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 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 8, 10, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 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, 71, 73, 81, 85, 86, 87, 89, 90, 93, 94, 95, 96, 97, 98 }
B grade: { 6, 7, 9, 11, 12, 15, 16, 33, 34, 88, 91 }
C grade: { 70, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 92 }
F grade: { }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 6, 8, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37,
38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 57, 59, 60, 62, 63, 65, 66, 71, 72, 73, 81, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 }
B grade: { 7, 9, 10, 15, 16, 17, 18, 34, 52, 55, 56, 58, 61, 64, 67, 68, 69, 70, 84, 85 }
C grade: { 5, 74, 75, 76, 77, 78, 79, 80, 82, 83 }
F grade: { }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 8, 9, 24, 25, 26, 27, 44, 45, 46, 47, 48, 49, 52, 67, 68, 69, 73, 81, 86
B grade: { 6, 7, 51, 53, 54, 88, 90, 91 }
C grade: { }
F grade: { 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 50, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83,
84, 85, 87, 89, 92, 93, 94, 95, 96, 97, 98 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 17, 18, 19, 24, 28, 29, 30, 32, 33, 34, 35, 36, 37, 44, 45, 46, 47,
48, 49, 50, 51, 53, 73, 86, 87, 88, 89, 90, 93, 95, 96, 97, 98 }
B grade: { 6, 7, 9, 15, 16, 20, 21, 22, 23, 25, 26, 27, 31, 38, 39, 40, 41, 42, 43, 67, 68, 69, 70, 71, 81, 91
}
C grade: { }
F grade: { 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85,
92, 94 }
2.1.6 Sympy
A grade: { 5, 13, 24, 44, 73 }
B grade: { 1, 2, 3, 4, 6, 25, 26, 27, 45, 46 }
C grade: { }
F grade: { 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 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, 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
}
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 29, 30, 31, 32,
33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 67, 68, 69, 73, 86, 87, 89, 92, 93, 94, 95, 96
}
B grade: { 6, 7, 15, 16, 23, 47, 49, 53, 81, 88, 90, 91 }
C grade: { 48, 50, 54 }
F grade: { 24, 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 82,
83, 84, 85, 97, 98 }
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 |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 26 | 42 | 50 | 62 | 473 | 42 |
normalized size | 1 | 1. | 0.79 | 1.27 | 1.52 | 1.88 | 14.33 | 1.27 |
time (sec) |
N/A |
0.052 |
0.004 |
0.083 |
1.424 |
1.891 |
16.231 |
1.153 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 16 | 19 | 39 | 162 | 19 |
normalized size | 1 | 1. | 1. | 0.84 | 1. | 2.05 | 8.53 | 1. |
time (sec) |
N/A |
0.045 |
0.003 |
0.018 |
0.946 |
1.734 |
18.335 |
1.118 |
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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 |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 18 | 25 | 28 | 38 | 153 | 30 |
normalized size | 1 | 1. | 0.9 | 1.25 | 1.4 | 1.9 | 7.65 | 1.5 |
time (sec) |
N/A |
0.045 |
0.003 |
0.022 |
1.452 |
1.745 |
4.435 |
1.133 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 8 | 9 | 15 | 36 | 9 |
normalized size | 1 | 1. | 1. | 1.14 | 1.29 | 2.14 | 5.14 | 1.29 |
time (sec) |
N/A |
0.041 |
0.002 |
0.015 |
0.946 |
1.853 |
2.009 |
1.123 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 5 | 5 | 5 | 8 | 7 | 7 | 2 | 7 |
normalized size | 1 | 1. | 1. | 1.6 | 1.4 | 1.4 | 0.4 | 1.4 |
time (sec) |
N/A |
0.04 |
0.001 |
0.022 |
1.414 |
1.916 |
0.998 |
1.171 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
A |
B |
B |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 21 | 9 | 28 | 77 | 19 | 31 |
normalized size | 1 | 1. | 2.62 | 1.12 | 3.5 | 9.62 | 2.38 | 3.88 |
time (sec) |
N/A |
0.025 |
0.007 |
0.014 |
0.952 |
2.012 |
0.264 |
1.165 |
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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 | 22 | 22 | 51 | 44 | 50 | 153 | 0 | 51 |
normalized size | 1 | 1. | 2.32 | 2. | 2.27 | 6.95 | 0. | 2.32 |
time (sec) |
N/A |
0.044 |
0.008 |
0.034 |
0.949 |
1.892 |
0. |
1.16 |
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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 |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 21 | 18 | 23 | 76 | 0 | 23 |
normalized size | 1 | 1. | 1.11 | 0.95 | 1.21 | 4. | 0. | 1.21 |
time (sec) |
N/A |
0.048 |
0.003 |
0.03 |
0.942 |
1.825 |
0. |
1.175 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
