/A |
0.157 |
3.919 |
0.082 |
1.069 |
2.634 |
0. |
2.653 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 402 | 402 | 660 | 442 | 522 | 1661 | 0 | 873 |
normalized size |
1 |
1. |
1.64 |
1.1 |
1.3 |
4.13 |
0. |
2.17 |
time (sec) |
N/A |
0.306 |
6.259 |
0.127 |
1.154 |
4.568 |
0. |
2.8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 289 | 361 | 0 | 840 | 0 | 626 |
normalized size |
1 |
1. |
1.05 |
1.32 |
0. |
3.07 |
0. |
2.28 |
time (sec) |
N/A |
0.354 |
3.124 |
0.079 |
0. |
2.327 |
0. |
1.342 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 249 | 565 | 378 | 481 | 0 | 451 |
normalized size |
1 |
1. |
1.58 |
3.58 |
2.39 |
3.04 |
0. |
2.85 |
time (sec) |
N/A |
0.339 |
2.592 |
0.068 |
1.655 |
2.289 |
0. |
1.196 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 139 | 205 | 0 | 597 | 0 | 325 |
normalized size |
1 |
1. |
0.83 |
1.22 |
0. |
3.55 |
0. |
1.93 |
time (sec) |
N/A |
0.223 |
1.375 |
0.065 |
0. |
2.278 |
0. |
1.386 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 170 | 238 | 194 | 278 | 0 | 248 |
normalized size |
1 |
1. |
1.81 |
2.53 |
2.06 |
2.96 |
0. |
2.64 |
time (sec) |
N/A |
0.163 |
0.723 |
0.059 |
1.572 |
2.123 |
0. |
1.148 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 79 | 100 | 0 | 435 | 0 | 159 |
normalized size |
1 |
1. |
0.88 |
1.11 |
0. |
4.83 |
0. |
1.77 |
time (sec) |
N/A |
0.106 |
0.336 |
0.05 |
0. |
2.046 |
0. |
1.334 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 75 | 65 | 0 | 450 | 0 | 127 |
normalized size |
1 |
1. |
1.14 |
0.98 |
0. |
6.82 |
0. |
1.92 |
time (sec) |
N/A |
0.129 |
0.105 |
0.056 |
0. |
2.377 |
0. |
1.436 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 47 | 53 | 63 | 246 | 0 | 81 |
normalized size | 1 | 1. | 0.94 | 1.06 | 1.26 | 4.92 | 0. | 1.62 |
time (sec) |
N/A |
0.06 |
0.131 |
0.062 |
1.068 |
2.055 |
0. |
1.208 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 179 | 162 | 0 | 644 | 0 | 282 |
normalized size |
1 |
1. |
1.47 |
1.33 |
0. |
5.28 |
0. |
2.31 |
time (sec) |
N/A |
0.307 |
0.827 |
0.069 |
0. |
2.683 |
0. |
1.351 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 95 | 144 | 131 | 500 | 0 | 194 |
normalized size |
1 |
1. |
0.88 |
1.33 |
1.21 |
4.63 |
0. |
1.8 |
time (sec) |
N/A |
0.104 |
0.456 |
0.076 |
1.064 |
2.154 |
0. |
1.181 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 150 | 273 | 227 | 902 | 0 | 339 |
normalized size |
1 |
1. |
0.89 |
1.62 |
1.34 |
5.34 |
0. |
2.01 |
time (sec) |
N/A |
0.151 |
2.164 |
0.083 |
1.095 |
2.412 |
0. |
1.244 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 297 | 297 | 526 | 1211 | 1079 | 1388 | 0 | 992 |
normalized size |
1 |
1. |
1.77 |
4.08 |
3.63 |
4.67 |
0. |
3.34 |
time (sec) |
N/A |
0.914 |
6.48 |
0.103 |
1.796 |
2.896 |
0. |
1.233 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 373 | 724 | 684 | 986 | 0 | 693 |
normalized size |
1 |
1. |
1.72 |
3.34 |
3.15 |
4.54 |
0. |
3.19 |
time (sec) |
N/A |
0.562 |
3.807 |
0.099 |
1.53 |
2.632 |
0. |
1.216 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 246 | 352 | 396 | 640 | 0 | 355 |
normalized size |
1 |
1. |
1.66 |
2.38 |
2.68 |
4.32 |
0. |
2.4 |
time (sec) |
N/A |
0.295 |
3.26 |
0.089 |
1.556 |
2.249 |
0. |
1.177 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 109 | 75 | 100 | 663 | 0 | 100 |
normalized size | 1 | 1. | 1.51 | 1.04 | 1.39 | 9.21 | 0. | 1.39 |
time (sec) |
N/A |
0.065 |
0.373 |
0.092 |
0.987 |
2.199 |
0. |
1.219 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 244 | 189 | 194 | 1004 | 0 | 274 |
normalized size |
1 |
1. |
1.74 |
1.35 |
1.39 |
7.17 |
0. |
1.96 |
time (sec) |
N/A |
0.122 |
2.506 |
0.153 |
1.092 |
2.374 |
0. |
1.298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 219 | 219 | 589 | 343 | 304 | 1770 | 0 | 448 |
normalized size |
1 |
1. |
2.69 |
1.57 |
1.39 |
8.08 |
0. |
2.05 |
time (sec) |
N/A |
0.198 |
6.231 |
0.122 |
1.225 |
2.59 |
0. |
1.239 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 382 | 382 | 683 | 1449 | 1469 | 2137 | 0 | 1246 |
normalized size |
1 |
1. |
1.79 |
3.79 |
3.85 |
5.59 |
0. |
3.26 |
time (sec) |
N/A |
1.432 |
6.604 |
0.118 |
1.933 |
3.59 |
0. |
1.286 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 285 | 285 | 501 | 882 | 1004 | 1569 | 0 | 794 |
normalized size |
1 |
1. |
1.76 |
3.09 |
3.52 |
5.51 |
0. |
2.79 |
time (sec) |
N/A |
0.85 |
6.438 |
0.109 |
1.811 |
3.095 |
0. |
1.27 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 316 | 542 | 625 | 1152 | 0 | 651 |
normalized size |
1 |
1. |
1.53 |
2.63 |
3.03 |
5.59 |
0. |
3.16 |
time (sec) |
N/A |
0.396 |
3.959 |
0.115 |
1.849 |
2.483 |
0. |
1.237 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 241 | 96 | 146 | 1219 | 0 | 153 |
normalized size |
1 |
1. |
2.54 |
1.01 |
1.54 |
12.83 |
0. |
1.61 |
time (sec) |
N/A |
0.077 |
2.589 |
0.119 |
1.146 |
2.46 |
0. |
