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, 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 }
B grade: { }
C grade: { }
F grade: { 16, 17, 18, 19, 20 }
2.1.2 Mathematica
A grade: { 1, 2, 4, 5, 6, 8, 9, 10, 14, 15, 21, 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, 51, 53, 54, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
76, 77 }
B grade: { 50, 63, 64 }
C grade: { 3, 7, 11, 12, 13, 18, 19, 55, 75 }
F grade: { 16, 17, 20, 22, 23, 52 }
2.1.3 Maple
A grade: { 4, 5, 8, 9, 10, 13, 14, 15, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35, 36, 37, 41, 42, 46, 47, 48,
49, 55, 56, 57, 60, 61, 62, 65, 66, 67, 71, 72, 76, 77 }
B grade: { 1, 2, 3, 6, 7, 11, 12, 32, 33, 34, 38, 39, 40, 43, 44, 45, 53, 54, 58, 59, 63, 64, 68, 69, 70, 73, 74, 75
}
C grade: { }
F grade: { 16, 17, 18, 19, 20, 50, 51, 52 }
2.1.4 Maxima
A grade: { 3, 4, 5, 9, 10, 14, 15, 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, 54, 56, 57, 61, 62, 65, 66, 67, 71, 72, 73, 74, 76, 77
}
B grade: { 1, 2, 6, 8, 11, 12, 53, 58, 59, 63, 64, 68, 69 }
C grade: { }
F grade: { 7, 13, 16, 17, 18, 19, 20, 50, 51, 52, 55, 60, 70, 75 }
2.1.5 FriCAS
A grade: { 4, 5, 9, 10, 14, 15, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 45, 46, 47, 48, 49, 50, 51, 52, 56,
57, 61, 62, 66, 67, 71, 72, 76, 77 }
B grade: { 8, 38, 39, 43, 44, 70, 75 }
C grade: { 1, 2, 3, 6, 7, 11, 12, 13, 53, 54, 55, 58, 59, 60, 63, 64, 65, 68, 69, 73, 74 }
F grade: { 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 }
2.1.6 Sympy
A grade: { 4, 5, 8, 9, 10, 14, 15, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 48, 49, 56, 57, 61, 62, 66, 67, 71,
72, 76, 77 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 16, 17, 18, 19, 20, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46,
47, 50, 51, 52, 53, 54, 55, 58, 59, 60, 63, 64, 65, 68, 69, 70, 73, 74, 75 }
2.1.7 Giac
A grade: { 4, 5, 9, 10, 14, 15, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 56, 57, 61, 62, 66, 67, 71, 72, 76, 77 }
B grade: { 8, 36 }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 16, 17, 18, 19, 20, 50, 51, 52, 53, 54, 55, 58, 59, 60, 63, 64, 65, 68, 69, 70,
73, 74, 75 }
2.1.8 Mupad
A grade: { 4, 5, 9, 10, 14, 15, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 48, 49, 56, 57, 61, 62, 66, 67, 71, 72,
76, 77 }
B grade: { 8, 32, 33, 34, 38, 39, 40, 43, 44, 45 }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 11, 12, 13, 16, 17, 18, 19, 20, 35, 36, 37, 41, 42, 46, 47, 50, 51, 52, 53, 54, 55, 58, 59,
60, 63, 64, 65, 68, 69, 70, 73, 74, 75 }
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 | 117 | 117 | 156 | 394 | 286 | 531 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 3.37 | 2.44 | 4.54 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.187 |
1.733 |
0.304 |
0.502 |
0.598 |
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 | 84 | 84 | 143 | 234 | 176 | 329 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.70 | 2.79 | 2.10 | 3.92 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.155 |
1.464 |
0.191 |
0.477 |
0.496 |
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 |
C |
B |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 210 | 109 | 78 | 171 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.68 | 1.91 | 1.37 | 3.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.090 |
4.418 |
0.166 |
0.483 |
0.459 |
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 | 17 | 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 | -0.06 |
time (sec) |
N/A |
0.022 |
9.599 |
0.229 |
0.000 |
0.451 |
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 | 17 | 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 | -0.06 |
time (sec) |
N/A |
0.022 |
16.805 |
0.225 |
0.000 |
0.506 |
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 | 119 | 119 | 179 | 328 | 343 | 1505 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.50 | 2.76 | 2.88 | 12.65 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.210 |
2.100 |
0.197 |
0.645 |
0.690 |
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 |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 301 | 177 | 0 | 840 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.42 | 2.01 | 0.00 | 9.55 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.137 |
6.345 |
0.164 |
0.000 |
0.579 |
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 | 40 | 40 | 77 | 65 | 127 | 232 | 66 | 134 | 56 |
normalized size | 1 | 1.00 | 1.92 | 1.62 | 3.18 | 5.80 | 1.65 | 3.35 | 1.40 |
time (sec) |
N/A |
0.031 |
0.247 |
0.108 |
0.386 |
0.505 |
0.247 |
0.146 |
0.095 |
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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 | 19 | 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 |
0.037 |
19.335 |
0.237 |
0.000 |
0.537 |
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 | 19 | 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 |
0.035 |
19.614 |
