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 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 11, 13, 15, 16, 19, 22, 24, 26, 27, 30, 34, 35, 36, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48,
49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 66, 67, 68, 69, 70, 71, 72, 73, 74, 85, 87, 88, 90, 91, 92, 93,
94, 95, 96 }
B grade: { 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 89 }
C grade: { 5, 6, 7, 8, 9, 10, 12, 14, 17, 18, 20, 21, 23, 25, 28, 29, 31, 32, 33, 39, 41 }
F grade: { 58, 63, 64, 65}
2.1.3 Maple
A grade: { 1, 2, 11, 12, 15, 16, 19, 22, 23, 26, 27, 30, 34, 35, 36, 38, 59, 66, 67, 68, 90, 94, 95, 96
}
B grade: { 37 }
C grade: { 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 18, 20, 21, 24, 25, 28, 29, 31, 32, 33, 39, 40, 41 }
F grade: { 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 69, 70, 71,
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93 }
2.1.4 Maxima
A grade: { 11, 15, 22, 26, 59, 90, 94, 95, 96
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 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, 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, 93
}
2.1.5 FriCAS
A grade: { 11, 12, 14, 22, 23, 26, 31, 32, 33, 34, 35, 59, 90, 94, 95, 96 }
B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 16, 17, 18, 19, 20, 21, 24, 25, 27, 28, 29, 30, 36, 37, 38, 40, 66,
67, 68 }
C grade: { }
F grade: { 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63,
64, 65, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93
}
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 31, 36,
38, 40, 66, 67, 68 }
B grade: { 26, 34, 35, 37 }
C grade: { 12, 23, 42, 43, 44, 47 }
F grade: { 32, 33, 39, 41, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 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
}
2.1.7 Giac
A grade: { 1, 2, 3, 10, 11, 13, 14, 15, 16, 19, 21, 22, 24, 25, 27, 30, 31, 32, 33, 34, 35, 36, 38, 40, 59, 90, 94,
95, 96 }
B grade: { 4, 26, 66, 67, 68 }
C grade: { }
F grade: { 5, 6, 7, 8, 9, 12, 17, 18, 20, 23, 28, 29, 37, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54,
55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 91, 92, 93 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 305 | 305 | 334 | 329 | 0 | 6589 | 165 | 397 |
normalized size |
1 |
1. |
1.1 |
1.08 |
0. |
21.6 |
0.54 |
1.3 |
time (sec) |
N/A |
0.249 |
0.098 |
0.076 |
0. |
2.608 |
2.139 |
1.124 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 323 | 323 | 337 | 386 | 0 | 6541 | 168 | 424 |
normalized size |
1 |
1. |
1.04 |
1.2 |
0. |
20.25 |
0.52 |
1.31 |
time (sec) |
N/A |
0.189 |
0.11 |
0.12 |
0. |
2.413 |
2.183 |
1.142 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 754 | 754 | 534 | 34 | 0 | 6978 | 199 | 811 |
normalized size | 1 | 1. | 0.71 | 0.05 | 0. | 9.25 | 0.26 | 1.08 |
time (sec) |
N/A |
1.247 |
0.623 |
0.023 |
0. |
3.366 |
12.622 |
1.189 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
F |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 329 | 329 | 425 | 39 | 0 | 6946 | 202 | 855 |
normalized size | 1 | 1. | 1.29 | 0.12 | 0. | 21.11 | 0.61 | 2.6 |
time (sec) |
N/A |
0.209 |
0.136 |
0.015 |
0. |
3.305 |
12.459 |
1.221 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 67 | 53 | 0 | 6279 | 136 | 0 |
normalized size |
1 |
1. |
0.08 |
0.07 |
0. |
7.94 |
0.17 |
0. |
time (sec) |
N/A |
0.863 |
0.045 |
0.059 |
0. |
1.945 |
5.785 |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 67 | 53 | 0 | 6279 | 136 | 0 |
normalized size |
1 |
1. |
0.08 |
0.07 |
0. |
7.94 |
0.17 |
0. |
time (sec) |
N/A |
0.805 |
0.036 |
0.049 |
0. |
1.856 |
5.415 |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 349 | 349 | 69 | 55 | 0 | 6279 | 136 | 0 |
normalized size |
1 |
1. |
0.2 |
0.16 |
0. |
17.99 |
0.39 |
0. |
time (sec) |
N/A |
0.422 |
0.045 |
0.031 |
0. |
1.9 |
5.869 |
0. |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 751 | 751 | 69 | 55 | 0 | 6278 | 136 | 0 |
normalized size |
1 |
1. |
0.09 |
0.07 |
0. |
8.36 |
0.18 |
0. |
time (sec) |
N/A |
0.925 |
0.04 |
0.034 |
0. |
1.948 |
5.335 |
0. |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 55 | 42 | 0 | 3723 | 75 | 0 |
normalized size | 1 | 1. | 0.13 | 0.1 | 0. | 9.06 | 0.18 | 0. |
time (sec) |
N/A |
0.292 |
0.027 |
0.052 |
0. |
1.56 |
2.249 |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 451 | 451 | 55 | 42 | 0 | 3098 | 24 | 342 |
normalized size | 1 | 1. | 0.12 | 0.09 | 0. | 6.87 | 0.05 | 0.76 |
time (sec) |
N/A |
0.407 |
0.014 |
0.007 |
0. |
1.624 |
1.061 |