A |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 75 | 66 | 69 | 232 | 0 | 63 |
normalized size | 1 | 1. | 2.14 | 1.89 | 1.97 | 6.63 | 0. | 1.8 |
time (sec) |
N/A |
0.055 |
0.006 |
0.037 |
0.952 |
1.97 |
0. |
1.129 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 143 | 138 | 0 | 547 | 0 | 134 |
normalized size |
1 |
1. |
1.83 |
1.77 |
0. |
7.01 |
0. |
1.72 |
time (sec) |
N/A |
0.09 |
0.243 |
0.024 |
0. |
2.087 |
0. |
1.142 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 116 | 86 | 0 | 383 | 0 | 80 |
normalized size |
1 |
1. |
2.15 |
1.59 |
0. |
7.09 |
0. |
1.48 |
time (sec) |
N/A |
0.073 |
0.168 |
0.019 |
0. |
1.777 |
0. |
1.127 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 90 | 46 | 0 | 248 | 0 | 41 |
normalized size |
1 |
1. |
2.5 |
1.28 |
0. |
6.89 |
0. |
1.14 |
time (sec) |
N/A |
0.053 |
0.161 |
0.017 |
0. |
1.745 |
0. |
1.128 |
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Problem 13 |
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 | 26 | 26 | 26 | 18 | 0 | 181 | 87 | 23 |
normalized size |
1 |
1. |
1. |
0.69 |
0. |
6.96 |
3.35 |
0.88 |
time (sec) |
N/A |
0.027 |
0.019 |
0.012 |
0. |
1.671 |
1.947 |
1.123 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 50 | 56 | 0 | 329 | 0 | 68 |
normalized size |
1 |
1. |
1.19 |
1.33 |
0. |
7.83 |
0. |
1.62 |
time (sec) |
N/A |
0.049 |
0.047 |
0.036 |
0. |
1.782 |
0. |
1.201 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F(-2) |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 140 | 111 | 0 | 713 | 0 | 139 |
normalized size |
1 |
1. |
2.26 |
1.79 |
0. |
11.5 |
0. |
2.24 |
time (sec) |
N/A |
0.086 |
0.508 |
0.041 |
0. |
2.121 |
0. |
1.157 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
B |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 204 | 205 | 0 | 1490 | 0 | 240 |
normalized size |
1 |
1. |
2.17 |
2.18 |
0. |
15.85 |
0. |
2.55 |
time (sec) |
N/A |
0.138 |
1.232 |
0.049 |
0. |
2.499 |
0. |
1.159 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 77 | 194 | 0 | 702 | 0 | 161 |
normalized size |
1 |
1. |
0.88 |
2.2 |
0. |
7.98 |
0. |
1.83 |
time (sec) |
N/A |
0.181 |
0.188 |
0.033 |
0. |
1.933 |
0. |
1.19 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 52 | 105 | 0 | 541 | 0 | 108 |
normalized size |
1 |
1. |
0.87 |
1.75 |
0. |
9.02 |
0. |
1.8 |
time (sec) |
N/A |
0.105 |
0.098 |
0.025 |
0. |
1.9 |
0. |
1.153 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 37 | 54 | 0 | 435 | 0 | 68 |
normalized size |
1 |
1. |
0.92 |
1.35 |
0. |
10.88 |
0. |
1.7 |
time (sec) |
N/A |
0.059 |
0.065 |
0.023 |
0. |
1.976 |
0. |
1.204 |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 29 | 21 | 0 | 406 | 0 | 50 |
normalized size |
1 |
1. |
0.97 |
0.7 |
0. |
13.53 |
0. |
1.67 |
time (sec) |
N/A |
0.019 |
0.057 |
0.014 |
0. |
1.803 |
0. |
1.136 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
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 | 41 | 41 | 40 | 39 | 0 | 571 | 0 | 74 |
normalized size |
1 |
1. |
0.98 |
0.95 |
0. |
13.93 |
0. |
1.8 |
time (sec) |
N/A |
0.056 |
0.089 |
0.03 |
0. |
1.911 |
0. |
1.177 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
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 | 61 | 61 | 59 | 65 | 0 | 936 | 0 | 122 |
normalized size |
1 |
1. |
0.97 |
1.07 |
0. |
15.34 |
0. |
2. |
time (sec) |
N/A |
0.08 |
0.2 |
0.038 |
0. |
1.98 |
0. |
1.217 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 90 | 106 | 0 | 1446 | 0 | 211 |
normalized size |
1 |
1. |
1.01 |
1.19 |
0. |
16.25 |
0. |
2.37 |
time (sec) |
N/A |
0.102 |
0.381 |
0.042 |
0. |
2.043 |
0. |
1.21 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 79 | 80 | 120 | 251 | 85 | 0 |
normalized size |
1 |
1. |
0.81 |
0.82 |
1.22 |
2.56 |
0.87 |
0. |
time (sec) |
N/A |
0.09 |
0.098 |
0.017 |
1.439 |
1.753 |
3.141 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 4 | 4 | 4 | 7 | 8 | 22 | 14 | 8 |
normalized size | 1 | 1. | 1. | 1.75 | 2. | 5.5 | 3.5 | 2. |
time (sec) |
N/A |
0.014 |
0.002 |
0.014 |
0.957 |
1.593 |
0.597 |
1.179 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 17 | 14 | 19 | 73 | 34 | 19 |
normalized size | 1 | 1. | 1.31 | 1.08 | 1.46 | 5.62 | 2.62 | 1.46 |
time (sec) |
N/A |
0.015 |
0.003 |
0.017 |
0.963 |
1.539 |
2.429 |
1.217 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 27 | 20 | 27 | 112 | 54 | 27 |
normalized size | 1 | 1. | 1.29 | 0.95 | 1.29 | 5.33 | 2.57 | 1.29 |
time (sec) |
N/A |
0.017 |
0.004 |
0.017 |
