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 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 3, 4, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 40, 41, 46, 47, 50, 51, 53, 54, 55, 59, 60, 61, 62 }
B grade: { 2, 39, 45 }
C grade: { 5, 6, 7, 18, 25, 26, 27, 28, 42, 43, 44, 49, 56, 57, 58 }
F grade: { 48, 52 }
2.1.3 Maple
A grade: { 4, 6, 7, 12, 13, 14, 29, 34, 35, 36, 37, 41, 43, 44, 50, 51, 55, 56, 59, 60 }
B grade: { 1, 2, 3, 9, 10, 11, 15, 16, 17, 19, 20, 21, 22, 30, 31, 32, 33, 38, 39, 40, 47, 54, 61, 62
}
C grade: { 5, 8, 18, 23, 24, 25, 26, 27, 28, 42, 45, 46, 48, 49, 53, 57, 58 }
F grade: { 52 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 6, 7, 13, 32, 33, 34, 36, 37, 50, 51, 55, 56 }
B grade: { 9, 10, 11, 14, 15, 16, 17, 20, 22, 24, 29, 30, 31, 38, 39, 40 }
C grade: { 54, 57 }
F grade: { 5, 8, 12, 18, 19, 21, 23, 25, 26, 27, 28, 35, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 58, 59, 60, 61,
62 }
2.1.5 FriCAS
A grade: { 11, 13, 14, 33, 34, 50, 51 }
B grade: { 9, 10, 15, 17, 20, 22, 31, 32, 36, 37 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 12, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 35, 38, 39, 40, 41, 42, 43, 44,
45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62 }
2.1.6 Sympy
A grade: { 9, 10, 11, 13, 14, 15, 17, 20, 22, 31, 32, 33, 34, 36 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 12, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 35, 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 }
2.1.7 Giac
A grade: { 50, 51 }
B grade: { 9, 10, 11, 13, 14, 15, 17, 20, 22, 31, 32, 33, 34, 36, 37 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 12, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 35, 38, 39, 40, 41, 42, 43, 44,
45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62 }
2.1.8 Mupad
A grade: { 50, 51 }
B grade: { 9, 10, 11, 13, 14, 15, 17, 20, 22, 31, 32, 33, 34, 36, 37 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 12, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 35, 38, 39, 40, 41, 42, 43, 44,
45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62 }
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 |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 263 | 187 | 967 | 320 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 3.68 | 1.22 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.339 |
1.260 |
0.060 |
0.327 |
0.477 |
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 |
B |
B |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 204 | 204 | 463 | 729 | 259 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.27 | 3.57 | 1.27 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.269 |
2.359 |
0.061 |
0.332 |
0.448 |
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 |
A |
B |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 98 | 365 | 202 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.72 | 2.68 | 1.49 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.200 |
0.281 |
0.057 |
0.336 |
0.549 |
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 |
A |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 55 | 103 | 139 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.68 | 1.27 | 1.72 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.086 |
0.068 |
0.275 |
0.324 |
0.449 |
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 |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 472 | 1022 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.19 | 6.91 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.090 |
2.645 |
0.854 |
0.000 |
0.433 |
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 |
C |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 251 | 251 | 208 | 342 | 244 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.83 | 1.36 | 0.97 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.699 |
1.437 |
0.069 |
0.339 |
0.410 |
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 |
C |
A |
A |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 271 | 467 | 360 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 1.26 | 0.97 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.801 |
2.350 |
0.077 |
0.347 |
0.569 |
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 |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 75 | 160 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.34 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.128 |
0.090 |
0.447 |
0.000 |
0.469 |
0.000 |
0.000 |
0.000 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 78 | 242 | 357 | 159 | 231 | 282 | 414 |
normalized size | 1 | 1.00 | 1.08 | 3.36 | 4.96 | 2.21 | 3.21 | 3.92 | 5.75 |
time (sec) |
N/A |
0.067 |
0.104 |
0.033 |
0.330 |
0.556 |
4.272 |
3.077 |
1.421 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 59 | 174 | 225 | 144 | 180 | 364 | 237 |
normalized size | 1 | 1.00 | 0.86 | 2.52 | 3.26 | 2.09 | 2.61 | 5.28 | 3.43 |
time (sec) |
N/A |
0.065 |
0.075 |
0.033 |
0.321 |
0.497 |
3.033 |
0.343 |
0.618 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 77 | 107 | 113 | 73 | 95 | 137 | 73 |
normalized size | 1 | 1.00 | 1.60 | 2.23 | 2.35 | 1.52 | 1.98 | 2.85 | 1.52 |
