Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 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, 58, 59, 60, 62, 63, 64,
65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 79, 82 }
B grade: { 5, 8, 10, 18, 25, 57, 61, 80, 83 }
C grade: { }
F grade: { 75, 78, 81, 84 }
2.1.3 Maple
A grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49,
50, 53, 54, 55, 58, 59, 60, 61, 64, 65, 66, 70, 71, 72 }
B grade: { 27, 69 }
C grade: { 73, 74, 76, 77, 79, 80, 82, 83 }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 62, 63, 67,
68, 75, 78, 81, 84 }
2.1.4 Maxima
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 22, 34, 39, 45, 53, 54, 58, 59, 61, 72 }
B grade: { 8, 10, 12, 15, 31, 32, 33, 36, 37, 38, 51, 52, 56, 57, 73, 76 }
C grade: { }
F grade: { 1, 3, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 35, 40, 41, 42, 43, 44, 46,
47, 48, 49, 50, 55, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84
}
2.1.5 FriCAS
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 53,
54, 55, 59, 60, 64, 65, 66, 70, 71, 72, 73, 76, 79, 82 }
B grade: { 3, 10, 12, 15, 18, 25, 27, 58, 61, 69, 74, 77, 80, 83 }
C grade: { 1, 8, 16, 23, 75, 78, 81, 84 }
F grade: { 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 62, 63, 67, 68 }
2.1.6 Sympy
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 53, 54,
55, 58, 59, 60, 65, 66, 70, 71, 72 }
B grade: { }
C grade: { }
F grade: { 1, 3, 8, 10, 12, 15, 16, 18, 20, 23, 25, 27, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56,
57, 61, 62, 63, 64, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84 }
2.1.7 Giac
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 17, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50,
53, 54, 55, 59, 60, 64, 65, 66, 69, 70, 71, 72 }
B grade: { 12, 15, 58, 61 }
C grade: { }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 62, 63, 67,
68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84 }
2.1.8 Mupad
A grade: { 2, 4, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 54, 55,
59, 60, 65, 66, 70, 71, 72 }
B grade: { 5, 12, 15, 20, 27, 53, 58, 61, 64, 69, 73, 76, 79 }
C grade: { }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 62, 63, 67,
68, 74, 75, 77, 78, 80, 81, 82, 83, 84 }
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 |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 159 | 0 | 0 | 425 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 0.00 | 0.00 | 3.29 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.150 |
0.258 |
1.207 |
0.000 |
0.558 |
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 |
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 |
0.016 |
3.228 |
1.243 |
0.000 |
0.609 |
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 |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 118 | 0 | 0 | 288 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.40 | 0.00 | 0.00 | 3.43 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.083 |
0.091 |
1.220 |
0.000 |
0.592 |
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 | 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 |
0.016 |
2.553 |
1.261 |
0.000 |
0.482 |
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 |
B |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 57 | 39 | 31 | 44 | 42 | 30 | 69 |
normalized size | 1 | 1.00 | 2.19 | 1.50 | 1.19 | 1.69 | 1.62 | 1.15 | 2.65 |
time (sec) |
N/A |
0.023 |
0.026 |
0.125 |
0.325 |
0.494 |
2.722 |
0.274 |
0.624 |
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Problem 6 |
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 | 22 | 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 |
0.017 |
2.284 |
0.916 |
0.000 |
0.499 |
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 |
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 |
0.017 |
2.327 |
1.077 |
0.000 |
0.558 |
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 |
B |
F |
B |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 639 | 0 | 805 | 683 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.80 | 0.00 | 3.53 | 3.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.369 |
3.220 |
2.691 |
0.828 |
0.584 |
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 |
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 |
0.023 |
14.067 |
2.457 |
0.000 |
0.440 |
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 |
A |
A |
B |
F |
B |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 268 | 0 | 607 | 451 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.14 | 0.00 | 4.86 | 3.61 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.159 |
4.728 |
2.621 |
0.653 |
0.667 |
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 |
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 |
0.023 |
14.061 |
2.030 |
0.000 |
0.444 |
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 |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 86 | 61 | 98 | 94 | 0 | 84 | 102 |
normalized size | 1 | 1.00 | 1.91 | 1.36 | 2.18 | 2.09 | 0.00 | 1.87 | 2.27 |
time (sec) |
N/A |
0.051 |
0.400 |
0.790 |
0.494 |
0.476 |
0.000 |
0.342 |
1.160 |
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Problem 13 |