0.235 |
0.000 |
0.469 |
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 |
C |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 237 | 237 | 801 | 677 | 595 | 5569 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.38 | 2.86 | 2.51 | 23.50 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.392 |
12.750 |
0.311 |
0.570 |
0.622 |
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 |
C |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 458 | 367 | 392 | 3071 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.92 | 2.34 | 2.50 | 19.56 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.248 |
7.940 |
0.329 |
0.557 |
0.586 |
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 |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 263 | 166 | 0 | 1462 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.63 | 1.66 | 0.00 | 14.62 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.137 |
6.144 |
0.217 |
0.000 |
0.543 |
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 | 19 | 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 |
0.038 |
31.072 |
0.811 |
0.000 |
0.546 |
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 | 19 | 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 |
0.037 |
23.147 |
0.978 |
0.000 |
0.513 |
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 |
F |
F |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1392 | 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 | -0.00 |
time (sec) |
N/A |
0.132 |
39.854 |
0.215 |
0.000 |
0.000 |
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 |
F |
F |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1363 | 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 | -0.00 |
time (sec) |
N/A |
0.106 |
29.418 |
0.191 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
F |
C |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1280 | 0 | 556 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.029 |
5.320 |
0.262 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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|
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|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
C |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1280 | 0 | 556 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.031 |
4.386 |
0.253 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
F |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1365 | 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 | -0.00 |
time (sec) |
N/A |
0.110 |
27.752 |
0.206 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1341 | 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 | -0.00 |
time (sec) |
N/A |
0.149 |
28.724 |
0.220 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F(-1) |
A |
A |
F(-2) |
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 |
180.002 |
0.290 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
F(-1) |
A |
A |
F(-2) |
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 |
0.055 |
180.003 |
0.225 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1343 | 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 | -0.00 |
time (sec) |
N/A |
0.155 |
35.593 |
0.243 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.069 |
28.754 |
0.220 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.054 |
2.093 |
0.238 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
2.455 |
0.256 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
F(-2) |
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 |
0.072 |
26.265 |
0.284 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
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 | 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 |
146.540 |
0.139 |
0.000 |
0.488 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 | 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 |
9.920 |
0.105 |
0.000 |
0.455 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
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 | 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 |
7.624 |
0.145 |
0.000 |
0.429 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 244 | 929 | 186 | 304 | 0 | 193 | 273 |
normalized size | 1 | 1.00 | 1.44 | 5.50 | 1.10 | 1.80 | 0.00 | 1.14 | 1.62 |
time (sec) |
N/A |
0.195 |
0.440 |
0.197 |
0.480 |
0.752 |
0.000 |
0.143 |
1.307 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 169 | 446 | 126 | 192 | 0 | 123 | 187 |
normalized size | 1 | 1.00 | 1.39 | 3.66 | 1.03 | 1.57 | 0.00 | 1.01 | 1.53 |
time (sec) |
N/A |
0.118 |
0.293 |
0.155 |
0.405 |
0.480 |
0.000 |
0.132 |
1.182 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 81 | 165 | 74 | 101 | 0 | 67 | 76 |
normalized size | 1 | 1.00 | 1.09 | 2.23 | 1.00 | 1.36 | 0.00 | 0.91 | 1.03 |
time (sec) |
N/A |
0.054 |
0.308 |
0.157 |
0.344 |
0.420 |
0.000 |
0.161 |
1.127 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 122 | 61 | 48 | 73 | 0 | 49 | -1 |