0.952 |
1.589 |
9.119 |
1.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
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 | 78 | 78 | 111 | 78 | 0 | 597 | 0 | 130 |
normalized size |
1 |
1. |
1.42 |
1. |
0. |
7.65 |
0. |
1.67 |
time (sec) |
N/A |
0.084 |
0.385 |
0.02 |
0. |
1.911 |
0. |
1.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
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 | 56 | 56 | 86 | 50 | 0 | 441 | 0 | 88 |
normalized size |
1 |
1. |
1.54 |
0.89 |
0. |
7.88 |
0. |
1.57 |
time (sec) |
N/A |
0.071 |
0.185 |
0.015 |
0. |
1.871 |
0. |
1.169 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 | 38 | 38 | 38 | 33 | 0 | 319 | 0 | 55 |
normalized size |
1 |
1. |
1. |
0.87 |
0. |
8.39 |
0. |
1.45 |
time (sec) |
N/A |
0.055 |
0.029 |
0.013 |
0. |
1.878 |
0. |
1.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 21 | 0 | 228 | 0 | 42 |
normalized size |
1 |
1. |
1. |
0.72 |
0. |
7.86 |
0. |
1.45 |
time (sec) |
N/A |
0.031 |
0.011 |
0.011 |
0. |
1.783 |
0. |
1.126 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 38 | 47 | 0 | 329 | 0 | 77 |
normalized size |
1 |
1. |
0.93 |
1.15 |
0. |
8.02 |
0. |
1.88 |
time (sec) |
N/A |
0.052 |
0.056 |
0.028 |
0. |
1.878 |
0. |
1.188 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 152 | 92 | 0 | 536 | 0 | 115 |
normalized size |
1 |
1. |
2.58 |
1.56 |
0. |
9.08 |
0. |
1.95 |
time (sec) |
N/A |
0.098 |
0.361 |
0.039 |
0. |
1.997 |
0. |
1.22 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 215 | 165 | 0 | 709 | 0 | 171 |
normalized size |
1 |
1. |
2.39 |
1.83 |
0. |
7.88 |
0. |
1.9 |
time (sec) |
N/A |
0.166 |
1.098 |
0.042 |
0. |
2.135 |
0. |
1.172 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
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 | 87 | 87 | 76 | 122 | 0 | 666 | 0 | 140 |
normalized size |
1 |
1. |
0.87 |
1.4 |
0. |
7.66 |
0. |
1.61 |
time (sec) |
N/A |
0.196 |
0.213 |
0.022 |
0. |
1.944 |
0. |
1.162 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
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 | 60 | 60 | 52 | 60 | 0 | 533 | 0 | 97 |
normalized size |
1 |
1. |
0.87 |
1. |
0. |
8.88 |
0. |
1.62 |
time (sec) |
N/A |
0.098 |
0.121 |
0.02 |
0. |
1.891 |
0. |
1.174 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
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 | 38 | 38 | 36 | 32 | 0 | 447 | 0 | 65 |
normalized size |
1 |
1. |
0.95 |
0.84 |
0. |
11.76 |
0. |
1.71 |
time (sec) |
N/A |
0.06 |
0.079 |
0.017 |
0. |
1.837 |
0. |
1.184 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 29 | 21 | 0 | 406 | 0 | 50 |
normalized size |
1 |
1. |
0.97 |
0.7 |
0. |
13.53 |
0. |
1.67 |
time (sec) |
N/A |
0.019 |
0.048 |
0.001 |
0. |
2.199 |
0. |
1.177 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
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 | 37 | 37 | 38 | 33 | 0 | 543 | 0 | 49 |
normalized size |
1 |
1. |
1.03 |
0.89 |
0. |
14.68 |
0. |
1.32 |
time (sec) |
N/A |
0.061 |
0.074 |
0.028 |
0. |
1.928 |
0. |
1.124 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 55 | 51 | 0 | 672 | 0 | 96 |
normalized size |
1 |
1. |
0.98 |
0.91 |
0. |
12. |
0. |
1.71 |
time (sec) |
N/A |
0.086 |
0.135 |
0.03 |
0. |
1.893 |
0. |
1.191 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 80 | 80 | 0 | 832 | 0 | 140 |
normalized size |
1 |
1. |
1.01 |
1.01 |
0. |
10.53 |
0. |
1.77 |
time (sec) |
N/A |
0.101 |
0.319 |
0.034 |
0. |
1.848 |
0. |
1.183 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 70 | 81 | 0 | 774 | 0 | 93 |
normalized size |
1 |
1. |
1.08 |
1.25 |
0. |
11.91 |
0. |
1.43 |
time (sec) |
N/A |
0.049 |
0.222 |
0.02 |
0. |
1.91 |
0. |
1.162 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 106 | 175 | 0 | 1381 | 0 | 201 |
normalized size |
1 |
1. |
0.99 |
1.64 |
0. |
12.91 |
0. |
1.88 |
time (sec) |
N/A |
0.117 |
0.615 |
0.022 |
0. |
2.189 |
0. |
1.151 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
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 | 34 | 34 | 15 | 14 | 18 | 99 | 63 | 62 |
normalized size | 1 | 1. | 0.44 | 0.41 | 0.53 | 2.91 | 1.85 | 1.82 |
time (sec) |
N/A |
0.013 |
0.024 |
0.011 |
1.484 |
1.617 |
1.075 |
1.186 |
|
|
|
|
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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 | 55 | 55 | 35 | 27 | 35 | 178 | 218 | 80 |
normalized size | 1 | 1. | 0.64 | 0.49 | 0.64 | 3.24 | 3.96 | 1.45 |
time (sec) |
N/A |
0.026 |
0.076 |
0.017 |
1.492 |
