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 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 4, 5, 6, 8, 9, 10, 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, 40, 41, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 58, 60, 61 }
B grade: { 3, 7, 11, 37, 38, 39, 42, 43, 47, 48, 57, 59 }
C grade: { }
F grade: { }
2.1.3 Maple
A grade: { 4, 5, 8, 9, 10, 14, 15, 16, 17, 19, 20, 21, 25, 26, 30, 31, 32, 33, 40, 41, 45, 46, 50, 51, 55, 56, 60,
61 }
B grade: { 1, 2, 3, 6, 7, 11, 12, 13, 18, 22, 23, 24, 27, 28, 29, 37, 38, 39, 42, 43, 44, 47, 48, 49, 52, 53, 54, 57,
58, 59 }
C grade: { }
F grade: { 34, 35, 36 }
2.1.4 Maxima
A grade: { 4, 5, 9, 10, 14, 15, 19, 20, 21, 25, 26, 30, 31, 32, 33, 40, 41, 46, 50, 51, 55, 56 }
B grade: { 1, 2, 3, 6, 7, 8, 11, 12, 13, 37, 38, 39, 42, 43, 44, 47, 48, 49, 52, 53, 54, 57, 58, 59
}
C grade: { }
F grade: { 16, 17, 18, 22, 23, 24, 27, 28, 29, 34, 35, 36, 45, 60, 61 }
2.1.5 FriCAS
A grade: { 4, 5, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
40, 41, 45, 46, 50, 51, 55, 56, 60, 61 }
B grade: { 3, 7, 8, 13, 39, 44, 49, 54, 59 }
C grade: { 1, 2, 6, 11, 12, 37, 38, 42, 43, 47, 48, 52, 53, 57, 58 }
F grade: { }
2.1.6 Sympy
A grade: { 4, 5, 8, 9, 10, 14, 15, 16, 17, 18, 22, 23, 24, 27, 28, 29, 32, 33, 40, 41, 45, 46, 50, 51, 55, 56, 60,
61 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 19, 20, 21, 25, 26, 30, 31, 34, 35, 36, 37, 38, 39, 42, 43, 44, 47, 48, 49, 52,
53, 54, 57, 58, 59 }
2.1.7 Giac
A grade: { 4, 5, 9, 10, 14, 15, 16, 17, 18, 23, 24, 28, 29, 32, 33, 40, 41, 45, 46, 50, 51, 55, 56, 60, 61
}
B grade: { 8, 19, 20, 21, 22, 25, 26, 27, 30, 31 }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 34, 35, 36, 37, 38, 39, 42, 43, 44, 47, 48, 49, 52, 53, 54, 57, 58, 59
}
2.1.8 Mupad
A grade: { 4, 5, 9, 10, 14, 15, 32, 33, 40, 41, 45, 46, 50, 51, 55, 56, 60, 61 }
B grade: { 8, 16, 17, 18, 22, 23, 24, 27, 28, 29 }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 19, 20, 21, 25, 26, 30, 31, 34, 35, 36, 37, 38, 39, 42, 43, 44, 47, 48, 49, 52,
53, 54, 57, 58, 59 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 184 | 240 | 391 | 306 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.82 | 2.38 | 3.87 | 3.03 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.171 |
0.714 |
0.862 |
0.484 |
0.557 |
0.000 |
0.000 |
0.000 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 136 | 198 | 257 | 244 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.84 | 2.68 | 3.47 | 3.30 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.140 |
0.464 |
0.798 |
0.486 |
0.574 |
0.000 |
0.000 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 135 | 150 | 140 | 174 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.55 | 2.83 | 2.64 | 3.28 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.085 |
3.728 |
0.823 |
0.456 |
0.526 |
0.000 |
0.000 |
0.000 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.016 |
1.898 |
0.896 |
0.000 |
0.544 |
0.000 |
0.000 |
0.000 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.08 |
time (sec) |
N/A |
0.017 |
3.325 |
1.083 |
0.000 |
0.624 |
0.000 |
0.000 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 171 | 231 | 953 | 372 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.76 | 2.38 | 9.82 | 3.84 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.178 |
0.918 |
0.952 |
0.594 |
0.688 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 153 | 183 | 384 | 281 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.07 | 2.47 | 5.19 | 3.80 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.119 |
5.355 |
0.898 |
0.618 |
1.163 |
0.000 |
0.000 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 44 | 30 | 269 | 75 | 68 | 1250 | 54 |
normalized size | 1 | 1.00 | 1.42 | 0.97 | 8.68 | 2.42 | 2.19 | 40.32 | 1.74 |
time (sec) |
N/A |
0.023 |
0.219 |
0.719 |
0.467 |
0.740 |
0.460 |
4.743 |
0.452 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.030 |
3.816 |
1.052 |
0.000 |
2.102 |
0.000 |
0.000 |
0.000 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.030 |
3.429 |
1.118 |
0.000 |
0.857 |
0.000 |
0.000 |
0.000 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 461 | 444 | 1970 | 565 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.28 | 2.20 | 9.75 | 2.80 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.301 |
6.807 |
1.060 |
0.754 |
2.053 |
0.000 |
0.000 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 221 | 293 | 1216 | 423 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.75 | 2.33 | 9.65 | 3.36 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.186 |
5.485 |
1.008 |