normalized size | 1 | 1.00 | 0.78 | 0.39 | 0.31 | 0.46 | 0.00 | 0.31 | -0.01 |
time (sec) |
N/A |
0.295 |
0.272 |
0.649 |
0.528 |
0.417 |
0.000 |
0.147 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
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 | 159 | 159 | 206 | 90 | 56 | 217 | 0 | 348 | -1 |
normalized size | 1 | 1.00 | 1.30 | 0.57 | 0.35 | 1.36 | 0.00 | 2.19 | -0.01 |
time (sec) |
N/A |
0.240 |
0.805 |
0.622 |
0.739 |
0.456 |
0.000 |
0.193 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 264 | 211 | 68 | 342 | 0 | 180 | -1 |
normalized size | 1 | 1.00 | 1.25 | 1.00 | 0.32 | 1.62 | 0.00 | 0.85 | -0.00 |
time (sec) |
N/A |
0.323 |
1.152 |
0.648 |
0.960 |
0.441 |
0.000 |
0.147 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 230 | 230 | 420 | 1918 | 296 | 573 | 0 | 383 | 267 |
normalized size | 1 | 1.00 | 1.83 | 8.34 | 1.29 | 2.49 | 0.00 | 1.67 | 1.16 |
time (sec) |
N/A |
0.279 |
1.138 |
0.255 |
0.788 |
0.524 |
0.000 |
0.138 |
1.251 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 170 | 170 | 207 | 913 | 190 | 361 | 0 | 227 | 165 |
normalized size | 1 | 1.00 | 1.22 | 5.37 | 1.12 | 2.12 | 0.00 | 1.34 | 0.97 |
time (sec) |
N/A |
0.189 |
0.987 |
0.242 |
0.635 |
0.425 |
0.000 |
0.154 |
1.176 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 114 | 331 | 106 | 192 | 0 | 109 | 89 |
normalized size | 1 | 1.00 | 0.86 | 2.49 | 0.80 | 1.44 | 0.00 | 0.82 | 0.67 |
time (sec) |
N/A |
0.131 |
0.544 |
0.241 |
1.452 |
0.483 |
0.000 |
0.148 |
1.136 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 297 | 297 | 199 | 106 | 81 | 133 | 0 | 78 | -1 |
normalized size | 1 | 1.00 | 0.67 | 0.36 | 0.27 | 0.45 | 0.00 | 0.26 | -0.00 |
time (sec) |
N/A |
0.770 |
0.472 |
0.794 |
1.071 |
0.454 |
0.000 |
0.130 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 420 | 420 | 442 | 163 | 100 | 609 | 0 | 633 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.39 | 0.24 | 1.45 | 0.00 | 1.51 | -0.00 |
time (sec) |
N/A |
0.786 |
1.416 |
0.907 |
1.953 |
0.501 |
0.000 |
0.205 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 336 | 336 | 615 | 3296 | 407 | 844 | 0 | 573 | 376 |
normalized size | 1 | 1.00 | 1.83 | 9.81 | 1.21 | 2.51 | 0.00 | 1.71 | 1.12 |
time (sec) |
N/A |
0.379 |
2.854 |
0.343 |
2.500 |
0.533 |
0.000 |
0.163 |
1.352 |
|
|
|
|
|
|
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Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 371 | 1529 | 255 | 532 | 0 | 331 | 236 |
normalized size | 1 | 1.00 | 1.51 | 6.22 | 1.04 | 2.16 | 0.00 | 1.35 | 0.96 |
time (sec) |
N/A |
0.266 |
1.549 |
0.297 |
1.757 |
0.452 |
0.000 |
0.155 |
1.241 |
|
|
|
|
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|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 183 | 183 | 185 | 533 | 139 | 286 | 0 | 151 | 129 |
normalized size | 1 | 1.00 | 1.01 | 2.91 | 0.76 | 1.56 | 0.00 | 0.83 | 0.70 |
time (sec) |
N/A |
0.212 |
0.798 |
0.286 |
1.048 |
0.420 |
0.000 |
0.147 |
1.128 |
|
|
|
|
|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 437 | 437 | 312 | 151 | 114 | 193 | 0 | 107 | -1 |
normalized size | 1 | 1.00 | 0.71 | 0.35 | 0.26 | 0.44 | 0.00 | 0.24 | -0.00 |
time (sec) |
N/A |
1.821 |
0.720 |
1.063 |
4.527 |
0.469 |
0.000 |
0.141 |
0.000 |
|
|
|
|
|
|
|
|
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|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 692 | 692 | 794 | 239 | 140 | 1164 | 0 | 912 | -1 |
normalized size | 1 | 1.00 | 1.15 | 0.35 | 0.20 | 1.68 | 0.00 | 1.32 | -0.00 |
time (sec) |
N/A |
1.812 |
3.131 |
2.114 |
7.711 |
0.464 |
0.000 |
0.233 |
0.000 |
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
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|
|
|
Problem 48 |
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 |
0.050 |
34.654 |
0.255 |
0.000 |
0.530 |
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 |
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 |
0.027 |
13.985 |
0.335 |
0.000 |
0.502 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 186 | 0 | 0 | 148 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.09 | 0.00 | 0.00 | 1.66 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.115 |
1.198 |
0.379 |
0.000 |
0.466 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
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 | 153 | 153 | 195 | 0 | 0 | 248 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.27 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.179 |
11.173 |
0.372 |
0.000 |
0.476 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F(-1) |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 0 | 0 | 0 | 345 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 1.54 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.236 |
180.002 |
0.418 |
0.000 |
0.690 |
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 | 137 | 137 | 161 | 452 | 304 | 583 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.18 | 3.30 | 2.22 | 4.26 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.265 |
