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 }
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, 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, 91, 92, 96, 97 }
B grade: { }
C grade: { 90, 93, 94, 95, 98, 99 }
F grade: { }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22, 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, 66, 68, 69, 70, 71, 72, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 97 }
B grade: { 90, 93, 94, 95, 96 }
C grade: { 14, 19, 21, 23, 24, 25, 26, 27, 28, 73, 76, 98, 99 }
F grade: { 29, 30, 31, 32, 33, 34, 65, 67, 74, 75, 77, 78 }
2.1.4 Maxima
A grade: { 1, 3, 8, 10, 15, 17, 22, 37, 43, 45, 46, 47, 48, 61, 62, 63, 64, 66, 68, 88, 89, 91, 92,
97
B grade: { 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 90, 95, 96 }
C grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 35, 36, 38, 39, 40, 41, 42, 44, 49, 50, 51, 52, 53,
54, 55, 56, 57, 58, 59, 60, 85, 86, 87 }
F grade: { 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 93, 94, 98, 99
}
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, 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, 66, 68, 69, 70, 71, 72, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97
}
B grade: { }
C grade: { 93, 94, 98, 99 }
F grade: { 65, 67, 73, 74, 75, 76, 77, 78 }
2.1.6 Sympy
A grade: { 1, 3, 4, 8, 10, 11, 15, 17, 18, 22, 36, 37, 38, 39, 43, 46, 47, 48, 63, 88, 89, 90, 91, 92, 97
}
B grade: { 2, 9, 16, 45, 61 }
C grade: { }
F grade: { 5, 6, 7, 12, 13, 14, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 40, 41, 42, 44, 49,
50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 93, 94, 95, 96, 98, 99 }
2.1.7 Giac
A grade: { 1, 3, 5, 8, 10, 12, 15, 17, 19, 22, 37, 45, 46, 47, 48, 61, 62, 63, 64, 66, 68, 88, 89, 96, 97
}
B grade: { 7, 14, 21, 90, 91, 92, 95 }
C grade: { 2, 4, 9, 11, 16, 18, 49, 50, 51, 55, 56, 57, 85, 86, 87 }
F grade: { 6, 13, 20, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 52, 53,
54, 58, 59, 60, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 93, 94, 98, 99
}
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 |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 29 | 31 | 36 | 66 | 36 | 36 |
normalized size | 1 | 1. | 0.85 | 0.91 | 1.06 | 1.94 | 1.06 | 1.06 |
time (sec) |
N/A |
0.032 |
0.049 |
0.023 |
1.333 |
1.569 |
1.087 |
1.13 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
B |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 82 | 58 | 338 | 220 | 209 | 182 |
normalized size | 1 | 1. | 0.9 | 0.64 | 3.71 | 2.42 | 2.3 | 2. |
time (sec) |
N/A |
0.069 |
0.145 |
0.025 |
2.102 |
1.643 |
2.13 |
1.152 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 30 | 19 | 18 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 2. | 1.27 | 1.2 |
time (sec) |
N/A |
0.014 |
0.003 |
0.023 |
1.354 |
1.571 |
0.208 |
1.159 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 57 | 44 | 308 | 185 | 61 | 128 |
normalized size | 1 | 1. | 0.81 | 0.63 | 4.4 | 2.64 | 0.87 | 1.83 |
time (sec) |
N/A |
0.021 |
0.09 |
0.025 |
2.25 |
1.593 |
0.565 |
1.162 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 22 | 58 | 122 | 0 | 28 |
normalized size | 1 | 1. | 0.96 | 0.88 | 2.32 | 4.88 | 0. | 1.12 |
time (sec) |
N/A |
0.029 |
0.054 |
0.025 |
1.468 |
1.532 |
0. |
1.129 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 81 | 57 | 355 | 209 | 0 | 0 |
normalized size | 1 | 1. | 1.01 | 0.71 | 4.44 | 2.61 | 0. | 0. |
time (sec) |
N/A |
0.045 |
0.202 |
0.024 |
1.739 |
1.687 |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 39 | 65 | 178 | 0 | 117 |
normalized size | 1 | 1. | 1. | 0.93 | 1.55 | 4.24 | 0. | 2.79 |
time (sec) |
N/A |
0.089 |
0.068 |
0.024 |
1.545 |
1.593 |
0. |
1.109 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 40 | 42 | 57 | 105 | 78 | 74 |
normalized size | 1 | 1. | 0.78 | 0.82 | 1.12 | 2.06 | 1.53 | 1.45 |
time (sec) |
N/A |
0.052 |
0.13 |
0.03 |
1.16 |
1.644 |
2.186 |
1.14 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
B |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 87 | 63 | 383 | 231 | 201 | 159 |
normalized size | 1 | 1. | 0.96 | 0.69 | 4.21 | 2.54 | 2.21 | 1.75 |
time (sec) |
N/A |
0.097 |
0.178 |
0.031 |
1.892 |
1.713 |
3.318 |
1.171 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 27 | 34 | 31 | 63 | 60 | 35 |
normalized size | 1 | 1. | 0.87 | 1.1 | 1. | 2.03 | 1.94 | 1.13 |
time (sec) |
N/A |
0.029 |
0.045 |
0.026 |
1.178 |
1.618 |
0.518 |