1.179 |
0.665 |
0.000 |
0.000 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 179 | 197 | 591 | 291 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.97 | 2.16 | 6.49 | 3.20 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.107 |
4.295 |
0.803 |
0.882 |
0.657 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.028 |
6.506 |
2.916 |
0.000 |
0.552 |
0.000 |
0.000 |
0.000 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.030 |
5.270 |
3.788 |
0.000 |
0.920 |
0.000 |
0.000 |
0.000 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 246 | 170 | 0 | 153 | 318 | 243 | 423 |
normalized size | 1 | 1.00 | 1.30 | 0.90 | 0.00 | 0.81 | 1.68 | 1.29 | 2.24 |
time (sec) |
N/A |
0.200 |
0.628 |
2.069 |
0.000 |
0.755 |
0.365 |
0.421 |
1.236 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 149 | 108 | 0 | 95 | 197 | 143 | 241 |
normalized size | 1 | 1.00 | 1.09 | 0.79 | 0.00 | 0.69 | 1.44 | 1.04 | 1.76 |
time (sec) |
N/A |
0.123 |
0.366 |
1.864 |
0.000 |
0.499 |
0.287 |
0.418 |
0.769 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 107 | 177 | 0 | 48 | 104 | 67 | 105 |
normalized size | 1 | 1.00 | 1.27 | 2.11 | 0.00 | 0.57 | 1.24 | 0.80 | 1.25 |
time (sec) |
N/A |
0.054 |
0.247 |
0.622 |
0.000 |
0.483 |
0.226 |
0.651 |
0.382 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 77 | 204 | 111 | 51 | 0 | 367 | -1 |
normalized size | 1 | 1.00 | 0.48 | 1.27 | 0.69 | 0.32 | 0.00 | 2.28 | -0.01 |
time (sec) |
N/A |
0.278 |
0.284 |
0.597 |
0.449 |
0.565 |
0.000 |
0.552 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 215 | 271 | 122 | 72 | 0 | 367 | -1 |
normalized size | 1 | 1.00 | 1.30 | 1.63 | 0.73 | 0.43 | 0.00 | 2.21 | -0.01 |
time (sec) |
N/A |
0.227 |
1.245 |
0.575 |
0.791 |
0.644 |
0.000 |
47.649 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 283 | 143 | 160 | 118 | 0 | 1630 | -1 |
normalized size | 1 | 1.00 | 1.25 | 0.63 | 0.70 | 0.52 | 0.00 | 7.18 | -0.00 |
time (sec) |
N/A |
0.312 |
1.592 |
1.635 |
0.910 |
0.833 |
0.000 |
0.619 |
0.000 |
|
|
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 362 | 2261 | 0 | 253 | 653 | 433 | 294 |
normalized size | 1 | 1.00 | 1.34 | 8.37 | 0.00 | 0.94 | 2.42 | 1.60 | 1.09 |
time (sec) |
N/A |
0.276 |
1.605 |
2.155 |
0.000 |
1.905 |
0.636 |
0.513 |
1.119 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 255 | 1073 | 0 | 151 | 406 | 247 | 186 |
normalized size | 1 | 1.00 | 1.26 | 5.31 | 0.00 | 0.75 | 2.01 | 1.22 | 0.92 |
time (sec) |
N/A |
0.198 |
0.737 |
1.948 |
0.000 |
1.514 |
0.480 |
0.504 |
0.579 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 165 | 390 | 0 | 69 | 214 | 108 | 102 |
normalized size | 1 | 1.00 | 1.09 | 2.58 | 0.00 | 0.46 | 1.42 | 0.72 | 0.68 |
time (sec) |
N/A |
0.138 |
0.613 |
1.662 |
0.000 |
0.758 |
0.356 |
1.734 |
0.338 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 305 | 305 | 136 | 382 | 194 | 80 | 0 | 987 | -1 |
normalized size | 1 | 1.00 | 0.45 | 1.25 | 0.64 | 0.26 | 0.00 | 3.24 | -0.00 |
time (sec) |
N/A |
0.752 |
0.609 |
1.425 |
0.963 |
0.882 |
0.000 |
1.834 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 434 | 434 | 203 | 537 | 214 | 129 | 0 | 2369 | -1 |
normalized size | 1 | 1.00 | 0.47 | 1.24 | 0.49 | 0.30 | 0.00 | 5.46 | -0.00 |
time (sec) |
N/A |
0.681 |
0.587 |
1.429 |
0.809 |
0.605 |
0.000 |
64.087 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 664 | 3997 | 0 | 353 | 935 | 623 | 418 |
normalized size | 1 | 1.00 | 1.68 | 10.09 | 0.00 | 0.89 | 2.36 | 1.57 | 1.06 |
time (sec) |
N/A |
0.381 |
2.850 |
1.721 |
0.000 |
0.949 |
0.843 |
0.611 |
1.624 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 369 | 1843 | 0 | 207 | 578 | 351 | 263 |
normalized size | 1 | 1.00 | 1.26 | 6.27 | 0.00 | 0.70 | 1.97 | 1.19 | 0.89 |
time (sec) |
N/A |
0.269 |
0.812 |
1.481 |
0.000 |
0.813 |
0.636 |
0.552 |
1.001 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 244 | 653 | 0 | 94 | 301 | 151 | 144 |
normalized size | 1 | 1.00 | 1.17 | 3.12 | 0.00 | 0.45 | 1.44 | 0.72 | 0.69 |
time (sec) |
N/A |
0.218 |
0.663 |
1.061 |
0.000 |
0.658 |
0.458 |
2.084 |
0.625 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 449 | 449 | 197 | 560 | 275 | 113 | 0 | 1887 | -1 |
normalized size | 1 | 1.00 | 0.44 | 1.25 | 0.61 | 0.25 | 0.00 | 4.20 | -0.00 |
time (sec) |
N/A |
1.732 |
0.578 |
0.641 |
0.902 |
0.833 |
0.000 |
1.535 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 712 | 712 | 292 | 756 | 300 | 180 | 0 | 4524 | -1 |
normalized size | 1 | 1.00 | 0.41 | 1.06 | 0.42 | 0.25 | 0.00 | 6.35 | -0.00 |
time (sec) |
N/A |
1.643 |
0.643 |
0.645 |
1.652 |
0.764 |
0.000 |