time (sec) |
N/A |
0.034 |
0.049 |
0.033 |
0.314 |
0.557 |
1.664 |
0.394 |
1.842 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 89 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.045 |
0.025 |
0.048 |
0.000 |
0.516 |
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 |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 69 | 86 | 95 | 85 | 270 | 137 | 122 |
normalized size | 1 | 1.00 | 1.10 | 1.37 | 1.51 | 1.35 | 4.29 | 2.17 | 1.94 |
time (sec) |
N/A |
0.059 |
0.071 |
0.038 |
0.315 |
0.819 |
2.834 |
0.184 |
1.369 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 100 | 88 | 131 | 88 | 313 | 134 | 67 |
normalized size | 1 | 1.00 | 1.59 | 1.40 | 2.08 | 1.40 | 4.97 | 2.13 | 1.06 |
time (sec) |
N/A |
0.049 |
0.063 |
0.037 |
0.321 |
0.572 |
3.546 |
0.333 |
1.732 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 148 | 732 | 827 | 383 | 581 | 791 | 1730 |
normalized size | 1 | 1.00 | 0.93 | 4.60 | 5.20 | 2.41 | 3.65 | 4.97 | 10.88 |
time (sec) |
N/A |
0.248 |
0.192 |
0.067 |
0.622 |
0.739 |
8.073 |
0.251 |
2.124 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 150 | 583 | 619 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 3.26 | 3.46 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.237 |
0.470 |
0.062 |
0.628 |
0.663 |
0.000 |
0.000 |
0.000 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 134 | 390 | 316 | 191 | 238 | 369 | 432 |
normalized size | 1 | 1.00 | 1.41 | 4.11 | 3.33 | 2.01 | 2.51 | 3.88 | 4.55 |
time (sec) |
N/A |
0.135 |
0.103 |
0.063 |
0.605 |
0.472 |
3.227 |
0.347 |
1.563 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 424 | 893 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.52 | 5.32 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.303 |
0.393 |
0.215 |
0.000 |
0.511 |
0.000 |
0.000 |
0.000 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 126 | 396 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 3.81 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.181 |
0.254 |
0.071 |
0.000 |
0.496 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 136 | 371 | 329 | 270 | 1102 | 356 | 776 |
normalized size | 1 | 1.00 | 1.14 | 3.12 | 2.76 | 2.27 | 9.26 | 2.99 | 6.52 |
time (sec) |
N/A |
0.174 |
0.168 |
0.077 |
0.359 |
0.486 |
4.310 |
0.183 |
2.418 |
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 180 | 180 | 218 | 492 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.21 | 2.73 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.270 |
0.538 |
0.079 |
0.000 |
0.477 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 218 | 431 | 613 | 547 | 3516 | 758 | 2746 |
normalized size | 1 | 1.00 | 1.27 | 2.51 | 3.56 | 3.18 | 20.44 | 4.41 | 15.97 |
time (sec) |
N/A |
0.262 |
0.263 |
0.077 |
0.377 |
0.523 |
10.589 |
0.199 |
3.424 |
|
|
|
|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 263 | 336 | 1768 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.28 | 6.72 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.467 |
0.743 |
0.858 |
0.000 |
0.651 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 213 | 6834 | 629 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 42.71 | 3.93 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.263 |
1.135 |
0.612 |
0.637 |
0.464 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 257 | 257 | 599 | 1842 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.33 | 7.17 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.492 |
0.511 |
0.183 |
0.000 |
0.438 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 248 | 2001 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.73 | 13.99 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.304 |
0.605 |
0.511 |
0.000 |
0.501 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 335 | 5796 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.02 | 34.92 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.335 |
1.178 |
0.681 |
0.000 |
0.488 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 393 | 2247 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.46 | 8.35 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.514 |
1.334 |
0.985 |
0.000 |
0.523 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 31 | 34 | 58 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.48 | 1.62 | 2.76 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.022 |
0.003 |
0.046 |
0.317 |
0.456 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 52 | 59 | 132 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.62 | 1.84 | 4.12 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.031 |
0.006 |
0.046 |
0.337 |
0.459 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 270 | 786 | 333 | 386 | 644 | 3990 | 737 |
normalized size | 1 | 1.00 | 1.61 | 4.68 | 1.98 | 2.30 | 3.83 | 23.75 | 4.39 |
time (sec) |
N/A |
0.331 |
0.281 |
0.043 |
0.363 |
0.506 |
7.640 |
0.634 |
1.724 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 174 | 477 | 207 | 242 | 369 | 1717 | 381 |
normalized size | 1 | 1.00 | 1.45 | 3.98 | 1.72 | 2.02 | 3.08 | 14.31 | 3.18 |
time (sec) |
N/A |
0.204 |
0.168 |
0.038 |
0.319 |
0.479 |
4.567 |
0.296 |