1.116 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 67 | 45 | 338 | 163 | 56 | 111 |
normalized size | 1 | 1. | 0.96 | 0.64 | 4.83 | 2.33 | 0.8 | 1.59 |
time (sec) |
N/A |
0.044 |
0.061 |
0.035 |
1.913 |
1.633 |
1.047 |
1.162 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 34 | 32 | 69 | 153 | 0 | 47 |
normalized size | 1 | 1. | 0.92 | 0.86 | 1.86 | 4.14 | 0. | 1.27 |
time (sec) |
N/A |
0.052 |
0.067 |
0.046 |
1.366 |
1.602 |
0. |
1.168 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 76 | 62 | 369 | 180 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0.82 | 4.86 | 2.37 | 0. | 0. |
time (sec) |
N/A |
0.067 |
0.177 |
0.03 |
1.458 |
1.678 |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
C |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 50 | 89 | 82 | 194 | 0 | 144 |
normalized size | 1 | 1. | 0.88 | 1.56 | 1.44 | 3.4 | 0. | 2.53 |
time (sec) |
N/A |
0.118 |
0.128 |
0.138 |
1.266 |
1.645 |
0. |
1.166 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 55 | 66 | 78 | 138 | 92 | 78 |
normalized size | 1 | 1. | 0.7 | 0.84 | 0.99 | 1.75 | 1.16 | 0.99 |
time (sec) |
N/A |
0.074 |
0.164 |
0.033 |
1.088 |
1.612 |
4.013 |
1.137 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
B |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 160 | 130 | 697 | 450 | 439 | 350 |
normalized size | 1 | 1. | 0.85 | 0.69 | 3.71 | 2.39 | 2.34 | 1.86 |
time (sec) |
N/A |
0.182 |
0.432 |
0.033 |
2.15 |
1.781 |
5.788 |
1.191 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 26 | 36 | 61 | 44 | 35 |
normalized size | 1 | 1. | 1. | 0.79 | 1.09 | 1.85 | 1.33 | 1.06 |
time (sec) |
N/A |
0.028 |
0.017 |
0.029 |
1.175 |
1.565 |
0.97 |
1.162 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 116 | 101 | 653 | 373 | 129 | 250 |
normalized size | 1 | 1. | 0.76 | 0.66 | 4.27 | 2.44 | 0.84 | 1.63 |
time (sec) |
N/A |
0.089 |
0.237 |
0.033 |
2.22 |
1.623 |
1.564 |
1.166 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
C |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 50 | 125 | 120 | 261 | 0 | 63 |
normalized size | 1 | 1. | 0.91 | 2.27 | 2.18 | 4.75 | 0. | 1.15 |
time (sec) |
N/A |
0.083 |
0.105 |
0.103 |
1.471 |
1.593 |
0. |
1.167 |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 166 | 128 | 721 | 412 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 0.76 | 4.29 | 2.45 | 0. | 0. |
time (sec) |
N/A |
0.144 |
0.644 |
0.033 |
1.39 |
1.828 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
C |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 90 | 162 | 132 | 340 | 0 | 250 |
normalized size | 1 | 1. | 0.99 | 1.78 | 1.45 | 3.74 | 0. | 2.75 |
time (sec) |
N/A |
0.201 |
0.175 |
0.147 |
1.539 |
1.683 |
0. |
1.178 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 54 | 50 | 74 | 123 | 94 | 70 |
normalized size | 1 | 1. | 0.81 | 0.75 | 1.1 | 1.84 | 1.4 | 1.04 |
time (sec) |
N/A |
0.054 |
0.088 |
0.028 |
1.178 |
1.702 |
17.455 |
1.274 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 113 | 229 | 397 | 176 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
2.06 |
3.58 |
1.59 |
0. |
0. |
time (sec) |
N/A |
0.081 |
0.201 |
0.142 |
1.474 |
1.702 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 111 | 290 | 390 | 170 | 0 | 0 |
normalized size | 1 | 1. | 1. | 2.61 | 3.51 | 1.53 | 0. | 0. |
time (sec) |
N/A |
0.079 |
0.158 |
0.077 |
1.525 |
1.754 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 89 | 290 | 365 | 132 | 0 | 0 |
normalized size | 1 | 1. | 1.1 | 3.58 | 4.51 | 1.63 | 0. | 0. |
time (sec) |
N/A |
0.063 |
0.09 |
0.066 |
1.608 |
1.708 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 89 | 338 | 359 | 132 | 0 | 0 |
normalized size | 1 | 1. | 1.1 | 4.17 | 4.43 | 1.63 | 0. | 0. |
time (sec) |
N/A |
0.065 |
0.071 |
0.078 |
1.447 |
1.711 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 114 | 338 | 355 | 163 | 0 | 0 |
normalized size | 1 | 1. | 1.16 | 3.45 | 3.62 | 1.66 | 0. | 0. |
time (sec) |
N/A |
0.076 |
0.182 |
0.067 |
1.413 |
1.695 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 117 | 358 | 355 | 177 | 0 | 0 |
normalized size | 1 | 1. | 1.12 | 3.44 | 3.41 | 1.7 | 0. | 0. |
time (sec) |
N/A |
0.075 |
0.156 |
0.069 |
1.445 |
1.788 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 142 | 0 | 421 | 242 | 0 | 0 |
normalized size |
1 |
1. |
1.08 |
0. |
3.19 |
1.83 |
0. |
0. |
time (sec) |
N/A |
0.175 |
0.458 |
0.094 |
1.495 |
1.81 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 142 | 0 | 424 | 236 | 0 | 0 |