1.27 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 456 | 234 | 259 | 1818 | 0 | 320 |
normalized size |
1 |
1. |
2.56 |
1.31 |
1.46 |
10.21 |
0. |
1.8 |
time (sec) |
N/A |
0.153 |
3.227 |
0.13 |
1.202 |
2.599 |
0. |
1.346 |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 265 | 265 | 494 | 410 | 379 | 2344 | 0 | 516 |
normalized size |
1 |
1. |
1.86 |
1.55 |
1.43 |
8.85 |
0. |
1.95 |
time (sec) |
N/A |
0.239 |
4.675 |
0.137 |
1.219 |
3.015 |
0. |
1.238 |
|
|
|
|
|
|
|
|
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|
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|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 366 | 366 | 564 | 1215 | 1346 | 2412 | 0 | 1218 |
normalized size |
1 |
1. |
1.54 |
3.32 |
3.68 |
6.59 |
0. |
3.33 |
time (sec) |
N/A |
1.37 |
5.419 |
0.123 |
1.896 |
4.005 |
0. |
1.35 |
|
|
|
|
|
|
|
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|
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|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 264 | 264 | 395 | 668 | 894 | 1789 | 0 | 867 |
normalized size |
1 |
1. |
1.5 |
2.53 |
3.39 |
6.78 |
0. |
3.28 |
time (sec) |
N/A |
0.571 |
3.594 |
0.12 |
1.712 |
3.002 |
0. |
1.324 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 259 | 117 | 189 | 1901 | 0 | 174 |
normalized size |
1 |
1. |
2.23 |
1.01 |
1.63 |
16.39 |
0. |
1.5 |
time (sec) |
N/A |
0.088 |
2.064 |
0.131 |
1.14 |
2.846 |
0. |
1.225 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 528 | 278 | 308 | 2732 | 0 | 300 |
normalized size |
1 |
1. |
2.58 |
1.36 |
1.5 |
13.33 |
0. |
1.46 |
time (sec) |
N/A |
0.173 |
2.034 |
0.198 |
1.123 |
3.255 |
0. |
1.334 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 300 | 300 | 673 | 476 | 439 | 3507 | 0 | 578 |
normalized size |
1 |
1. |
2.24 |
1.59 |
1.46 |
11.69 |
0. |
1.93 |
time (sec) |
N/A |
0.271 |
1.634 |
0.165 |
1.24 |
4.431 |
0. |
1.361 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
B |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 41 | 26 | 68 | 203 | 0 | 59 |
normalized size | 1 | 1. | 1.58 | 1. | 2.62 | 7.81 | 0. | 2.27 |
time (sec) |
N/A |
0.074 |
0.041 |
0.025 |
1.85 |
2.354 |
0. |
1.296 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 205 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.9 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.45 |
2.52 |
0.392 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 166 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.93 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.268 |
1.194 |
0.248 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 109 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.145 |
0.257 |
0.488 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 765 | 765 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.173 |
12.792 |
0.164 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
F(-2) |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.463 |
3.184 |
0.644 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 435 | 435 | 910 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.09 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.803 |
6.579 |
0.556 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 276 | 276 | 270 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.367 |
1.088 |
0.473 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 48 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.055 |
0.875 |
0.239 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 78 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.56 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.13 |
1.244 |
0.229 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.979 |
3.069 |
0.542 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.855 |
2.185 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.487 |
1.52 |
0.23 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.7 |
2.852 |
0.189 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf size
of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the
integral was to solve. In this test, problem number [5] had the largest ratio of [ 0.6364
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
5 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
2 |
A |
9 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
3 |
A |
5 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
4 |
A |
8 |
6 |
1. |
11 |
0.546 |
|
|
|
|
|
|
|
5 |
A |
8 |
7 |
1. |
11 |
0.636 |
|
|
|
|
|
|
|
6 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
7 |
A |
8 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
8 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
9 |
A |
9 |
8 |
1. |
13 |
0.615 |
|
|
|
|
|
|
|
10 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
11 |
A |
8 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
12 |
A |
6 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