1.661 |
7.46 |
1.195 |
|
|
|
|
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Problem 46 |
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 | 71 | 71 | 51 | 35 | 55 | 251 | 439 | 92 |
normalized size | 1 | 1. | 0.72 | 0.49 | 0.77 | 3.54 | 6.18 | 1.3 |
time (sec) |
N/A |
0.052 |
0.123 |
0.016 |
1.458 |
1.635 |
34.938 |
1.227 |
|
|
|
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Problem 47 |
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 | 12 | 12 | 12 | 13 | 14 | 12 | 0 | 32 |
normalized size | 1 | 1. | 1. | 1.08 | 1.17 | 1. | 0. | 2.67 |
time (sec) |
N/A |
0.016 |
0.006 |
0.463 |
1.445 |
1.9 |
0. |
1.271 |
|
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 14 | 16 | 4 | 0 | 38 |
normalized size | 1 | 1. | 1. | 1. | 1.14 | 0.29 | 0. | 2.71 |
time (sec) |
N/A |
0.016 |
0.005 |
0.231 |
1.457 |
1.779 |
0. |
1.178 |
|
|
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 23 | 19 | 15 | 31 | 0 | 61 |
normalized size |
1 |
1. |
0.79 |
0.66 |
0.52 |
1.07 |
0. |
2.1 |
time (sec) |
N/A |
0.022 |
0.026 |
0.756 |
1.636 |
1.724 |
0. |
1.213 |
|
|
|
|
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|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 25 | 21 | 0 | 4 | 0 | 74 |
normalized size |
1 |
1. |
0.76 |
0.64 |
0. |
0.12 |
0. |
2.24 |
time (sec) |
N/A |
0.025 |
0.026 |
0.464 |
0. |
1.548 |
0. |
1.244 |
|
|
|
|
|
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|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 28 | 14 | 47 | 77 | 0 | 0 |
normalized size | 1 | 1. | 1.87 | 0.93 | 3.13 | 5.13 | 0. | 0. |
time (sec) |
N/A |
0.02 |
0.015 |
0.336 |
1.64 |
1.612 |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
F(-2) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 30 | 34 | 23 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.76 |
2. |
1.35 |
0. |
0. |
0. |
time (sec) |
N/A |
0.018 |
0.01 |
0.233 |
1.584 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
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|
|
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|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 51 | 37 | 405 | 150 | 0 | 105 |
normalized size |
1 |
1. |
1.59 |
1.16 |
12.66 |
4.69 |
0. |
3.28 |
time (sec) |
N/A |
0.027 |
0.044 |
0.812 |
1.638 |
1.61 |
0. |
1.275 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
F(-2) |
F(-1) |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 53 | 51 | 383 | 0 | 0 | 122 |
normalized size |
1 |
1. |
1.47 |
1.42 |
10.64 |
0. |
0. |
3.39 |
time (sec) |
N/A |
0.026 |
0.03 |
0.499 |
1.671 |
0. |
0. |
1.296 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 11 | 41 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.22 | 4.56 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.008 |
0.021 |
0.747 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 34 | 75 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.06 | 2.34 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.022 |
0.038 |
1.302 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 46 | 49 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.1 | 1.17 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.035 |
0.072 |
0.336 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 39 | 101 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
2.35 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.054 |
0.048 |
1.055 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 66 | 110 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
1.24 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.094 |
0.068 |
1.364 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 123 | 192 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
1.59 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.162 |
0.452 |
0.783 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
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|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 11 | 41 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.22 | 4.56 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.008 |
0.033 |
0.683 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 33 | 62 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 1.94 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.018 |
0.04 |
0.943 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
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|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 46 | 48 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.1 | 1.14 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.029 |