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 | 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 |
0.022 |
31.523 |
2.241 |
0.000 |
0.478 |
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 | 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 |
0.022 |
17.442 |
2.273 |
0.000 |
0.492 |
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 |
A |
A |
A |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 167 | 94 | 3543 | 183 | 0 | 211 | 491 |
normalized size | 1 | 1.00 | 1.86 | 1.04 | 39.37 | 2.03 | 0.00 | 2.34 | 5.46 |
time (sec) |
N/A |
0.076 |
0.086 |
0.863 |
0.581 |
0.517 |
0.000 |
0.309 |
10.321 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 488 | 0 | 0 | 1445 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 0.00 | 0.00 | 3.65 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.946 |
1.190 |
2.177 |
0.000 |
0.660 |
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 |
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 | 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 |
0.026 |
1.494 |
1.716 |
0.000 |
0.573 |
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 |
A |
B |
F |
F(-2) |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 987 | 0 | 0 | 1055 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.64 | 0.00 | 0.00 | 3.89 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.569 |
3.910 |
1.404 |
0.000 |
0.680 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 19 |
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 | 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 |
0.025 |
1.244 |
1.366 |
0.000 |
0.443 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-1) |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 66 | 73 | 0 | 261 | 0 | 84 | 163 |
normalized size | 1 | 1.00 | 1.05 | 1.16 | 0.00 | 4.14 | 0.00 | 1.33 | 2.59 |
time (sec) |
N/A |
0.118 |
0.149 |
0.666 |
0.000 |
0.540 |
0.000 |
0.505 |
1.681 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
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 | 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 |
0.025 |
1.037 |
0.924 |
0.000 |
0.573 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
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 |
0.017 |
0.247 |
0.047 |
0.000 |
0.495 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1124 | 1124 | 2033 | 0 | 0 | 3032 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.81 | 0.00 | 0.00 | 2.70 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.378 |
9.390 |
3.862 |
0.000 |
0.880 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
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 | 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 |
0.025 |
15.461 |
3.057 |
0.000 |
0.481 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-2) |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 616 | 616 | 2446 | 0 | 0 | 1906 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.97 | 0.00 | 0.00 | 3.09 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.201 |
15.291 |
3.213 |
0.000 |
0.874 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
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 | 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 |
0.024 |
11.874 |
2.198 |
0.000 |
0.485 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 158 | 261 | 0 | 536 | 0 | 174 | 2755 |
normalized size | 1 | 1.00 | 1.32 | 2.18 | 0.00 | 4.47 | 0.00 | 1.45 | 22.96 |
time (sec) |
N/A |
0.242 |
0.679 |
0.772 |
0.000 |
0.494 |
0.000 |
0.538 |
5.672 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
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 | 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 |
0.024 |
22.841 |
2.479 |
0.000 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
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 | 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 |
0.024 |
17.957 |
2.967 |
0.000 |
0.657 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 | 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 |
0.025 |
18.286 |
3.134 |
0.000 |
0.454 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 432 | 432 | 445 | 0 | 1498 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 3.47 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.426 |
0.574 |
2.041 |
4.119 |
0.624 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 316 | 316 | 333 | 0 | 956 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.00 | 3.03 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.289 |
0.384 |
1.577 |
0.887 |
0.590 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 260 | 0 | 534 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.30 | 0.00 | 2.67 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.178 |
0.430 |
1.722 |
0.940 |
0.480 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
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 |
0.017 |
5.841 |
2.002 |
0.000 |
0.768 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
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 | 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 |
0.017 |
6.795 |
2.058 |
0.000 |