13 |
A |
8 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
14 |
A |
5 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
15 |
A |
6 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
16 |
A |
4 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
17 |
A |
3 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
18 |
A |
7 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
19 |
A |
3 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
20 |
A |
9 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
|
21 |
A |
3 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
22 |
A |
8 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
23 |
A |
11 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
25 |
A |
9 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
26 |
A |
6 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
27 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
28 |
A |
10 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
29 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
30 |
A |
13 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
31 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
32 |
A |
16 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
33 |
A |
7 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
34 |
A |
13 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
35 |
A |
8 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
36 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
37 |
A |
12 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
38 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
39 |
A |
17 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
40 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
|
41 |
A |
19 |
8 |
1. |
21 |
0.381 |
|
|
|
|
|
|
|
42 |
A |
7 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
43 |
A |
16 |
9 |
1. |
19 |
0.474 |
|
|
|
|
|
|
|
44 |
A |
10 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
45 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
46 |
A |
14 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
47 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
48 |
A |
21 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
49 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
50 |
A |
25 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
51 |
A |
13 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
52 |
A |
8 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
53 |
A |
10 |
9 |
1. |
21 |
0.429 |
|
|
|
|
|
|
|
54 |
A |
7 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
55 |
A |
6 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
56 |
A |
6 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
57 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
58 |
A |
15 |
11 |
1. |
21 |
0.524 |
|
|
|
|
|
|
|
59 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
60 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
|
61 |
A |
9 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
62 |
A |
8 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
63 |
A |
7 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
64 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
65 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
66 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
67 |
A |
9 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
68 |
A |
8 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
69 |
A |
7 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
70 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
71 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
72 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
73 |
A |
8 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
74 |
A |
7 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
75 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
76 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
77 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
78 |
A |
6 |
5 |
1. |
9 |
0.556 |
|
|
|
|
|
|
|
79 |
A |
8 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
80 |
A |
6 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
|
81 |
A |
5 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
82 |
A |
14 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
83 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
84 |
A |
7 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
85 |
A |
6 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
86 |
A |
2 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
87 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
88 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
89 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
90 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
91 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|