Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 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, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 62
}
B grade: { 37, 41, 45, 49, 56, 61 }
C grade: { }
F grade: { }
2.1.3 Maple
A grade: { 1, 2, 3, 4, 7, 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, 54, 55 }
B grade: { 6, 50, 51, 52 }
C grade: { 5, 53 }
F grade: { 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 56, 57, 58, 59, 60, 61, 62 }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 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 }
B grade: { 5 }
C grade: { }
F grade: { 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62
}
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 5, 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 }
B grade: { 6, 7 }
C grade: { }
F grade: { 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62
}
2.1.6 Sympy
A grade: { 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 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 6, 7, 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 }
B grade: { 5 }
C grade: { }
F grade: { 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62
}
2.1.8 Mupad
A grade: { }
B grade: { 4, 5, 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, 53 }
C grade: { }
F grade: { 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62
}
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 83 | 86 | 77 | 75 | 0 | 117 | -1 |
normalized size | 1 | 1.00 | 0.70 | 0.72 | 0.65 | 0.63 | 0.00 | 0.98 | -0.01 |
time (sec) |
N/A |
0.070 |
0.258 |
0.098 |
1.436 |
0.682 |
0.000 |
0.593 |
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 |
A |
A |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 71 | 73 | 60 | 62 | 0 | 90 | -1 |
normalized size | 1 | 1.00 | 0.80 | 0.82 | 0.67 | 0.70 | 0.00 | 1.01 | -0.01 |
time (sec) |
N/A |
0.049 |
0.114 |
0.106 |
1.484 |
0.550 |
0.000 |
0.581 |
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 |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 55 | 58 | 38 | 44 | 0 | 58 | -1 |
normalized size | 1 | 1.00 | 0.93 | 0.98 | 0.64 | 0.75 | 0.00 | 0.98 | -0.02 |
time (sec) |
N/A |
0.028 |
0.066 |
0.117 |
1.074 |
0.527 |
0.000 |
0.454 |
0.000 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 29 | 43 | 20 | 32 | 0 | 30 | 33 |
normalized size | 1 | 1.00 | 1.12 | 1.65 | 0.77 | 1.23 | 0.00 | 1.15 | 1.27 |
time (sec) |
N/A |
0.013 |
0.027 |
0.000 |
1.034 |
0.638 |
0.000 |
0.392 |
0.002 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
C |
B |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 40 | 54 | 90 | 126 | 0 | 93 | 45 |
normalized size | 1 | 1.00 | 0.87 | 1.17 | 1.96 | 2.74 | 0.00 | 2.02 | 0.98 |
time (sec) |
N/A |
0.021 |
0.016 |
0.000 |
1.523 |
0.784 |
0.000 |
0.700 |
0.002 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-1) |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 63 | 138 | 0 | 153 | 0 | 81 | -1 |
normalized size | 1 | 1.00 | 0.82 | 1.79 | 0.00 | 1.99 | 0.00 | 1.05 | -0.01 |
time (sec) |
N/A |
0.041 |
0.087 |
0.150 |
0.000 |
0.802 |
0.000 |
1.115 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F(-1) |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 65 | 174 | 0 | 188 | 0 | 103 | -1 |
normalized size | 1 | 1.00 | 0.61 | 1.63 | 0.00 | 1.76 | 0.00 | 0.96 | -0.01 |
time (sec) |
N/A |
0.063 |
0.191 |
0.164 |
0.000 |
0.787 |
0.000 |
1.964 |
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 |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 69 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.036 |
0.101 |
0.078 |
0.000 |
0.567 |
0.000 |
0.000 |
0.000 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 69 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.034 |
0.068 |
0.146 |
0.000 |
0.583 |
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 |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 69 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.030 |
0.065 |
0.087 |
0.000 |
0.586 |
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 |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 67 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.032 |
0.056 |
0.099 |
0.000 |
0.514 |
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 |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 67 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.031 |