0.064 |
0.37 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 35 | 70 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
2.19 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.018 |
0.06 |
1.058 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 43 | 101 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.77 |
1.8 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.033 |
0.041 |
1.184 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 75 | 73 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
0.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.047 |
0.175 |
0.798 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 33 | 11 | 162 | 0 | 11 |
normalized size |
1 |
1. |
1. |
3.67 |
1.22 |
18. |
0. |
1.22 |
time (sec) |
N/A |
0.021 |
0.007 |
0.377 |
1.427 |
1.716 |
0. |
1.334 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 57 | 15 | 248 | 0 | 15 |
normalized size |
1 |
1. |
1. |
3.8 |
1. |
16.53 |
0. |
1. |
time (sec) |
N/A |
0.027 |
0.024 |
0.484 |
1.453 |
1.729 |
0. |
1.416 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 53 | 11 | 119 | 0 | 22 |
normalized size |
1 |
1. |
1. |
5.89 |
1.22 |
13.22 |
0. |
2.44 |
time (sec) |
N/A |
0.026 |
0.009 |
0.897 |
1.522 |
1.669 |
0. |
1.234 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 487 | 487 | 121 | 3348 | 0 | 1796 | 0 | 0 |
normalized size |
1 |
1. |
0.25 |
6.87 |
0. |
3.69 |
0. |
0. |
time (sec) |
N/A |
1.101 |
0.222 |
0.153 |
0. |
2.445 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 109 | 64 | 0 | 1774 | 0 | 0 |
normalized size |
1 |
1. |
1.08 |
0.63 |
0. |
17.56 |
0. |
0. |
time (sec) |
N/A |
0.116 |
0.189 |
0.035 |
0. |
2.525 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 292 | 292 | 45 | 227 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.15 |
0.78 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.191 |
0.07 |
0.099 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
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 | 45 | 45 | 24 | 21 | 27 | 135 | 78 | 72 |
normalized size | 1 | 1. | 0.53 | 0.47 | 0.6 | 3. | 1.73 | 1.6 |
time (sec) |
N/A |
0.018 |
0.054 |
0.02 |
1.455 |
2.184 |
4.633 |
1.238 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 494 | 494 | 130 | 150 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.26 |
0.3 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.918 |
0.204 |
0.027 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 146 | 60 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0.35 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.238 |
0.225 |
0.152 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 245 | 245 | 172 | 76 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.7 |
0.31 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.486 |
0.26 |
0.091 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 494 | 494 | 130 | 148 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.26 |
0.3 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.589 |
0.18 |
0.027 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 146 | 62 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
0.35 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.249 |
0.176 |
0.121 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 172 | 78 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.81 |
0.37 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.216 |
0.209 |
0.089 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 378 | 62 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.7 |
0.28 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.562 |
0.123 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 103 | 79 | 73 | 97 | 463 | 0 | 250 |
normalized size |
1 |
1.24 |
0.95 |
0.88 |
1.17 |
5.58 |
0. |
3.01 |
time (sec) |
N/A |
0.104 |
0.16 |
0.02 |
1.431 |
1.675 |
0. |
1.172 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 141 | 67 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
0.52 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.18 |
0.142 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 378 | 62 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.84 |
0.3 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.473 |
0.119 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 117 | 233 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.65 |