2.171 |
0.296 |
0.391 |
0.557 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 147 | 272 | 179 | 364 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.43 | 2.64 | 1.74 | 3.53 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.213 |
1.768 |
0.279 |
0.395 |
0.767 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 226 | 129 | 0 | 191 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.01 | 1.72 | 0.00 | 2.55 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.128 |
4.263 |
0.290 |
0.000 |
0.526 |
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 | 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 |
0.031 |
4.555 |
0.460 |
0.000 |
0.731 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
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 |
11.399 |
0.446 |
0.000 |
0.507 |
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 | 277 | 277 | 508 | 873 | 625 | 3744 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.83 | 3.15 | 2.26 | 13.52 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.548 |
7.901 |
0.528 |
0.434 |
1.021 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
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 | 211 | 211 | 232 | 510 | 411 | 2123 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 2.42 | 1.95 | 10.06 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.396 |
5.758 |
0.466 |
0.435 |
0.594 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 192 | 221 | 0 | 944 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.51 | 1.74 | 0.00 | 7.43 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.183 |
2.450 |
0.411 |
0.000 |
0.997 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
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 |
0.056 |
41.590 |
0.810 |
0.000 |
0.611 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
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 |
0.052 |
27.174 |
0.940 |
0.000 |
0.562 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 566 | 566 | 2010 | 1788 | 1297 | 12909 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.55 | 3.16 | 2.29 | 22.81 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.024 |
14.608 |
0.668 |
1.361 |
1.200 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 405 | 405 | 1142 | 1022 | 869 | 7298 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.82 | 2.52 | 2.15 | 18.02 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.700 |
11.846 |
0.587 |
0.967 |
0.840 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 265 | 459 | 475 | 3262 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 1.76 | 1.82 | 12.50 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.350 |
3.684 |
0.504 |
0.620 |
1.030 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 66 |
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 |
0.055 |
63.488 |
1.092 |
0.000 |
0.514 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
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 |
55.419 |
1.213 |
0.000 |
0.539 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
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 | 212 | 212 | 239 | 1143 | 528 | 740 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.13 | 5.39 | 2.49 | 3.49 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.341 |
3.487 |
0.679 |
0.697 |
0.764 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
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 | 157 | 157 | 191 | 720 | 337 | 500 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.22 | 4.59 | 2.15 | 3.18 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.290 |
3.868 |
0.660 |
0.865 |
0.602 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 144 | 357 | 0 | 306 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 3.31 | 0.00 | 2.83 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.166 |
3.326 |
0.660 |
0.000 |
0.602 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
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 |
0.063 |
15.577 |
0.569 |
0.000 |
0.576 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
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 |
24.330 |
0.593 |
0.000 |
0.752 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 642 | 642 | 1019 | 2278 | 1060 | 6160 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.59 | 3.55 | 1.65 | 9.60 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.212 |
13.078 |
0.942 |
1.864 |
0.682 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 506 | 1352 | 753 | 3693 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 2.84 | 1.58 | 7.76 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.651 |
9.391 |
0.850 |
1.925 |
0.556 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 196 | 196 | 476 | 565 | 0 | 1790 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.43 | 2.88 | 0.00 | 9.13 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.286 |