0.057 |
0.064 |
0.000 |
0.506 |
0.000 |
0.000 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 69 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.032 |
0.065 |
0.069 |
0.000 |
0.585 |
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 |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 74 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.035 |
0.072 |
0.334 |
0.000 |
0.585 |
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 |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 75 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.033 |
0.082 |
0.355 |
0.000 |
0.502 |
0.000 |
0.000 |
0.000 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 77 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.018 |
0.093 |
0.252 |
0.000 |
0.700 |
0.000 |
0.000 |
0.000 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 74 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.016 |
0.074 |
0.273 |
0.000 |
0.664 |
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 |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 20 | 18 | 24 | 26 | 41 | 30 | 38 |
normalized size | 1 | 1.00 | 0.65 | 0.58 | 0.77 | 0.84 | 1.32 | 0.97 | 1.23 |
time (sec) |
N/A |
0.012 |
0.028 |
0.033 |
1.272 |
0.508 |
0.583 |
0.372 |
0.428 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 43 | 48 | 68 | 59 | 187 | 59 | 67 |
normalized size | 1 | 1.00 | 0.77 | 0.86 | 1.21 | 1.05 | 3.34 | 1.05 | 1.20 |
time (sec) |
N/A |
0.035 |
0.088 |
0.037 |
1.353 |
0.581 |
1.560 |
0.451 |
0.326 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
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 | 81 | 81 | 56 | 79 | 111 | 90 | 359 | 75 | 96 |
normalized size | 1 | 1.00 | 0.69 | 0.98 | 1.37 | 1.11 | 4.43 | 0.93 | 1.19 |
time (sec) |
N/A |
0.062 |
0.192 |
0.041 |
1.156 |
0.617 |
2.991 |
0.431 |
0.385 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 21 |
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 | 106 | 106 | 66 | 110 | 151 | 121 | 592 | 88 | 96 |
normalized size | 1 | 1.00 | 0.62 | 1.04 | 1.42 | 1.14 | 5.58 | 0.83 | 0.91 |
time (sec) |
N/A |
0.093 |
0.264 |
0.033 |
1.214 |
0.604 |
6.291 |
0.327 |
0.515 |
|
|
|
|
|
|
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|
Problem 22 |
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 | 33 | 33 | 20 | 18 | 24 | 26 | 41 | 30 | 38 |
normalized size | 1 | 1.00 | 0.61 | 0.55 | 0.73 | 0.79 | 1.24 | 0.91 | 1.15 |
time (sec) |
N/A |
0.013 |
0.027 |
0.027 |
1.687 |
0.638 |
0.597 |
0.372 |
0.294 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 23 |
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 | 58 | 58 | 43 | 48 | 69 | 59 | 192 | 61 | 67 |
normalized size | 1 | 1.00 | 0.74 | 0.83 | 1.19 | 1.02 | 3.31 | 1.05 | 1.16 |
time (sec) |
N/A |
0.036 |
0.077 |
0.043 |
1.375 |
0.561 |
1.368 |
0.434 |
0.309 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 24 |
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 | 83 | 83 | 65 | 83 | 112 | 90 | 364 | 77 | 95 |
normalized size | 1 | 1.00 | 0.78 | 1.00 | 1.35 | 1.08 | 4.39 | 0.93 | 1.14 |
time (sec) |
N/A |
0.063 |
0.139 |
0.034 |
1.290 |
0.638 |
2.804 |
0.430 |
0.373 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
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 | 108 | 108 | 66 | 116 | 152 | 121 | 597 | 90 | 97 |
normalized size | 1 | 1.00 | 0.61 | 1.07 | 1.41 | 1.12 | 5.53 | 0.83 | 0.90 |
time (sec) |
N/A |
0.096 |
0.219 |
0.045 |
2.132 |
0.615 |
6.064 |
0.407 |
0.491 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
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 | 33 | 33 | 20 | 18 | 24 | 26 | 42 | 30 | 38 |
normalized size | 1 | 1.00 | 0.61 | 0.55 | 0.73 | 0.79 | 1.27 | 0.91 | 1.15 |
time (sec) |
N/A |
0.013 |
0.024 |
0.030 |
1.386 |
0.916 |
0.590 |
0.384 |
0.254 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
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 | 58 | 58 | 43 | 48 | 69 | 59 | 192 | 61 | 67 |
normalized size | 1 | 1.00 | 0.74 | 0.83 | 1.19 | 1.02 | 3.31 | 1.05 | 1.16 |
time (sec) |
N/A |
0.033 |
0.023 |
0.036 |
1.239 |
0.749 |
1.372 |
0.454 |
0.002 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
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 | 83 | 83 | 65 | 83 | 112 | 90 | 366 | 77 | 96 |