3.28 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.119 |
0.265 |
0.092 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 64 | 246 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
2.76 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.077 |
0.145 |
0.034 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
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 | 17 | 17 | 17 | 16 | 26 | 59 | 0 | 23 |
normalized size | 1 | 1. | 1. | 0.94 | 1.53 | 3.47 | 0. | 1.35 |
time (sec) |
N/A |
0.029 |
0.008 |
0.032 |
0.934 |
2.249 |
0. |
1.184 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 40 | 43 | 0 | 243 | 0 | 51 |
normalized size |
1 |
1. |
1. |
1.08 |
0. |
6.08 |
0. |
1.27 |
time (sec) |
N/A |
0.063 |
0.026 |
0.018 |
0. |
3.372 |
0. |
1.145 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 47 | 17 | 63 | 72 | 0 | 61 |
normalized size | 1 | 1. | 2.35 | 0.85 | 3.15 | 3.6 | 0. | 3.05 |
time (sec) |
N/A |
0.051 |
0.029 |
0.413 |
1.498 |
1.688 |
0. |
1.156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 30 | 0 | 184 | 0 | 32 |
normalized size |
1 |
1. |
1. |
1.2 |
0. |
7.36 |
0. |
1.28 |
time (sec) |
N/A |
0.06 |
0.012 |
0.02 |
0. |
2.122 |
0. |
1.155 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 10 | 81 | 51 | 0 | 36 |
normalized size | 1 | 1. | 1. | 0.91 | 7.36 | 4.64 | 0. | 3.27 |
time (sec) |
N/A |
0.035 |
0.01 |
0.019 |
1.457 |
1.872 |
0. |
1.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 44 | 8 | 53 | 59 | 0 | 45 |
normalized size | 1 | 1. | 4.89 | 0.89 | 5.89 | 6.56 | 0. | 5. |
time (sec) |
N/A |
0.053 |
0.021 |
0.21 |
1.469 |
1.701 |
0. |
1.171 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 217 | 125 | 0 | 0 | 0 | 193 |
normalized size |
1 |
1. |
1.42 |
0.82 |
0. |
0. |
0. |
1.26 |
time (sec) |
N/A |
0.197 |
0.259 |
0.032 |
0. |
0. |
0. |
1.204 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 34 | 0 | 340 | 0 | 51 |
normalized size |
1 |
1. |
1. |
0.76 |
0. |
7.56 |
0. |
1.13 |
time (sec) |
N/A |
0.073 |
0.025 |
0.179 |
0. |
26.956 |
0. |
1.173 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 21 | 0 | 0 | 0 | 32 |
normalized size |
1 |
1. |
1. |
0.75 |
0. |
0. |
0. |
1.14 |
time (sec) |
N/A |
0.067 |
0.016 |
0.03 |
0. |
0. |
0. |
1.174 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 44 | 0 | 259 | 0 | 51 |
normalized size |
1 |
1. |
1. |
0.98 |
0. |
5.76 |
0. |
1.13 |
time (sec) |
N/A |
0.077 |
0.031 |
0.032 |
0. |
3.212 |
0. |
1.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 31 | 0 | 189 | 0 | 32 |
normalized size | 1 | 1. | 1. | 1.11 | 0. | 6.75 | 0. | 1.14 |
time (sec) |
N/A |
0.071 |
0.016 |
0.033 |
0. |
2.885 |
0. |
1.151 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
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 | 47 | 47 | 46 | 39 | 0 | 254 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
0.83 |
0. |
5.4 |
0. |
0. |
time (sec) |
N/A |
0.079 |
0.03 |
0.02 |
0. |
2.102 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
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 | 29 | 29 | 29 | 24 | 0 | 192 | 0 | 0 |
normalized size |
1 |
1. |
1. |
0.83 |
0. |
6.62 |
0. |
0. |
time (sec) |
N/A |
0.077 |
0.015 |
0.02 |
0. |
1.965 |
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 [72] had the largest ratio of [ 0.75
]
|
|
|
|
|
|
|
| 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 |
4 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
2 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
3 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
4 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
6 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
7 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
8 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
9 |
A |
4 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
10 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
11 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
12 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
13 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
14 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
15 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
16 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
17 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
18 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
19 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
20 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
|
21 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