0.470 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 695 | 695 | 1242 | 0 | 6399 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.79 | 0.00 | 9.21 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.820 |
22.408 |
4.309 |
3.087 |
0.587 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 513 | 513 | 779 | 0 | 3856 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.52 | 0.00 | 7.52 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.612 |
14.102 |
4.128 |
1.600 |
0.511 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 333 | 333 | 449 | 0 | 1943 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.35 | 0.00 | 5.83 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.432 |
7.659 |
3.578 |
2.004 |
0.511 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
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 |
0.021 |
39.908 |
3.405 |
0.000 |
0.527 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
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 |
0.022 |
21.049 |
3.404 |
0.000 |
0.459 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1075 | 1075 | 1176 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.493 |
2.307 |
1.785 |
0.000 |
0.518 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
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|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 807 | 807 | 898 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.218 |
1.802 |
1.965 |
0.000 |
0.532 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 539 | 539 | 659 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.972 |
1.493 |
2.273 |
0.000 |
0.488 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
Problem 44 |
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 |
0.026 |
2.249 |
2.150 |
0.000 |
0.505 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
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|
Problem 45 |
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 |
0.015 |
0.581 |
0.042 |
0.000 |
0.618 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F(-2) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3205 | 3205 | 3831 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.240 |
14.942 |
3.015 |
0.000 |
0.500 |
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 |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2385 | 2385 | 2829 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
3.362 |
14.295 |
2.924 |
0.000 |
0.579 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1565 | 1565 | 1729 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.699 |
14.924 |
2.583 |
0.000 |
0.543 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 |
0.024 |
41.707 |
3.058 |
0.000 |
0.567 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
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 |
0.024 |
29.406 |
3.015 |
0.000 |
0.514 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 258 | 258 | 286 | 0 | 730 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.00 | 2.83 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.238 |
0.456 |
2.121 |
0.567 |
0.446 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 191 | 0 | 370 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 0.00 | 2.57 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.126 |
3.653 |
1.623 |
0.577 |
0.458 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 52 | 32 | 31 | 43 | 56 | 30 | 73 |
normalized size | 1 | 1.00 | 2.00 | 1.23 | 1.19 | 1.65 | 2.15 | 1.15 | 2.81 |
time (sec) |
N/A |
0.022 |
0.094 |
0.451 |
0.352 |
0.537 |
4.332 |
0.355 |
2.471 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
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 | 30 | 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 | -0.03 |
time (sec) |
N/A |
0.014 |
6.354 |
2.099 |
0.000 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
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 | 32 | 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 | -0.03 |
time (sec) |
N/A |
0.014 |
6.369 |
2.109 |
0.000 |
0.476 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 421 | 421 | 749 | 0 | 2815 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.78 | 0.00 | 6.69 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.538 |
8.381 |
4.521 |
0.608 |
0.483 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
B |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 241 | 241 | 681 | 0 | 1221 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.83 | 0.00 | 5.07 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.326 |
3.842 |
4.087 |
0.768 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
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 | 47 | 47 | 93 | 62 | 52 | 94 | 88 | 83 | 111 |
normalized size | 1 | 1.00 | 1.98 | 1.32 | 1.11 | 2.00 | 1.87 | 1.77 | 2.36 |
time (sec) |
N/A |
0.053 |
0.433 |
1.129 |
0.332 |
0.576 |
8.936 |
0.962 |
2.152 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
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 | 25 | 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 |
0.022 |
20.728 |
3.533 |
0.000 |
0.528 |