1.357 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 64 | 58 | 97 | 302 | 73 | 97 |
normalized size | 1 | 1. | 0.75 | 0.68 | 1.14 | 3.55 | 0.86 | 1.14 |
time (sec) |
N/A |
0.045 |
0.02 |
0.001 |
1.501 |
1.357 |
0.147 |
1.124 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
F |
A |
C |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 135 | 109 | 0 | 716 | 190 | 0 |
normalized size | 1 | 1. | 0.96 | 0.78 | 0. | 5.11 | 1.36 | 0. |
time (sec) |
N/A |
0.095 |
0.185 |
0.016 |
0. |
1.439 |
0.693 |
0. |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
C |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 347 | 347 | 258 | 27 | 0 | 3092 | 19 | 333 |
normalized size | 1 | 1. | 0.74 | 0.08 | 0. | 8.91 | 0.05 | 0.96 |
time (sec) |
N/A |
0.247 |
0.182 |
0.006 |
0. |
1.509 |
1.124 |
1.179 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 55 | 42 | 0 | 1196 | 20 | 331 |
normalized size | 1 | 1. | 0.17 | 0.13 | 0. | 3.61 | 0.06 | 1. |
time (sec) |
N/A |
0.235 |
0.016 |
0.006 |
0. |
1.462 |
1.23 |
1.156 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 31 | 42 | 36 | 123 | 26 | 39 |
normalized size | 1 | 1. | 1.15 | 1.56 | 1.33 | 4.56 | 0.96 | 1.44 |
time (sec) |
N/A |
0.008 |
0.014 |
0.011 |
1.5 |
1.231 |
0.142 |
1.096 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 131 | 96 | 0 | 815 | 49 | 198 |
normalized size | 1 | 1. | 1. | 0.73 | 0. | 6.22 | 0.37 | 1.51 |
time (sec) |
N/A |
0.086 |
0.08 |
0.029 |
0. |
1.373 |
0.883 |
1.232 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 53 | 40 | 0 | 1062 | 24 | 0 |
normalized size | 1 | 1. | 0.34 | 0.25 | 0. | 6.76 | 0.15 | 0. |
time (sec) |
N/A |
0.087 |
0.013 |
0.008 |
0. |
1.359 |
0.179 |
0. |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 55 | 42 | 0 | 1812 | 24 | 0 |
normalized size | 1 | 1. | 0.32 | 0.25 | 0. | 10.6 | 0.14 | 0. |
time (sec) |
N/A |
0.151 |
0.013 |
0.008 |
0. |
1.453 |
0.19 |
0. |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 111 | 78 | 0 | 616 | 49 | 166 |
normalized size | 1 | 1. | 0.95 | 0.67 | 0. | 5.26 | 0.42 | 1.42 |
time (sec) |
N/A |
0.057 |
0.045 |
0.051 |
0. |
1.278 |
0.861 |
1.214 |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
C |
F |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 511 | 511 | 57 | 44 | 0 | 3725 | 76 | 0 |
normalized size | 1 | 1. | 0.11 | 0.09 | 0. | 7.29 | 0.15 | 0. |
time (sec) |
N/A |
0.359 |
0.025 |
0.003 |
0. |
1.513 |
2.263 |
0. |
|
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 57 | 44 | 0 | 2790 | 26 | 320 |
normalized size | 1 | 1. | 0.14 | 0.11 | 0. | 6.79 | 0.06 | 0.78 |
time (sec) |
N/A |
0.321 |
0.014 |
0.006 |
0. |
1.585 |
1.054 |
1.338 |
|
|
|
|
|
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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 | 97 | 97 | 90 | 68 | 111 | 371 | 82 | 111 |
normalized size | 1 | 1. | 0.93 | 0.7 | 1.14 | 3.82 | 0.85 | 1.14 |
time (sec) |
N/A |
0.052 |
0.064 |
0.008 |
1.483 |
1.318 |
0.171 |
1.11 |
|
|
|
|
|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
C |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 129 | 109 | 0 | 444 | 148 | 0 |
normalized size | 1 | 1. | 0.92 | 0.78 | 0. | 3.17 | 1.06 | 0. |
time (sec) |
N/A |
0.099 |
0.177 |
0.012 |
0. |
1.365 |
0.612 |
0. |
|
|
|
|
|
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|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 347 | 347 | 257 | 29 | 0 | 3092 | 20 | 333 |
normalized size | 1 | 1. | 0.74 | 0.08 | 0. | 8.91 | 0.06 | 0.96 |
time (sec) |
N/A |
0.27 |
0.164 |
0.006 |
0. |
1.469 |
1.121 |
1.197 |
|
|
|
|
|
|
|
|
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|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 355 | 355 | 57 | 44 | 0 | 2313 | 26 | 342 |
normalized size | 1 | 1. | 0.16 | 0.12 | 0. | 6.52 | 0.07 | 0.96 |
time (sec) |
N/A |
0.277 |
0.015 |
0.006 |
0. |
1.52 |
1.258 |
1.173 |
|
|
|
|
|
|
|
|
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|
|
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|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 25 | 10 | 23 | 66 | 17 | 26 |
normalized size | 1 | 1. | 1.92 | 0.77 | 1.77 | 5.08 | 1.31 | 2. |
time (sec) |
N/A |
0.005 |
0.005 |
0.003 |
1.479 |
1.302 |
0.123 |
1.128 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 129 | 110 | 0 | 905 | 51 | 198 |
normalized size | 1 | 1. | 1. | 0.85 | 0. | 7.02 | 0.4 | 1.53 |
time (sec) |
N/A |
0.118 |
0.077 |
0.02 |
0. |
1.411 |
0.879 |
1.21 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 55 | 42 | 0 | 1004 | 26 | 0 |
normalized size | 1 | 1. | 0.33 | 0.25 | 0. | 6.08 | 0.16 | 0. |