normalized size | 1 | 1.00 | 0.78 | 1.00 | 1.35 | 1.08 | 4.41 | 0.93 | 1.16 |
time (sec) |
N/A |
0.064 |
0.103 |
0.038 |
1.062 |
1.105 |
2.801 |
0.390 |
0.359 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
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 | 108 | 108 | 66 | 116 | 152 | 121 | 597 | 90 | 97 |
normalized size | 1 | 1.00 | 0.61 | 1.07 | 1.41 | 1.12 | 5.53 | 0.83 | 0.90 |
time (sec) |
N/A |
0.095 |
0.025 |
0.040 |
0.683 |
0.725 |
6.060 |
1.221 |
0.002 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 | 31 | 31 | 20 | 18 | 24 | 26 | 44 | 30 | 38 |
normalized size | 1 | 1.00 | 0.65 | 0.58 | 0.77 | 0.84 | 1.42 | 0.97 | 1.23 |
time (sec) |
N/A |
0.013 |
0.026 |
0.032 |
1.505 |
0.604 |
0.591 |
0.373 |
0.255 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
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 | 56 | 56 | 43 | 48 | 68 | 59 | 190 | 59 | 67 |
normalized size | 1 | 1.00 | 0.77 | 0.86 | 1.21 | 1.05 | 3.39 | 1.05 | 1.20 |
time (sec) |
N/A |
0.029 |
0.023 |
0.041 |
1.427 |
0.991 |
1.571 |
0.596 |
0.002 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
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 | 81 | 81 | 65 | 79 | 111 | 90 | 362 | 75 | 95 |
normalized size | 1 | 1.00 | 0.80 | 0.98 | 1.37 | 1.11 | 4.47 | 0.93 | 1.17 |
time (sec) |
N/A |
0.061 |
0.099 |
0.037 |
1.265 |
0.929 |
3.051 |
0.416 |
0.358 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
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 | 106 | 106 | 66 | 110 | 151 | 121 | 595 | 88 | 96 |
normalized size | 1 | 1.00 | 0.62 | 1.04 | 1.42 | 1.14 | 5.61 | 0.83 | 0.91 |
time (sec) |
N/A |
0.096 |
0.025 |
0.042 |
1.967 |
0.846 |
6.287 |
0.443 |
0.002 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
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 | 65 | 65 | 65 | 36 | 48 | 46 | 41 | 34 | 17 |
normalized size | 1 | 1.00 | 1.00 | 0.55 | 0.74 | 0.71 | 0.63 | 0.52 | 0.26 |
time (sec) |
N/A |
0.019 |
0.025 |
0.033 |
0.296 |
0.518 |
0.545 |
0.397 |
0.361 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
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 | 90 | 90 | 143 | 72 | 91 | 88 | 228 | 62 | 47 |
normalized size | 1 | 1.00 | 1.59 | 0.80 | 1.01 | 0.98 | 2.53 | 0.69 | 0.52 |
time (sec) |
N/A |
0.041 |
0.082 |
0.037 |
0.300 |
0.657 |
1.234 |
0.400 |
0.320 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
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 | 115 | 115 | 217 | 108 | 135 | 129 | 474 | 78 | 76 |
normalized size | 1 | 1.00 | 1.89 | 0.94 | 1.17 | 1.12 | 4.12 | 0.68 | 0.66 |
time (sec) |
N/A |
0.075 |
0.196 |
0.036 |
0.823 |
0.883 |
2.465 |
0.617 |
0.674 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 296 | 144 | 174 | 170 | 813 | 91 | 102 |
normalized size | 1 | 1.00 | 2.11 | 1.03 | 1.24 | 1.21 | 5.81 | 0.65 | 0.73 |
time (sec) |
N/A |
0.113 |
0.246 |
0.038 |
0.955 |
0.627 |
5.239 |
0.388 |
1.969 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
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 | 63 | 63 | 63 | 40 | 50 | 46 | 44 | 38 | 17 |
normalized size | 1 | 1.00 | 1.00 | 0.63 | 0.79 | 0.73 | 0.70 | 0.60 | 0.27 |
time (sec) |
N/A |
0.018 |
0.024 |
0.034 |
1.270 |
0.910 |
0.570 |
0.473 |
0.332 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
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 | 88 | 88 | 139 | 80 | 94 | 88 | 240 | 68 | 47 |
normalized size | 1 | 1.00 | 1.58 | 0.91 | 1.07 | 1.00 | 2.73 | 0.77 | 0.53 |
time (sec) |
N/A |
0.042 |
0.078 |
0.040 |
0.991 |
0.840 |
1.251 |
1.335 |
0.343 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
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 | 113 | 113 | 211 | 120 | 137 | 129 | 490 | 84 | 76 |
normalized size | 1 | 1.00 | 1.87 | 1.06 | 1.21 | 1.14 | 4.34 | 0.74 | 0.67 |
time (sec) |
N/A |
0.072 |
0.145 |
0.042 |
0.669 |
0.983 |
2.475 |
0.397 |
0.673 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 288 | 160 | 177 | 170 | 831 | 97 | 102 |
normalized size | 1 | 1.00 | 2.09 | 1.16 | 1.28 | 1.23 | 6.02 | 0.70 | 0.74 |
time (sec) |
N/A |
0.113 |
0.235 |
0.042 |
1.376 |
0.722 |
5.304 |
0.454 |
2.013 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
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 | 63 | 63 | 63 | 40 | 50 | 46 | 44 | 38 | 17 |