normalized size | 1 | 1. | 1.08 | 0. | 3.21 | 1.79 | 0. | 0. |
time (sec) |
N/A |
0.124 |
0.345 |
0.089 |
1.412 |
1.827 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 122 | 0 | 392 | 176 | 0 | 0 |
normalized size | 1 | 1. | 1.22 | 0. | 3.92 | 1.76 | 0. | 0. |
time (sec) |
N/A |
0.13 |
0.226 |
0.085 |
1.422 |
1.744 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 120 | 0 | 393 | 170 | 0 | 0 |
normalized size | 1 | 1. | 1.25 | 0. | 4.09 | 1.77 | 0. | 0. |
time (sec) |
N/A |
0.068 |
0.232 |
0.099 |
1.451 |
1.77 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 137 | 0 | 369 | 188 | 0 | 0 |
normalized size | 1 | 1. | 1.17 | 0. | 3.15 | 1.61 | 0. | 0. |
time (sec) |
N/A |
0.163 |
0.34 |
0.089 |
1.347 |
1.766 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 137 | 0 | 373 | 196 | 0 | 0 |
normalized size |
1 |
1. |
1.18 |
0. |
3.22 |
1.69 |
0. |
0. |
time (sec) |
N/A |
0.1 |
0.368 |
0.092 |
1.447 |
1.742 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 39 | 77 | 144 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.26 | 2.48 | 4.65 | 0. | 0. |
time (sec) |
N/A |
0.072 |
0.031 |
0.037 |
1.287 |
1.595 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 21 | 58 | 109 | 15 | 0 |
normalized size | 1 | 1. | 1. | 1.05 | 2.9 | 5.45 | 0.75 | 0. |
time (sec) |
N/A |
0.027 |
0.047 |
0.033 |
1.421 |
1.573 |
1.915 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 14 | 18 | 28 | 15 | 18 |
normalized size | 1 | 1. | 1. | 1.08 | 1.38 | 2.15 | 1.15 | 1.38 |
time (sec) |
N/A |
0.014 |
0.003 |
0.026 |
1.055 |
1.511 |
1.759 |
1.133 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 29 | 42 | 69 | 70 | 31 | 0 |
normalized size | 1 | 1. | 0.97 | 1.4 | 2.3 | 2.33 | 1.03 | 0. |
time (sec) |
N/A |
0.025 |
0.048 |
0.032 |
1.291 |
1.578 |
3.44 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 46 | 92 | 68 | 95 | 46 | 0 |
normalized size | 1 | 1. | 1. | 2. | 1.48 | 2.07 | 1. | 0. |
time (sec) |
N/A |
0.047 |
0.004 |
0.033 |
1.368 |
1.515 |
6.182 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 80 | 57 | 533 | 208 | 0 | 0 |
normalized size | 1 | 1. | 1.01 | 0.72 | 6.75 | 2.63 | 0. | 0. |
time (sec) |
N/A |
0.05 |
0.134 |
0.033 |
1.418 |
1.689 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 22 | 58 | 123 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 0.88 | 2.32 | 4.92 | 0. | 0. |
time (sec) |
N/A |
0.028 |
0.045 |
0.037 |
1.35 |
1.59 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 62 | 48 | 495 | 186 | 0 | 0 |
normalized size | 1 | 1. | 0.84 | 0.65 | 6.69 | 2.51 | 0. | 0. |
time (sec) |
N/A |
0.032 |
0.109 |
0.035 |
1.378 |
1.608 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 39 | 22 | 0 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 2.6 | 1.47 | 0. |
time (sec) |
N/A |
0.015 |
0.003 |
0.024 |
1.149 |
1.558 |
6.099 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 88 | 64 | 359 | 235 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0.66 | 3.7 | 2.42 | 0. | 0. |
time (sec) |
N/A |
0.053 |
0.156 |
0.036 |
1.332 |
1.67 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 18 | 14 | 16 | 50 | 39 | 16 |
normalized size | 1 | 1. | 0.95 | 0.74 | 0.84 | 2.63 | 2.05 | 0.84 |
time (sec) |
N/A |
0.021 |
0.029 |
0.032 |
1.14 |
1.644 |
0.357 |
1.112 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 22 | 7 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 2.75 | 0.88 | 1. |
time (sec) |
N/A |
0.009 |
0.002 |
0.023 |
1.142 |
1.622 |
0.42 |
1.143 |
|
|
|
|
|
|
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|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 17 | 22 | 55 | 20 | 22 |
normalized size | 1 | 1. | 1. | 0.77 | 1. | 2.5 | 0.91 | 1. |
time (sec) |
N/A |
0.011 |
0.015 |
0.027 |
1.161 |
1.637 |
0.41 |
1.113 |
|
|
|
|
|
|
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|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 31 | 34 | 31 | 86 | 51 | 31 |
normalized size | 1 | 1. | 0.86 | 0.94 | 0.86 | 2.39 | 1.42 | 0.86 |
time (sec) |
N/A |
0.021 |
0.028 |
0.026 |
1.077 |
1.605 |
0.387 |
1.117 |
|
|
|
|
|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 235 | 235 | 165 | 196 | 459 | 462 | 0 | 325 |
normalized size | 1 | 1. | 0.7 | 0.83 | 1.95 | 1.97 | 0. | 1.38 |
time (sec) |
N/A |
0.348 |
0.568 |
0.033 |
2.769 |
1.784 |
0. |
1.154 |
|
|
|
|
|
|
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|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 141 | 131 | 419 | 366 | 0 | 261 |