time (sec) |
N/A |
0.104 |
0.014 |
0.007 |
0. |
1.417 |
0.182 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 57 | 44 | 0 | 1751 | 26 | 0 |
normalized size | 1 | 1. | 0.34 | 0.26 | 0. | 10.36 | 0.15 | 0. |
time (sec) |
N/A |
0.142 |
0.013 |
0.006 |
0. |
1.556 |
0.186 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 114 | 90 | 0 | 686 | 51 | 182 |
normalized size | 1 | 1. | 0.91 | 0.72 | 0. | 5.49 | 0.41 | 1.46 |
time (sec) |
N/A |
0.067 |
0.054 |
0.026 |
0. |
1.347 |
0.868 |
1.205 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 71 | 47 | 0 | 315 | 136 | 144 |
normalized size | 1 | 1. | 0.53 | 0.35 | 0. | 2.33 | 1.01 | 1.07 |
time (sec) |
N/A |
0.124 |
0.036 |
0.051 |
0. |
1.408 |
1.003 |
1.162 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 72 | 62 | 0 | 355 | 0 | 166 |
normalized size |
1 |
1. |
0.44 |
0.38 |
0. |
2.16 |
0. |
1.01 |
time (sec) |
N/A |
0.095 |
0.037 |
0.039 |
0. |
1.389 |
0. |
1.142 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 180 | 180 | 89 | 62 | 0 | 436 | 0 | 177 |
normalized size |
1 |
1. |
0.49 |
0.34 |
0. |
2.42 |
0. |
0.98 |
time (sec) |
N/A |
0.122 |
0.046 |
0.01 |
0. |
1.437 |
0. |
1.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 49 | 43 | 0 | 238 | 112 | 58 |
normalized size |
1 |
1. |
1. |
0.88 |
0. |
4.86 |
2.29 |
1.18 |
time (sec) |
N/A |
0.03 |
0.023 |
0.007 |
0. |
1.272 |
0.439 |
1.097 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 86 | 161 | 0 | 643 | 423 | 115 |
normalized size |
1 |
1. |
1. |
1.87 |
0. |
7.48 |
4.92 |
1.34 |
time (sec) |
N/A |
0.081 |
0.09 |
0.003 |
0. |
1.299 |
1.268 |
1.101 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 253 | 253 | 293 | 266 | 0 | 1489 | 109 | 347 |
normalized size |
1 |
1. |
1.16 |
1.05 |
0. |
5.89 |
0.43 |
1.37 |
time (sec) |
N/A |
0.211 |
0.106 |
0.01 |
0. |
1.362 |
0.839 |
1.102 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
B |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 251 | 560 | 0 | 5042 | 428 | 0 |
normalized size |
1 |
1. |
1.21 |
2.69 |
0. |
24.24 |
2.06 |
0. |
time (sec) |
N/A |
0.543 |
0.191 |
0.027 |
0. |
1.909 |
10.624 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 311 | 311 | 346 | 334 | 0 | 6369 | 167 | 406 |
normalized size |
1 |
1. |
1.11 |
1.07 |
0. |
20.48 |
0.54 |
1.31 |
time (sec) |
N/A |
0.29 |
0.115 |
0.044 |
0. |
2.898 |
2.481 |
1.147 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
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 | 716 | 716 | 88 | 67 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.12 |
0.09 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.634 |
0.056 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 753 | 753 | 551 | 45 | 0 | 6888 | 204 | 873 |
normalized size | 1 | 1. | 0.73 | 0.06 | 0. | 9.15 | 0.27 | 1.16 |
time (sec) |
N/A |
1.436 |
0.918 |
0.003 |
0. |
5.356 |
18.942 |
1.229 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
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 | 433 | 433 | 88 | 67 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.2 |
0.15 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.989 |
0.078 |
0.005 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 127 | 0 | 0 | 0 | 337 | 0 |
normalized size | 1 | 1. | 0.9 | 0. | 0. | 0. | 2.39 | 0. |
time (sec) |
N/A |
0.145 |
0.247 |
0.078 |
0. |
0. |
10.355 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 107 | 0 | 0 | 0 | 207 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 0. | 1.93 | 0. |
time (sec) |
N/A |
0.097 |
0.151 |
0.062 |
0. |
0. |
7.577 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 83 | 0 | 0 | 0 | 153 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 0. | 1.84 | 0. |
time (sec) |
N/A |
0.027 |
0.039 |
0.045 |
0. |
0. |
5.797 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
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 | 152 | 152 | 131 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.86 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.111 |
0.144 |
0.079 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
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 | 205 | 205 | 186 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.91 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.174 |
0.267 |
0.141 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 81 | 0 | 0 | 0 | 158 | 0 |
normalized size | 1 | 1. | 1. | 0. | 0. | 0. | 1.95 | 0. |
time (sec) |
N/A |
0.028 |
0.061 |
0.043 |
0. |
0. |
6.497 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