1.387 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 138 | 184 | 109 | 134 | 173 | 536 | 136 |
normalized size | 1 | 1.00 | 1.42 | 1.90 | 1.12 | 1.38 | 1.78 | 5.53 | 1.40 |
time (sec) |
N/A |
0.169 |
0.045 |
0.036 |
0.324 |
0.520 |
2.348 |
0.207 |
1.337 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 48 | 44 | 36 | 61 | 46 | 200 | 48 |
normalized size | 1 | 1.00 | 1.20 | 1.10 | 0.90 | 1.52 | 1.15 | 5.00 | 1.20 |
time (sec) |
N/A |
0.024 |
0.016 |
0.027 |
0.318 |
0.456 |
0.602 |
0.518 |
1.440 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 126 | 202 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.136 |
0.076 |
0.123 |
0.000 |
0.494 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 125 | 141 | 121 | 263 | 1658 | 896 | 170 |
normalized size | 1 | 1.00 | 1.09 | 1.23 | 1.05 | 2.29 | 14.42 | 7.79 | 1.48 |
time (sec) |
N/A |
0.169 |
0.181 |
0.038 |
0.322 |
0.613 |
10.012 |
0.273 |
1.638 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 174 | 236 | 291 | 834 | 0 | 4720 | 417 |
normalized size | 1 | 1.00 | 1.04 | 1.41 | 1.74 | 4.99 | 0.00 | 28.26 | 2.50 |
time (sec) |
N/A |
0.254 |
0.320 |
0.045 |
0.336 |
1.602 |
0.000 |
0.412 |
3.034 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 562 | 562 | 1082 | 4401 | 1363 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.93 | 7.83 | 2.43 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.041 |
7.481 |
0.087 |
0.647 |
0.593 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 795 | 2694 | 806 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.13 | 7.20 | 2.16 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.640 |
3.809 |
0.071 |
0.624 |
0.569 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 220 | 271 | 857 | 415 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 3.88 | 1.88 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.462 |
0.541 |
0.064 |
0.617 |
0.515 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 107 | 174 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.121 |
0.189 |
0.227 |
0.000 |
0.420 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 1757 | 1984 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 8.21 | 9.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.154 |
24.276 |
0.967 |
0.000 |
0.588 |
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 |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 480 | 485 | 425 | 783 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.01 | 0.89 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.713 |
7.526 |
0.080 |
0.000 |
0.509 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 750 | 750 | 1968 | 1428 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.62 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.126 |
14.789 |
0.094 |
0.000 |
0.551 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 546 | 546 | 1868 | 12111 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.42 | 22.18 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.046 |
10.161 |
22.267 |
0.000 |
0.705 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 326 | 325 | 566 | 20255 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.74 | 62.13 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.726 |
1.155 |
1.684 |
0.000 |
0.660 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 205 | 346 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.55 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.230 |
0.272 |
0.286 |
0.000 |
0.521 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 308 | 308 | 0 | 4064 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 13.19 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.193 |
22.912 |
0.868 |
0.000 |
0.568 |
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 |
C |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1089 | 1094 | 1946 | 5728 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.79 | 5.26 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.827 |
23.211 |
1.003 |
0.000 |
0.905 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
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 |
0.068 |
4.509 |
1.619 |
0.000 |
0.696 |
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 |
F(-1) |
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 |
0.069 |
0.303 |
1.401 |
0.000 |
0.533 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.257 |
0.081 |
1.417 |
0.000 |
0.696 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 780 | 780 | 623 | 587 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.80 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.395 |
0.758 |
0.913 |
0.000 |
0.547 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 481 | 481 | 365 | 1300 | 589 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 2.70 | 1.22 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.606 |
0.307 |
0.742 |
0.586 |
0.515 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 138 | 176 | 192 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 1.47 | 1.60 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.130 |
0.013 |
0.122 |
0.331 |