7.064 |
0.783 |
0.000 |
0.774 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
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 |
0.061 |
156.930 |
1.620 |
0.000 |
0.533 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
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 |
0.057 |
128.017 |
1.598 |
0.000 |
0.522 |
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
[.6250]
|
|
|
|
|
|
|
| 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 |
14 |
0.429 |
|
|
|
|
|
|
|
2 |
A |
5 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
3 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
4 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
5 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
6 |
A |
7 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
7 |
A |
6 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
8 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
9 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
10 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
11 |
A |
13 |
10 |
1.00 |
16 |
0.625 |
|
|
|
|
|
|
|
12 |
A |
9 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
13 |
A |
7 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
15 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
16 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
17 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
18 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
19 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
20 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
21 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
22 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
23 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
24 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
25 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
26 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
27 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
28 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
29 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
30 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
31 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
32 |
A |
5 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
33 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
34 |
A |
3 |
3 |
1.00 |
18 |
0.167 |
|
|
|
|
|
|
|
35 |
A |
7 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
36 |
A |
7 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
37 |
A |
8 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
38 |
A |
10 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
39 |
A |
8 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
40 |
A |
7 |
3 |
1.00 |
18 |
0.167 |
|
|
|
|
|
|
|
41 |
A |
21 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
42 |
A |
24 |
7 |
1.00 |
20 |
0.350 |
|
|
|
|
|
|
|
43 |
A |
14 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
44 |
A |
11 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
45 |
A |
11 |
3 |
1.00 |
18 |
0.167 |
|
|
|
|
|
|
|
46 |
A |
53 |
7 |
1.00 |
20 |
0.350 |
|
|
|
|
|
|
|
47 |
A |
60 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
48 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
50 |
A |
2 |
2 |
1.00 |
20 |
0.100 |
|
|
|
|
|
|
|
51 |
A |
4 |
2 |
1.00 |
20 |
0.100 |
|
|
|
|
|
|
|
52 |
A |
5 |
2 |
1.00 |
20 |
0.100 |
|
|
|
|
|
|
|
53 |
A |
8 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
54 |
A |
7 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
55 |
A |
6 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
56 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
57 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
58 |
A |
15 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
59 |
A |
13 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
60 |
A |
9 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
61 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
62 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
63 |
A |
28 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
64 |
A |
22 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
65 |
A |
16 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
66 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
67 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
68 |
A |
6 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
69 |
A |
5 |
5 |
1.00 |
20 |
0.250 |
|
|
|
|
|
|
|
70 |
A |
4 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
71 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
72 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
73 |
A |
28 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
74 |
A |
24 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
75 |
A |
5 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
76 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
77 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|