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 | 288 | 288 | 188 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.65 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.252 |
0.282 |
0.072 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 203 | 203 | 136 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.67 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.167 |
0.16 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
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 | 134 | 134 | 83 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.054 |
0.042 |
0.066 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
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 | 333 | 333 | 227 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.68 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.224 |
0.291 |
0.139 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
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 | 410 | 410 | 298 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.379 |
0.503 |
0.146 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
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 | 424 | 424 | 188 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.44 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.383 |
0.307 |
0.088 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
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 | 272 | 272 | 136 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.5 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.247 |
0.183 |
0.081 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
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 | 184 | 184 | 83 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.45 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.101 |
0.048 |
0.079 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
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 | 582 | 582 | 346 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.416 |
0.464 |
0.17 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
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 | 701 | 701 | 426 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.692 |
0.742 |
0.197 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.166 |
0.122 |
0.062 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.008 |
0.162 |
0.148 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 299 | 299 | 213 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.16 |
0.2 |
0.112 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 171 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.79 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.101 |
0.109 |
0.094 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 | 135 | 135 | 110 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.81 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.06 |
0.05 |
0.093 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.142 |
0.081 |
0.092 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.235 |
0.103 |
0.076 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 357 | 357 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.338 |
0.294 |
0.086 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 57 | 66 | 0 | 315 | 656 | 279 |
normalized size |
1 |
1. |
0.92 |
1.06 |
0. |
5.08 |
10.58 |
4.5 |
time (sec) |
N/A |
0.039 |
0.147 |
0.01 |
0. |
1.43 |
1.402 |
1.137 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 123 | 138 | 0 | 1161 | 3128 | 1118 |
normalized size |
1 |
1. |
0.93 |
1.05 |
0. |
8.8 |
23.7 |
8.47 |
time (sec) |
N/A |
0.102 |
0.255 |
0.013 |
0. |
1.389 |
13.201 |
1.139 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 205 | 226 | 0 | 2761 | 9190 | 2881 |
normalized size |
1 |
1. |
0.94 |
1.04 |
0. |
12.67 |
42.16 |
13.22 |
time (sec) |
N/A |
0.201 |
0.442 |
0.014 |
0. |
1.455 |
108.281 |
1.238 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
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 | 308 | 308 | 295 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.96 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.699 |
0.876 |
0.052 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
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 | 224 | 224 | 216 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.96 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.476 |
0.532 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
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 | 154 | 154 | 134 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.12 |