normalized size |
1 |
1. |
0.83 |
0.78 |
2.48 |
2.17 |
0. |
1.54 |
time (sec) |
N/A |
0.196 |
0.363 |
0.03 |
2.435 |
1.763 |
0. |
1.155 |
|
|
|
|
|
|
|
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|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 94 | 64 | 346 | 250 | 0 | 193 |
normalized size | 1 | 1. | 0.95 | 0.65 | 3.49 | 2.53 | 0. | 1.95 |
time (sec) |
N/A |
0.113 |
0.153 |
0.032 |
1.952 |
1.923 |
0. |
1.16 |
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 110 | 78 | 358 | 300 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0.71 | 3.25 | 2.73 | 0. | 0. |
time (sec) |
N/A |
0.143 |
0.248 |
0.03 |
1.86 |
2.022 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 180 | 129 | 359 | 405 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 0.7 | 1.95 | 2.2 | 0. | 0. |
time (sec) |
N/A |
0.238 |
0.238 |
0.03 |
1.503 |
2.076 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 238 | 180 | 362 | 490 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 0.72 | 1.45 | 1.96 | 0. | 0. |
time (sec) |
N/A |
0.337 |
0.316 |
0.032 |
1.436 |
2.131 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 310 | 310 | 174 | 219 | 497 | 591 | 0 | 302 |
normalized size | 1 | 1. | 0.56 | 0.71 | 1.6 | 1.91 | 0. | 0.97 |
time (sec) |
N/A |
0.36 |
0.659 |
0.04 |
2.148 |
2.255 |
0. |
1.186 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 148 | 145 | 455 | 444 | 0 | 238 |
normalized size |
1 |
1. |
0.68 |
0.67 |
2.09 |
2.04 |
0. |
1.09 |
time (sec) |
N/A |
0.251 |
0.442 |
0.037 |
1.968 |
2.085 |
0. |
1.18 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 103 | 67 | 392 | 271 | 0 | 167 |
normalized size | 1 | 1. | 1.01 | 0.66 | 3.84 | 2.66 | 0. | 1.64 |
time (sec) |
N/A |
0.17 |
0.189 |
0.039 |
2.965 |
2.083 |
0. |
1.173 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 116 | 87 | 379 | 296 | 0 | 0 |
normalized size | 1 | 1. | 1. | 0.75 | 3.27 | 2.55 | 0. | 0. |
time (sec) |
N/A |
0.187 |
0.254 |
0.037 |
1.744 |
2.092 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 185 | 146 | 381 | 455 | 0 | 0 |
normalized size | 1 | 1. | 0.81 | 0.64 | 1.67 | 2. | 0. | 0. |
time (sec) |
N/A |
0.25 |
0.268 |
0.04 |
1.572 |
2.184 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 328 | 328 | 249 | 207 | 383 | 581 | 0 | 0 |
normalized size | 1 | 1. | 0.76 | 0.63 | 1.17 | 1.77 | 0. | 0. |
time (sec) |
N/A |
0.351 |
0.375 |
0.039 |
2.034 |
2.265 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 66 | 58 | 63 | 166 | 513 | 63 |
normalized size | 1 | 1. | 0.77 | 0.67 | 0.73 | 1.93 | 5.97 | 0.73 |
time (sec) |
N/A |
0.068 |
0.099 |
0.029 |
1.79 |
1.906 |
5.291 |
1.15 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 8 | 8 | 8 | 7 | 8 | 22 | 0 | 8 |
normalized size |
1 |
1. |
1. |
0.88 |
1. |
2.75 |
0. |
1. |
time (sec) |
N/A |
0.01 |
0.002 |
0.023 |
1.744 |
1.828 |
0. |
1.147 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
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 | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.02 |
0.987 |
1.156 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
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 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
1.261 |
1.145 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
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 | 93 | 93 | 89 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.102 |
0.205 |
1.874 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
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 | 38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.049 |
0.934 |
1.342 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 149 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.14 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.167 |
0.441 |
1.907 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
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 | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.054 |
1.158 |
1.388 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 24 | 25 | 0 | 131 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
0.96 |
0. |
5.04 |
0. |
0. |
time (sec) |
N/A |
0.034 |
0.065 |
0.034 |
0. |
1.895 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 37 | 45 | 0 | 165 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
1.05 |
0. |
3.84 |
0. |
0. |
time (sec) |
N/A |
0.058 |
0.089 |
0.036 |
0. |