87.906 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.051 |
10.378 |
0.706 |
0.000 |
0.714 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.029 |
5.738 |
1.006 |
0.000 |
0.633 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 190 | 0 | 0 | 84 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.94 | 0.00 | 0.00 | 0.86 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.124 |
1.292 |
1.287 |
0.000 |
0.542 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 152 | 0 | 0 | 140 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.185 |
2.832 |
2.102 |
0.000 |
0.681 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 251 | 251 | 238 | 0 | 0 | 192 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.242 |
4.099 |
2.342 |
0.000 |
0.551 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 730 | 857 | 966 | 626 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.97 | 5.83 | 6.57 | 4.26 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.255 |
7.503 |
1.320 |
1.164 |
0.739 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 406 | 516 | 520 | 403 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.62 | 4.61 | 4.64 | 3.60 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.210 |
2.571 |
1.221 |
1.753 |
0.607 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 204 | 240 | 208 | 224 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.46 | 2.89 | 2.51 | 2.70 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.123 |
5.036 |
1.113 |
0.930 |
0.520 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.029 |
2.227 |
1.779 |
0.000 |
0.648 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.028 |
8.192 |
1.799 |
0.000 |
0.503 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 295 | 295 | 1611 | 1571 | 4012 | 1154 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.46 | 5.33 | 13.60 | 3.91 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.531 |
7.433 |
1.819 |
4.352 |
0.904 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 729 | 899 | 1945 | 715 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.21 | 3.96 | 8.57 | 3.15 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.383 |
7.224 |
1.636 |
1.993 |
0.827 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 200 | 365 | 776 | 378 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.46 | 2.66 | 5.66 | 2.76 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.174 |
2.251 |
1.348 |
1.447 |
0.875 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.053 |
19.847 |
5.793 |
0.000 |
0.502 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.051 |
16.277 |
7.245 |
0.000 |
0.456 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 603 | 603 | 3045 | 3113 | 11204 | 2749 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.05 | 5.16 | 18.58 | 4.56 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.981 |
8.544 |
2.398 |
35.800 |
0.706 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 433 | 433 | 2013 | 1740 | 5411 | 1564 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.65 | 4.02 | 12.50 | 3.61 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.649 |
7.898 |
2.066 |
3.977 |
1.176 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 276 | 745 | 2017 | 721 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 2.68 | 7.26 | 2.59 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.323 |
3.647 |
1.809 |
1.212 |
0.608 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.053 |
9.594 |
8.519 |
0.000 |
0.631 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.051 |
12.557 |
11.166 |
0.000 |
0.508 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 345 | 1386 | 987 | 1029 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.43 | 5.73 | 4.08 | 4.25 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.341 |
2.135 |
2.556 |
0.846 |
0.594 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 181 | 181 | 289 | 881 | 719 | 730 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.60 | 4.87 | 3.97 | 4.03 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.288 |
1.547 |
2.273 |
0.823 |
0.747 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 182 | 445 | 406 | 475 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.44 | 3.53 | 3.22 | 3.77 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.162 |
1.857 |
2.251 |
0.665 |
0.656 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.064 |
1.967 |
3.290 |
0.000 |
0.534 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.059 |
3.944 |
5.052 |
0.000 |
0.640 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 839 | 839 | 1682 | 3446 | 4699 | 3359 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.00 | 4.11 | 5.60 | 4.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.969 |