0.075 |
0.021 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
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 | 243 | 243 | 200 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.469 |
0.447 |
0.06 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
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 | 368 | 368 | 327 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.707 |
0.941 |
0.136 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
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 | 552 | 552 | 509 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.023 |
1.873 |
0.163 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 750 | 750 | 2462 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.28 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.938 |
4.671 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 543 | 543 | 1835 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
3.38 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.818 |
2.783 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 362 | 328 | 1381 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0.91 |
3.81 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.63 |
1.768 |
0.053 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 726 | 726 | 8045 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
11.08 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.927 |
7.273 |
0.174 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1129 | 1129 | 11657 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
10.33 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.341 |
8.105 |
0.221 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1707 | 1707 | 9060 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
5.31 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
5.253 |
7.752 |
0.104 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1191 | 1191 | 7402 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
6.21 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
4.01 |
6.839 |
0.1 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 713 | 713 | 5848 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
8.2 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.663 |
6.535 |
0.094 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1708 | 1708 | 30258 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
17.72 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
5.074 |
8.656 |
0.329 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2446 | 2446 | 39502 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
16.15 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
8.935 |
10.109 |
0.448 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 292 | 292 | 424 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.45 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.355 |
1.595 |
0.062 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 690 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.35 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.348 |
4.543 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 292 | 292 | 245 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.338 |
0.349 |
0.018 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 414 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.39 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.346 |
1.532 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F(-2) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 6648 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
22.31 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.347 |
6.558 |
0.013 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.01 |
0.306 |
0.125 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 606 | 606 | 438 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.622 |
1.503 |
0.099 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 447 | 447 | 338 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.461 |
1.037 |
0.083 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
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 | 288 | 288 | 243 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.84 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.287 |
0.688 |
0.085 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
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 | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.011 |
0.159 |
0.085 |
0. |
0. |
0. |
0. |
|
|
|
|
|