normalized size | 1 | 1.00 | 1.00 | 0.63 | 0.79 | 0.73 | 0.70 | 0.60 | 0.27 |
time (sec) |
N/A |
0.017 |
0.021 |
0.029 |
1.020 |
0.624 |
0.557 |
0.468 |
0.261 |
|
|
|
|
|
|
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|
|
Problem 43 |
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 | 88 | 88 | 139 | 80 | 94 | 88 | 240 | 68 | 47 |
normalized size | 1 | 1.00 | 1.58 | 0.91 | 1.07 | 1.00 | 2.73 | 0.77 | 0.53 |
time (sec) |
N/A |
0.040 |
0.021 |
0.037 |
0.296 |
1.003 |
1.243 |
0.409 |
0.002 |
|
|
|
|
|
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|
Problem 44 |
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 | 113 | 113 | 211 | 120 | 137 | 129 | 490 | 84 | 75 |
normalized size | 1 | 1.00 | 1.87 | 1.06 | 1.21 | 1.14 | 4.34 | 0.74 | 0.66 |
time (sec) |
N/A |
0.072 |
0.125 |
0.040 |
0.596 |
1.480 |
2.476 |
0.717 |
0.650 |
|
|
|
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Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 288 | 160 | 177 | 170 | 831 | 97 | 102 |
normalized size | 1 | 1.00 | 2.09 | 1.16 | 1.28 | 1.23 | 6.02 | 0.70 | 0.74 |
time (sec) |
N/A |
0.108 |
0.022 |
0.039 |
1.113 |
1.604 |
5.277 |
0.849 |
0.002 |
|
|
|
|
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Problem 46 |
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 | 65 | 65 | 65 | 36 | 48 | 46 | 42 | 34 | 17 |
normalized size | 1 | 1.00 | 1.00 | 0.55 | 0.74 | 0.71 | 0.65 | 0.52 | 0.26 |
time (sec) |
N/A |
0.018 |
0.022 |
0.033 |
1.386 |
0.728 |
0.559 |
0.377 |
0.262 |
|
|
|
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Problem 47 |
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 | 90 | 90 | 143 | 72 | 91 | 88 | 231 | 62 | 47 |
normalized size | 1 | 1.00 | 1.59 | 0.80 | 1.01 | 0.98 | 2.57 | 0.69 | 0.52 |
time (sec) |
N/A |
0.041 |
0.019 |
0.040 |
0.300 |
2.022 |
1.232 |
0.508 |
0.002 |
|
|
|
|
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Problem 48 |
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 | 115 | 115 | 217 | 108 | 135 | 129 | 478 | 78 | 75 |
normalized size | 1 | 1.00 | 1.89 | 0.94 | 1.17 | 1.12 | 4.16 | 0.68 | 0.65 |
time (sec) |
N/A |
0.072 |
0.100 |
0.036 |
0.878 |
0.780 |
2.480 |
0.816 |
0.669 |
|
|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 296 | 144 | 174 | 170 | 816 | 91 | 102 |
normalized size | 1 | 1.00 | 2.11 | 1.03 | 1.24 | 1.21 | 5.83 | 0.65 | 0.73 |
time (sec) |
N/A |
0.120 |
0.022 |
0.043 |
0.940 |
0.604 |
5.250 |
0.449 |
0.002 |
|
|
|
|
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|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 177 | 662 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 3.36 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.282 |
0.788 |
0.305 |
0.000 |
0.883 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 134 | 450 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.85 | 2.87 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.171 |
0.534 |
0.246 |
0.000 |
1.140 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 57 | 170 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.98 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.037 |
0.069 |
0.250 |
0.000 |
0.731 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 57 | 75 | 0 | 0 | 0 | 0 | 52 |
normalized size | 1 | 1.00 | 1.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A |
0.039 |
0.048 |
0.104 |
0.000 |
0.896 |
0.000 |
0.000 |
0.390 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 83 | 217 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.78 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.199 |
0.488 |
0.000 |
0.863 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 158 | 489 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.71 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.233 |
0.908 |
0.579 |
0.000 |
0.743 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 246 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.077 |
1.866 |
0.079 |
0.000 |
1.825 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 118 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.067 |
0.174 |
0.207 |
0.000 |
0.892 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 118 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.063 |
0.163 |
0.168 |