10.660 |
2.917 |
4.717 |
0.874 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 650 | 650 | 718 | 2137 | 2592 | 2036 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 3.29 | 3.99 | 3.13 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.477 |
9.213 |
2.717 |
2.212 |
0.603 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 730 | 990 | 1181 | 1053 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.43 | 4.65 | 5.54 | 4.94 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.292 |
7.100 |
2.563 |
2.027 |
0.650 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.059 |
19.281 |
13.352 |
0.000 |
0.673 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.056 |
17.173 |
21.116 |
0.000 |
0.598 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi. It gives additional statistics for each integral. the column
steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf
size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder
the integral was to solve. In this test, problem number [11] had the largest ratio of
[.8333]
|
|
|
|
|
|
|
| Table 2.1:Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
6 |
6 |
1.00 |
10 |
0.600 |
|
|
|
|
|
|
|
2 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
3 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
4 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
5 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
6 |
A |
7 |
7 |
1.00 |
12 |
0.583 |
|
|
|
|
|
|
|
7 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
9 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
10 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
11 |
A |
13 |
10 |
1.00 |
12 |
0.833 |
|
|
|
|
|
|
|
12 |
A |
9 |
8 |
1.00 |
12 |
0.667 |
|
|
|
|
|
|
|
13 |
A |
7 |
7 |
1.00 |
10 |
0.700 |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
15 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
16 |
A |
5 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
17 |
A |
4 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
18 |
A |
3 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
19 |
A |
7 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
20 |
A |
7 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
21 |
A |
8 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
22 |
A |
10 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
23 |
A |
8 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
24 |
A |
7 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
25 |
A |
21 |
5 |
1.00 |
23 |
0.217 |
|
|
|
|
|
|
|
26 |
A |
24 |
7 |
1.00 |
23 |
0.304 |
|
|
|
|
|
|
|
27 |
A |
14 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
28 |
A |
11 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
29 |
A |
11 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
30 |
A |
53 |
7 |
1.00 |
23 |
0.304 |
|
|
|
|
|
|
|
31 |
A |
60 |
9 |
1.00 |
23 |
0.391 |
|
|
|
|
|
|
|
32 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
33 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
34 |
A |
2 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
35 |
A |
4 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
36 |
A |
5 |
2 |
1.00 |
23 |
0.087 |
|
|
|
|
|
|
|
37 |
A |
8 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
38 |
A |
7 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
39 |
A |
6 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
41 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
42 |
A |
15 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
43 |
A |
13 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
44 |
A |
9 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
46 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
47 |
A |
28 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
48 |
A |
22 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
49 |
A |
16 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
51 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
52 |
A |
6 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
53 |
A |
5 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
54 |
A |
4 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
56 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
57 |
A |
21 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
58 |
A |
18 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
59 |
A |
5 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
60 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
61 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|