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Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.011 |
0.197 |
0.059 |
0. |
0. |
0. |
0. |
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Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.012 |
0.71 |
0.074 |
0. |
0. |
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 [38] had the largest ratio of [ 0.5882
]
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| Table 2.1Rubi specific breakdown of results for each
integral
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# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
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1 |
A |
12 |
8 |
1. |
17 |
0.471 |
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2 |
A |
13 |
7 |
1. |
18 |
0.389 |
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3 |
A |
19 |
6 |
1. |
17 |
0.353 |
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4 |
A |
13 |
10 |
1. |
18 |
0.556 |
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5 |
A |
19 |
6 |
1. |
26 |
0.231 |
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6 |
A |
19 |
6 |
1. |
26 |
0.231 |
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7 |
A |
7 |
4 |
1. |
27 |
0.148 |
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8 |
A |
19 |
6 |
1. |
27 |
0.222 |
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9 |
A |
19 |
6 |
1. |
18 |
0.333 |
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10 |
A |
19 |
7 |
1. |
18 |
0.389 |
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11 |
A |
10 |
7 |
1. |
18 |
0.389 |
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12 |
A |
19 |
6 |
1. |
16 |
0.375 |
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13 |
A |
19 |
6 |
1. |
13 |
0.462 |
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14 |
A |
19 |
6 |
1. |
18 |
0.333 |
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15 |
A |
5 |
5 |
1. |
18 |
0.278 |
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16 |
A |
7 |
4 |
1. |
18 |
0.222 |
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17 |
A |
7 |
4 |
1. |
18 |
0.222 |
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18 |
A |
7 |
4 |
1. |
18 |
0.222 |
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19 |
A |
7 |
4 |
1. |
18 |
0.222 |
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20 |
A |
19 |
6 |
1. |
20 |
0.3 |
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21 |
A |
19 |
7 |
1. |
20 |
0.35 |
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22 |
A |
11 |
8 |
1. |
20 |
0.4 |
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23 |
A |
19 |
6 |
1. |
18 |
0.333 |
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24 |
A |
19 |
6 |
1. |
15 |
0.4 |
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25 |
A |
19 |
6 |
1. |
20 |
0.3 |
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26 |
A |
5 |
5 |
1. |
20 |
0.25 |
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27 |
A |
7 |
4 |
1. |
20 |
0.2 |
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28 |
A |
7 |
4 |
1. |
20 |
0.2 |
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29 |
A |
7 |
4 |
1. |
20 |
0.2 |
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30 |
A |
7 |
4 |
1. |
20 |
0.2 |
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31 |
A |
9 |
6 |
1. |
25 |
0.24 |
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32 |
A |
9 |
6 |
1. |
26 |
0.231 |
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33 |
A |
9 |
6 |
1. |
33 |
0.182 |
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34 |
A |
5 |
5 |
1. |
17 |
0.294 |
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35 |
A |
6 |
6 |
1. |
22 |
0.273 |
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36 |
A |
11 |
8 |
1. |
17 |
0.471 |
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37 |
A |
5 |
4 |
1. |
22 |
0.182 |
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38 |
A |
14 |
10 |
1. |
17 |
0.588 |
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39 |
A |
15 |
9 |
1. |
22 |
0.409 |
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40 |
A |
21 |
8 |
1. |
17 |
0.471 |
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41 |
A |
9 |
6 |
1. |
22 |
0.273 |
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42 |
A |
5 |
4 |
1. |
21 |
0.19 |
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43 |
A |
5 |
4 |
1. |
21 |
0.19 |
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44 |
A |
3 |
3 |
1. |
19 |
0.158 |
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45 |
A |
6 |
4 |
1. |
21 |
0.19 |