0.000 |
0.617 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 118 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.066 |
0.178 |
0.105 |
0.000 |
0.972 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 116 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.064 |
0.166 |
0.084 |
0.000 |
0.670 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
|
|
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|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 268 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.069 |
2.027 |
0.073 |
0.000 |
0.816 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 121 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.067 |
0.221 |
0.408 |
0.000 |
0.777 |
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 [50] had the largest ratio of
[.5000]
|
|
|
|
|
|
|
| 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 |
4 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
2 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
4 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
6 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
7 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
8 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
10 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
11 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
12 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
13 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
14 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
15 |
A |
2 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
16 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
|
|
|
|
|
|
|
17 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
|
|
|
|
|
|
|
18 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
|
|
|
|
|
|
|
19 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
21 |
A |
5 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
22 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
|
|
|
|
|
|
|
23 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
24 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
25 |
A |
5 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
26 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
|
|
|
|
|
|
|
27 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
28 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
29 |
A |
5 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
30 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
|
|
|
|
|
|
|
31 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
32 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
33 |
A |
5 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
34 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
35 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
36 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
37 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
38 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
39 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
40 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
41 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
42 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
43 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
44 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
45 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
46 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
48 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
49 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
50 |
A |
7 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
51 |
A |
6 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
52 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
53 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
54 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
55 |
A |
7 |
7 |
1.00 |
14 |
0.500 |
|
|
|
|
|
|
|
56 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
57 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
58 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
59 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
60 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
61 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
62 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|