1.862 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 53 | 52 | 0 | 274 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0.78 |
0. |
4.09 |
0. |
0. |
time (sec) |
N/A |
0.086 |
0.121 |
0.036 |
0. |
2.006 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 66 | 77 | 0 | 309 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0.97 |
0. |
3.91 |
0. |
0. |
time (sec) |
N/A |
0.094 |
0.141 |
0.039 |
0. |
2.025 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 92 | 75 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.11 | 0.9 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.022 |
0.09 |
0.092 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
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 | 102 | 102 | 94 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.92 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.069 |
0.247 |
0.165 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
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 | 179 | 179 | 173 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.079 |
0.24 |
180. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 115 | 111 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.1 | 1.06 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.075 |
0.2 |
0.162 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
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 | 141 | 141 | 129 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.16 |
0.516 |
0.126 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
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 | 229 | 229 | 221 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.212 |
0.562 |
0.178 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 45 | 45 | 0 | 190 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
0.96 |
0. |
4.04 |
0. |
0. |
time (sec) |
N/A |
0.086 |
0.094 |
0.036 |
0. |
1.667 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 53 | 65 | 0 | 209 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
0.94 |
0. |
3.03 |
0. |
0. |
time (sec) |
N/A |
0.121 |
0.187 |
0.044 |
0. |
1.736 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 95 | 101 | 0 | 366 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0.89 |
0. |
3.24 |
0. |
0. |
time (sec) |
N/A |
0.2 |
0.235 |
0.05 |
0. |
1.851 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 70 | 65 | 0 | 254 | 0 | 0 |
normalized size |
1 |
1. |
0.9 |
0.83 |
0. |
3.26 |
0. |
0. |
time (sec) |
N/A |
0.111 |
0.13 |
0.037 |
0. |
1.669 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 82 | 89 | 0 | 290 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
0.94 |
0. |
3.05 |
0. |
0. |
time (sec) |
N/A |
0.147 |
0.212 |
0.043 |
0. |
2.123 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 141 | 144 | 0 | 481 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0.87 |
0. |
2.92 |
0. |
0. |
time (sec) |
N/A |
0.253 |
0.356 |
0.05 |
0. |
2.055 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 76 | 131 | 346 | 278 | 0 | 215 |
normalized size | 1 | 1. | 0.77 | 1.32 | 3.49 | 2.81 | 0. | 2.17 |
time (sec) |
N/A |
0.068 |
0.265 |
0.029 |
2.781 |
1.667 |
0. |
1.13 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 42 | 63 | 266 | 158 | 0 | 161 |
normalized size | 1 | 1. | 0.89 | 1.34 | 5.66 | 3.36 | 0. | 3.43 |
time (sec) |
N/A |
0.032 |
0.047 |
0.028 |
2.371 |
1.641 |
0. |
1.142 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 36 | 113 | 107 | 0 | 74 |
normalized size | 1 | 1. | 1. | 1.24 | 3.9 | 3.69 | 0. | 2.55 |
time (sec) |
N/A |
0.006 |
0.008 |
0.028 |
1.763 |
1.542 |
0. |
1.09 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
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 | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.008 |
2.662 |
0.124 |
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 | 14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.009 |
5.288 |
0.116 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 346 | 346 | 224 | 825 | 907 | 248 | 274 | 1134 |
normalized size | 1 | 1. | 0.65 | 2.38 | 2.62 | 0.72 | 0.79 | 3.28 |
time (sec) |
N/A |
0.305 |
0.841 |
0.089 |
1.242 |
1.626 |
2.361 |
1.394 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 71 | 299 | 355 | 166 | 151 | 479 |
normalized size | 1 | 1. | 0.43 | 1.79 | 2.13 | 0.99 | 0.9 | 2.87 |
time (sec) |
N/A |
0.136 |
0.276 |
0.031 |
1.254 |
1.631 |
0.684 |
1.249 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 48 | 61 | 81 | 109 | 66 | 227 |