22 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
23 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
24 |
A |
7 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
25 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
26 |
A |
3 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
27 |
A |
3 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
28 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
29 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
30 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
31 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
32 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
34 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
35 |
A |
6 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
36 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
37 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
38 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
39 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
40 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
|
41 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
42 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
43 |
A |
5 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
44 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
45 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
46 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
47 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
48 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
49 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
50 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
51 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
52 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
53 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
54 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
55 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
56 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
57 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
58 |
A |
4 |
4 |
1. |
10 |
0.4 |
|
|
|
|
|
|
|
59 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
60 |
A |
6 |
6 |
1. |
12 |
0.5 |
|
|
|
|
|
|
|
|
61 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
62 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
63 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
64 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
65 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
66 |
A |
4 |
4 |
1. |
12 |
0.333 |
|
|
|
|
|
|
|
67 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
68 |
A |
2 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
69 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
70 |
A |
10 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
71 |
A |
4 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
72 |
A |
10 |
6 |
1. |
8 |
0.75 |
|
|
|
|
|
|
|
73 |
A |
3 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
74 |
A |
12 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
75 |
A |
7 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
76 |
A |
9 |
3 |
1. |
10 |
0.3 |
|
|
|
|
|
|
|
77 |
A |
12 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
78 |
A |
7 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
79 |
A |
9 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
80 |
A |
11 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
|
81 |
A |
7 |
3 |
1.24 |
8 |
0.375 |
|
|
|
|
|
|
|
82 |
A |
9 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
83 |
A |
11 |
5 |
1. |
10 |
0.5 |
|
|
|
|
|
|
|
84 |
A |
8 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
85 |
A |
10 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
86 |
A |
4 |
4 |
1. |
11 |
0.364 |
|
|
|
|
|
|
|
87 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
88 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
89 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
90 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
91 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
92 |
A |
11 |
10 |
1. |
15 |
0.667 |
|
|
|
|
|
|
|
93 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
94 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
95 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
96 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
97 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
98 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|