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 | 25 | 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 |
0.022 |
22.211 |
3.546 |
0.000 |
0.481 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 57 | 24 | 34 | 56 | 0 | 70 | 94 |
normalized size | 1 | 1.00 | 2.38 | 1.00 | 1.42 | 2.33 | 0.00 | 2.92 | 3.92 |
time (sec) |
N/A |
0.021 |
0.038 |
0.800 |
0.442 |
0.481 |
0.000 |
0.622 |
2.326 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 675 | 675 | 757 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.116 |
1.910 |
1.882 |
0.000 |
0.548 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 407 | 407 | 512 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.865 |
10.702 |
2.199 |
0.000 |
0.652 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 68 | 74 | 0 | 275 | 0 | 84 | 159 |
normalized size | 1 | 1.00 | 1.03 | 1.12 | 0.00 | 4.17 | 0.00 | 1.27 | 2.41 |
time (sec) |
N/A |
0.105 |
0.212 |
1.566 |
0.000 |
0.662 |
0.000 |
0.644 |
2.303 |
|
|
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Problem 65 |
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 | 25 | 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 |
0.025 |
3.577 |
2.230 |
0.000 |
0.536 |
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 |
F(-1) |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 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 |
0.025 |
3.480 |
1.983 |
0.000 |
0.677 |
0.000 |
0.000 |
0.000 |
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1977 | 1977 | 2293 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.985 |
13.346 |
3.151 |
0.000 |
0.446 |
0.000 |
0.000 |
0.000 |
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1157 | 1157 | 846 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.140 |
8.096 |
2.753 |
0.000 |
0.640 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 172 | 263 | 0 | 576 | 0 | 174 | 2737 |
normalized size | 1 | 1.00 | 1.38 | 2.10 | 0.00 | 4.61 | 0.00 | 1.39 | 21.90 |
time (sec) |
N/A |
0.215 |
0.692 |
1.534 |
0.000 |
0.560 |
0.000 |
0.297 |
5.351 |
|
|
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Problem 70 |
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 | 25 | 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 |
0.024 |
27.355 |
3.200 |
0.000 |
0.475 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 71 |
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 | 25 | 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 |
0.024 |
28.498 |
3.024 |
0.000 |
0.662 |
0.000 |
0.000 |
0.000 |
|
|
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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 | 32 | 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 | -0.03 |
time (sec) |
N/A |
0.049 |
2.843 |
2.771 |
0.000 |
0.506 |
0.000 |
0.000 |
0.000 |
|
|
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|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 61 | 158 | 128 | 62 | 0 | 0 | 106 |
normalized size | 1 | 1.00 | 1.36 | 3.51 | 2.84 | 1.38 | 0.00 | 0.00 | 2.36 |
time (sec) |
N/A |
0.050 |
0.133 |
2.316 |
0.464 |
0.506 |
0.000 |
0.000 |
2.159 |
|
|
|
|
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|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 185 | 731 | 0 | 384 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.31 | 5.18 | 0.00 | 2.72 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.109 |
0.219 |
2.878 |
0.000 |
0.532 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 0 | 0 | 0 | 557 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 2.52 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.184 |
3.960 |
3.438 |
0.000 |
0.576 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 102 | 275 | 207 | 116 | 0 | 0 | 182 |
normalized size | 1 | 1.00 | 1.28 | 3.44 | 2.59 | 1.45 | 0.00 | 0.00 | 2.28 |
time (sec) |
N/A |
0.092 |
0.703 |
2.254 |
1.253 |
0.503 |
0.000 |
0.000 |
2.171 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 286 | 674 | 0 | 568 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.34 | 3.15 | 0.00 | 2.65 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.200 |
6.282 |
1.949 |
0.000 |
0.600 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 0 | 0 | 0 | 886 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 2.35 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.396 |
12.739 |
5.073 |
0.000 |
0.574 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
A |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 79 | 315 | 0 | 301 | 0 | 0 | 229 |
normalized size | 1 | 1.00 | 0.93 | 3.71 | 0.00 | 3.54 | 0.00 | 0.00 | 2.69 |
time (sec) |
N/A |
0.154 |
0.255 |
2.662 |
0.000 |
0.593 |
0.000 |
0.000 |
2.311 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 338 | 338 | 1003 | 1332 | 0 | 1259 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.97 | 3.94 | 0.00 | 3.72 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.621 |
5.069 |
3.790 |
0.000 |
0.703 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 499 | 499 | 0 | 0 | 0 | 1697 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 3.40 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.941 |
1.879 |
3.674 |
0.000 |