normalized size | 1 | 1. | 0.89 | 1.13 | 1.5 | 2.02 | 1.22 | 4.2 |
time (sec) |
N/A |
0.027 |
0.073 |
0.033 |
1.154 |
1.575 |
0.536 |
1.182 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 145 | 271 | 0 | 360 | 0 | 0 |
normalized size | 1 | 1. | 1.15 | 2.15 | 0. | 2.86 | 0. | 0. |
time (sec) |
N/A |
0.239 |
0.669 |
0.058 |
0. |
1.725 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 240 | 714 | 0 | 489 | 0 | 0 |
normalized size | 1 | 1. | 1.3 | 3.88 | 0. | 2.66 | 0. | 0. |
time (sec) |
N/A |
0.349 |
1.225 |
0.181 |
0. |
1.823 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
B |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 537 | 537 | 382 | 1809 | 1821 | 464 | 0 | 1490 |
normalized size | 1 | 1. | 0.71 | 3.37 | 3.39 | 0.86 | 0. | 2.77 |
time (sec) |
N/A |
0.511 |
1.107 |
0.102 |
1.479 |
1.704 |
0. |
1.613 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 117 | 655 | 706 | 293 | 0 | 500 |
normalized size | 1 | 1. | 0.45 | 2.51 | 2.7 | 1.12 | 0. | 1.92 |
time (sec) |
N/A |
0.231 |
0.417 |
0.035 |
1.254 |
1.638 |
0. |
1.238 |
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Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 65 | 131 | 159 | 155 | 94 | 109 |
normalized size | 1 | 1. | 0.76 | 1.54 | 1.87 | 1.82 | 1.11 | 1.28 |
time (sec) |
N/A |
0.055 |
0.111 |
0.034 |
1.118 |
1.625 |
1.678 |
1.263 |
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Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 234 | 234 | 243 | 279 | 0 | 833 | 0 | 0 |
normalized size | 1 | 1. | 1.04 | 1.19 | 0. | 3.56 | 0. | 0. |
time (sec) |
N/A |
0.468 |
0.433 |
0.149 |
0. |
1.771 |
0. |
0. |
|
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Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 332 | 332 | 138 | 933 | 0 | 1137 | 0 | 0 |
normalized size | 1 | 1. | 0.42 | 2.81 | 0. | 3.42 | 0. | 0. |
time (sec) |
N/A |
0.741 |
0.621 |
0.32 |
0. |
2.06 |
0. |
0. |
|
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|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf size
of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the
integral was to solve. In this test, problem number [35] had the largest ratio of [ 0.625
]
|
|
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| Table 2.1Rubi specific breakdown of results for each
integral
|
|
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|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
2 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
6 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
7 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
9 |
A |
6 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
10 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
11 |
A |
5 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
13 |
A |
6 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
14 |
A |
7 |
6 |
1. |
14 |
0.429 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
16 |
A |
10 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
18 |
A |
8 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
19 |
A |
8 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
20 |
A |
9 |
5 |
1. |
14 |
0.357 |
|
|
|
|
|
|
|
|
21 |
A |
12 |
6 |
1. |
14 |
0.429 |
|
|
|
|
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|
22 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
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|
|
23 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
24 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
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|
25 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
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|
26 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
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|
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|
27 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
28 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
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|
29 |
A |
7 |
5 |
1. |
16 |
0.312 |
|
|
|
|
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|
30 |
A |
7 |
5 |
1. |
16 |
0.312 |
|
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31 |
A |
6 |
4 |
1. |
16 |
0.25 |
|
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|
32 |
A |
6 |
4 |
1. |
16 |
0.25 |
|
|
|
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|
33 |
A |
7 |
5 |
1. |