0.483 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 759 | 297 | 192 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.08 | 1.60 | 1.03 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.237 |
4.146 |
0.115 |
0.321 |
0.528 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
C |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 545 | 545 | 1456 | 20505 | 647 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.67 | 37.62 | 1.19 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.911 |
25.322 |
1.814 |
0.550 |
1.122 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 832 | 832 | 917 | 650 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.430 |
8.063 |
0.890 |
0.000 |
0.563 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 585 | 585 | 549 | 738 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.013 |
0.539 |
0.100 |
0.000 |
0.507 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 661 | 661 | 598 | 970 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.072 |
0.638 |
0.104 |
0.000 |
0.726 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 335 | 335 | 403 | 2140 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.20 | 6.39 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.721 |
0.572 |
0.825 |
0.000 |
0.613 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 114 | 194 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.37 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.263 |
0.121 |
0.061 |
0.000 |
0.786 |
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 [7] had the largest ratio of
[1.333]
|
|
|
|
|
|
|
| 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 |
19 |
15 |
1.00 |
12 |
1.250 |
|
|
|
|
|
|
|
2 |
A |
15 |
13 |
1.00 |
12 |
1.083 |
|
|
|
|
|
|
|
3 |
A |
12 |
10 |
1.00 |
10 |
1.000 |
|
|
|
|
|
|
|
4 |
A |
6 |
6 |
1.00 |
8 |
0.750 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
6 |
A |
17 |
15 |
1.00 |
12 |
1.250 |
|
|
|
|
|
|
|
7 |
A |
21 |
16 |
1.00 |
12 |
1.333 |
|
|
|
|
|
|
|
8 |
A |
4 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
9 |
A |
6 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
10 |
A |
6 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
11 |
A |
5 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
12 |
A |
3 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
13 |
A |
7 |
7 |
1.00 |
21 |
0.333 |
|
|
|
|
|
|
|
14 |
A |
5 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
15 |
A |
13 |
9 |
1.00 |
23 |
0.391 |
|
|
|
|
|
|
|
16 |
A |
11 |
10 |
1.00 |
23 |
0.435 |
|
|
|
|
|
|
|
17 |
A |
8 |
7 |
1.00 |
21 |
0.333 |
|
|
|
|
|
|
|
18 |
A |
8 |
7 |
1.00 |
23 |
0.304 |
|
|
|
|
|
|
|
19 |
A |
6 |
6 |
1.00 |
23 |
0.261 |
|
|
|
|
|
|
|
20 |
A |
10 |
9 |
1.00 |
23 |
0.391 |
|
|
|
|
|
|
|
21 |
A |
10 |
9 |
1.00 |
23 |
0.391 |
|
|
|
|
|
|
|
22 |
A |
15 |
10 |
1.00 |
23 |
0.435 |
|
|
|
|
|
|
|
23 |
A |
14 |
11 |
1.00 |
23 |
0.478 |
|
|
|
|
|
|
|
24 |
A |
10 |
10 |
1.00 |
21 |
0.476 |
|
|
|
|
|
|
|
25 |
A |
10 |
8 |
1.00 |
23 |
0.348 |
|
|
|
|
|
|
|
26 |
A |
7 |
8 |
1.00 |
23 |
0.348 |
|
|
|
|
|
|
|
27 |
A |
9 |
8 |
1.00 |
23 |
0.348 |
|
|
|
|
|
|
|
28 |
A |
16 |
13 |
1.00 |
23 |
0.565 |
|
|
|
|
|
|
|
29 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
30 |
A |
3 |
3 |
1.00 |
19 |
0.158 |
|
|
|
|
|
|
|
31 |
A |
7 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
32 |
A |
7 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
33 |
A |
7 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
34 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
35 |
A |
5 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
36 |
A |
7 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
37 |
A |
5 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
38 |
A |
20 |
15 |
1.00 |
20 |
0.750 |
|
|
|
|
|
|
|
39 |
A |
16 |
13 |
1.00 |
20 |
0.650 |
|
|
|
|
|
|
|
40 |
A |
13 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
41 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
42 |
A |
2 |
2 |
1.00 |
20 |
0.100 |
|
|
|
|
|
|
|
43 |
A |
21 |
19 |
1.01 |
20 |
0.950 |
|
|
|
|
|
|
|
44 |
A |
26 |
18 |
1.00 |
20 |
0.900 |
|
|
|
|
|
|
|
45 |
A |
21 |
14 |
1.00 |
20 |
0.700 |
|
|
|
|
|
|
|
46 |
A |
15 |
11 |
1.00 |
18 |
0.611 |
|
|
|
|
|
|
|
47 |
A |
6 |
7 |
1.00 |
12 |
0.583 |
|
|
|
|
|
|
|
48 |
A |
2 |
2 |
1.00 |
20 |
0.100 |
|
|
|
|
|
|
|
49 |
A |
30 |
18 |
1.00 |
20 |
0.900 |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
51 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
52 |
A |
6 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
53 |
A |
23 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
54 |
A |
17 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
55 |
A |
5 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
56 |
A |
15 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
57 |
A |
25 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
58 |
A |
31 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
59 |
A |
31 |
13 |
1.00 |
18 |
0.722 |
|
|
|
|
|
|
|
60 |
A |
37 |
16 |
1.00 |
18 |
0.889 |
|
|
|
|
|
|
|
61 |
A |
12 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
62 |
A |
6 |
5 |
1.00 |
32 |
0.156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|