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46 |
A |
7 |
4 |
1. |
21 |
0.19 |
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47 |
A |
3 |
3 |
1. |
20 |
0.15 |
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48 |
A |
9 |
5 |
1. |
21 |
0.238 |
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49 |
A |
7 |
5 |
1. |
21 |
0.238 |
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50 |
A |
4 |
4 |
1. |
19 |
0.21 |
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51 |
A |
10 |
5 |
1. |
21 |
0.238 |
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52 |
A |
11 |
5 |
1. |
21 |
0.238 |
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53 |
A |
11 |
5 |
1. |
21 |
0.238 |
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54 |
A |
8 |
5 |
1. |
21 |
0.238 |
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55 |
A |
5 |
4 |
1. |
19 |
0.21 |
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56 |
A |
15 |
5 |
1. |
21 |
0.238 |
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57 |
A |
16 |
5 |
1. |
21 |
0.238 |
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58 |
A |
6 |
5 |
1. |
23 |
0.217 |
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59 |
A |
0 |
0 |
0. |
0 |
0. |
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60 |
A |
10 |
5 |
1. |
21 |
0.238 |
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61 |
A |
8 |
5 |
1. |
21 |
0.238 |
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62 |
A |
6 |
5 |
1. |
19 |
0.263 |
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63 |
A |
6 |
5 |
1. |
21 |
0.238 |
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64 |
A |
8 |
5 |
1. |
21 |
0.238 |
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65 |
A |
10 |
5 |
1. |
21 |
0.238 |
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66 |
A |
2 |
1 |
1. |
22 |
0.045 |
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67 |
A |
2 |
1 |
1. |
24 |
0.042 |
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68 |
A |
2 |
1 |
1. |
24 |
0.042 |
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69 |
A |
5 |
3 |
1. |
26 |
0.115 |
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70 |
A |
5 |
3 |
1. |
26 |
0.115 |
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71 |
A |
3 |
2 |
1. |
24 |
0.083 |
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72 |
A |
6 |
3 |
1. |
26 |
0.115 |
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73 |
A |
7 |
3 |
1. |
26 |
0.115 |
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74 |
A |
8 |
3 |
1. |
26 |
0.115 |
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75 |
A |
9 |
4 |
1. |
26 |
0.154 |
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76 |
A |
9 |
5 |
1. |
26 |
0.192 |
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77 |
A |
4 |
3 |
0.91 |
24 |
0.125 |
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78 |
A |
10 |
4 |
1. |
26 |
0.154 |
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79 |
A |
11 |
4 |
1. |
26 |
0.154 |
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80 |
A |
11 |
4 |
1. |
26 |
0.154 |
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81 |
A |
11 |
5 |
1. |
26 |
0.192 |
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82 |
A |
5 |
3 |
1. |
24 |
0.125 |
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83 |
A |
15 |
4 |
1. |
26 |
0.154 |
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84 |
A |
16 |
4 |
1. |
26 |
0.154 |
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85 |
A |
6 |
5 |
1. |
26 |
0.192 |
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86 |
A |
6 |
5 |
1. |
26 |
0.192 |
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87 |
A |
6 |
5 |
1. |
26 |
0.192 |
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88 |
A |
6 |
5 |
1. |
26 |
0.192 |
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89 |
A |
6 |
5 |
1. |
26 |
0.192 |
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90 |
A |
0 |
0 |
0. |
0 |
0. |
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91 |
A |
10 |
5 |
1. |
26 |
0.192 |
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92 |
A |
8 |
5 |
1. |
26 |
0.192 |
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93 |
A |
6 |
5 |
1. |
24 |
0.208 |
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94 |
A |
0 |
0 |
0. |
0 |
0. |
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95 |
A |
0 |
0 |
0. |
0 |
0. |
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96 |
A |
0 |
0 |
0. |
0 |
0. |
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