16 |
0.312 |
|
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|
34 |
A |
7 |
6 |
1. |
16 |
0.375 |
|
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|
|
35 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
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|
36 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
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|
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|
37 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
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|
38 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
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|
39 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
40 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
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|
|
|
41 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
42 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
43 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
44 |
A |
5 |
5 |
1. |
12 |
0.417 |
|
|
|
|
|
|
|
45 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
46 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
47 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
48 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
49 |
A |
13 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
50 |
A |
10 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
51 |
A |
7 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
52 |
A |
8 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
53 |
A |
11 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
54 |
A |
14 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
55 |
A |
15 |
10 |
1. |
18 |
0.556 |
|
|
|
|
|
|
|
56 |
A |
12 |
9 |
1. |
18 |
0.5 |
|
|
|
|
|
|
|
57 |
A |
9 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
58 |
A |
10 |
9 |
1. |
18 |
0.5 |
|
|
|
|
|
|
|
59 |
A |
12 |
10 |
1. |
18 |
0.556 |
|
|
|
|
|
|
|
60 |
A |
16 |
9 |
1. |
18 |
0.5 |
|
|
|
|
|
|
|
|
61 |
A |
7 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
62 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
63 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
64 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
65 |
A |
3 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
66 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
67 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
68 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
69 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
70 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
71 |
A |
8 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
72 |
A |
8 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
73 |
A |
3 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
74 |
A |
5 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
75 |
A |
8 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
76 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
77 |
A |
5 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
78 |
A |
8 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
79 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
80 |
A |
7 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
|
81 |
A |
12 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
82 |
A |
6 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
83 |
A |
8 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
84 |
A |
14 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
85 |
A |
7 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
86 |
A |
5 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
87 |
A |
1 |
1 |
1. |
8 |
0.125 |
|
|
|
|
|
|
|
88 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
89 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
90 |
A |
14 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
91 |
A |
8 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
92 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
93 |
A |
8 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
94 |
A |
10 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
95 |
A |
20 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
96 |
A |
11 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
97 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
98 |
A |
11 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
99 |
A |
13 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|