0.667 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 156 | 176 | 712 | 0 | 630 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.13 | 4.56 | 0.00 | 4.04 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.286 |
0.948 |
2.953 |
0.000 |
0.559 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F(-1) |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 778 | 778 | 2839 | 2865 | 0 | 2455 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.65 | 3.68 | 0.00 | 3.16 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.302 |
10.321 |
2.860 |
0.000 |
0.859 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1417 | 1417 | 0 | 0 | 0 | 3785 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 2.67 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
2.442 |
10.666 |
7.378 |
0.000 |
0.911 |
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 [23] had the largest ratio of
[.6667]
|
|
|
|
|
|
|
| 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 |
10 |
6 |
1.00 |
16 |
0.375 |
|
|
|
|
|
|
|
2 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
3 |
A |
8 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
4 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
5 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
6 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
7 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
8 |
A |
15 |
11 |
1.00 |
18 |
0.611 |
|
|
|
|
|
|
|
9 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
10 |
A |
10 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
11 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
12 |
A |
5 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
13 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
15 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
16 |
A |
13 |
8 |
1.00 |
18 |
0.444 |
|
|
|
|
|
|
|
17 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
18 |
A |
11 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
19 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
20 |
A |
5 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
21 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
22 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
23 |
A |
31 |
12 |
1.00 |
18 |
0.667 |
|
|
|
|
|
|
|
24 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
25 |
A |
22 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
26 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
27 |
A |
7 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
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 |
20 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
32 |
A |
16 |
7 |
1.00 |
18 |
0.389 |
|
|
|
|
|
|
|
33 |
A |
12 |
7 |
1.00 |
16 |
0.438 |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
36 |
A |
30 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
37 |
A |
24 |
10 |
1.00 |
20 |
0.500 |
|
|
|
|
|
|
|
38 |
A |
18 |
10 |
1.00 |
18 |
0.556 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
41 |
A |
23 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
42 |
A |
19 |
9 |
1.00 |
20 |
0.450 |
|
|
|
|
|
|
|
43 |
A |
15 |
9 |
1.00 |
18 |
0.500 |
|
|
|
|
|
|
|
44 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
46 |
A |
61 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
47 |
A |
49 |
11 |
1.00 |
20 |
0.550 |
|
|
|
|
|
|
|
48 |
A |
37 |
11 |
1.00 |
18 |
0.611 |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
51 |
A |
14 |
7 |
1.00 |
20 |
0.350 |
|
|
|
|
|
|
|
52 |
A |
10 |
6 |
1.00 |
20 |
0.300 |
|
|
|
|
|
|
|
53 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
56 |
A |
21 |
10 |
1.00 |
22 |
0.454 |
|
|
|
|
|
|
|
57 |
A |
15 |
11 |
1.00 |
22 |
0.500 |
|
|
|
|
|
|
|
58 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
60 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
61 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
62 |
A |
17 |
9 |
1.00 |
22 |
0.409 |
|
|
|
|
|
|
|
63 |
A |
13 |
8 |
1.00 |
22 |
0.364 |
|
|
|
|
|
|
|
64 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
65 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
66 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
67 |
A |
43 |
11 |
1.00 |
22 |
0.500 |
|
|
|
|
|
|
|
68 |
A |
31 |
12 |
1.00 |
22 |
0.546 |
|
|
|
|
|
|
|
69 |
A |
7 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
70 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
71 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
72 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
73 |
A |
5 |
4 |
1.00 |
20 |
0.200 |
|
|
|
|
|
|
|
74 |
A |
9 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
75 |
A |
11 |
7 |
1.00 |
22 |
0.318 |
|
|
|
|
|
|
|
76 |
A |
6 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
77 |
A |
11 |
8 |
1.00 |
24 |
0.333 |
|
|
|
|
|
|
|
78 |
A |
16 |
12 |
1.00 |
24 |
0.500 |
|
|
|
|
|
|
|
79 |
A |
6 |
6 |
1.00 |
22 |
0.273 |
|
|
|
|
|
|
|
80 |
A |
12 |
8 |
1.00 |
24 |
0.333 |
|
|
|
|
|
|
|
81 |
A |
14 |
9 |
1.00 |
24 |
0.375 |
|
|
|
|
|
|
|
82 |
A |
8 |
8 |
1.00 |
22 |
0.364 |
|
|
|
|
|
|
|
83 |
A |
23 |
11 |
1.00 |
24 |
0.458 |
|
|
|
|
|
|
|
84 |
A |
32 |
13 |
1.00 |
24 |
0.542 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|