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, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112,
113 }
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, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62,
63, 64, 65, 66, 67, 68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92,
93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
}
B grade: { 31, 42, 70, 71, 72 }
C grade: { 40, 69 }
F grade: { 57}
2.1.3 Maple
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, 33, 34, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63,
64, 65, 66, 67, 68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92,
93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
}
B grade: { 35, 36, 40, 48, 51, 57, 69, 70, 71, 72 }
C grade: { 32, 42 }
F grade: { }
2.1.4 Maxima
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28,
29, 30, 31, 33, 34, 35, 37, 39, 41, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
60, 61, 62, 63, 64, 65, 66, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91,
92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112,
113
B grade: { 36, 38, 68, 70, 71, 72, 87 }
C grade: { 10, 11, 47 }
F grade: { 27, 32, 40, 42, 67, 69 }
2.1.5 FriCAS
A grade: { 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 33, 34, 35, 36, 38, 41, 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, 71, 72, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 90, 91,
92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
}
B grade: { 1, 9, 37, 39, 40, 42, 69, 70, 73, 74, 83, 84, 100 }
C grade: { }
F grade: { 32 }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 38, 41, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 74, 75,
76, 77, 78, 79, 80, 81, 85, 86, 88, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110, 111, 112, 113 }
B grade: { 7, 18, 37, 39, 50, 51, 56, 66, 73, 82, 83, 84, 100 }
C grade: { 71, 72 }
F grade: { 35, 36, 40, 42, 69, 70, 87, 90, 98 }
2.1.7 Giac
A grade: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31,
33, 34, 35, 36, 37, 38, 39, 41, 44, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,
64, 65, 66, 67, 68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92,
93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
}
B grade: { 1, 25, 43, 45, 70, 71, 72 }
C grade: { 47 }
F grade: { 32, 40, 42, 69 }
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 |
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grade |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 18 | 14 | 22 | 126 | 19 | 46 |
normalized size | 1 | 1. | 1.5 | 1.17 | 1.83 | 10.5 | 1.58 | 3.83 |
time (sec) |
N/A |
0.01 |
0.003 |
0. |
1.414 |
1.655 |
0.066 |
1.063 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 12 | 20 | 53 | 14 | 20 |
normalized size | 1 | 1. | 1. | 0.92 | 1.54 | 4.08 | 1.08 | 1.54 |
time (sec) |
N/A |
0.005 |
0.004 |
0.005 |
1.413 |
1.506 |
0.105 |
1.079 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 14 | 11 | 15 | 38 | 15 | 15 |
normalized size | 1 | 1. | 0.74 | 0.58 | 0.79 | 2. | 0.79 | 0.79 |
time (sec) |
N/A |
0.003 |
0.003 |
0.001 |
0.936 |
1.5 |
0.223 |
1.09 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 3 | 3 | 11 | 2 | 3 |
normalized size | 1 | 1. | 1. | 1.5 | 1.5 | 5.5 | 1. | 1.5 |
time (sec) |
N/A |
0.002 |
0.001 |
0. |
0.927 |
1.582 |
0.053 |
1.093 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 7 | 8 | 18 | 5 | 8 |
normalized size | 1 | 1. | 1. | 0.78 | 0.89 | 2. | 0.56 | 0.89 |
time (sec) |
N/A |
0.006 |
0.001 |
0. |
0.927 |
1.633 |
0.079 |
1.079 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 19 | 7 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 2.38 | 0.88 | 1. |
time (sec) |
N/A |
0.011 |
0.004 |
0.005 |
0.936 |
1.599 |
0.066 |
1.066 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 10 | 12 | 28 | 22 | 12 |
normalized size | 1 | 1. | 1. | 0.77 | 0.92 | 2.15 | 1.69 | 0.92 |
time (sec) |
N/A |
0.002 |
0.002 |
0.002 |
0.925 |
1.568 |
0.19 |
1.085 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 14 | 14 | 15 | 46 | 15 | 15 |
normalized size | 1 | 1. | 0.74 | 0.74 | 0.79 | 2.42 | 0.79 | 0.79 |
time (sec) |
N/A |
0.007 |
0.014 |
0. |
0.934 |
1.641 |
0.298 |
1.098 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 39 | 8 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 4.88 | 1. | 1. |
time (sec) |
N/A |
0.012 |
0.004 |
0.013 |
0.94 |
1.607 |
0.064 |
1.072 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 4 | 4 | 4 | 4 | 20 | 26 | 3 | 4 |
normalized size | 1 | 1. | 1. | 1. | 5. | 6.5 | 0.75 | 1. |
time (sec) |
N/A |
0.012 |
0.005 |
0.004 |
1.065 |
1.931 |
0.641 |
1.06 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 3 | 18 | 23 | 2 | 3 |
normalized size | 1 | 1. | 1. | 1.5 | 9. | 11.5 | 1. | 1.5 |
time (sec) |
N/A |
0.011 |
0.013 |
0.001 |
1.055 |
1.86 |
0.54 |
1.117 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 8 | 9 | 20 | 5 | 9 |
normalized size | 1 | 1. | 1. | 1. | 1.12 | 2.5 | 0.62 | 1.12 |
time (sec) |
N/A |
0.003 |
0.003 |
0.002 |
0.946 |
1.82 |
0.072 |
1.07 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 7 | 8 | 15 | 5 | 8 |
normalized size | 1 | 1. | 1. | 1. | 1.14 | 2.14 | 0.71 | 1.14 |
time (sec) |
N/A |
0.02 |
0.005 |
0.002 |
0.935 |
1.886 |
0.08 |
1.07 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 26 | 22 | 26 | 53 | 20 | 26 |
normalized size | 1 | 1. | 0.93 | 0.79 | 0.93 | 1.89 | 0.71 | 0.93 |
time (sec) |
N/A |
0.02 |
0.014 |
0.002 |
0.928 |
1.802 |
0.087 |
1.098 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 17 | 22 | 42 | 15 | 22 |
normalized size | 1 | 1. | 1. | 0.77 | 1. | 1.91 | 0.68 | 1. |
time (sec) |
N/A |
0.005 |
0.002 |
0.001 |
0.933 |
1.878 |
0.083 |
1.074 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 20 | 5 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 2.5 | 0.62 | 1. |
time (sec) |
N/A |
0.007 |
0.001 |
0.001 |
0.913 |
1.915 |
0.054 |
1.081 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 7 | 8 | 18 | 5 | 8 |
normalized size | 1 | 1. | 1. | 0.78 | 0.89 | 2. | 0.56 | 0.89 |
time (sec) |
N/A |
0.006 |
0.001 |
0. |
0.925 |
1.913 |
0.075 |
1.07 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 10 | 12 | 28 | 22 | 12 |
normalized size | 1 | 1. | 1. | 0.77 | 0.92 | 2.15 | 1.69 | 0.92 |
time (sec) |
N/A |
0.002 |
0. |
0. |
0.93 |
1.701 |
0.18 |
1.06 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 6 | 6 | 6 | 7 | 19 | 5 | 7 |
normalized size | 1 | 1. | 1. | 1. | 1.17 | 3.17 | 0.83 | 1.17 |
time (sec) |
N/A |
0.015 |
0.004 |
0.001 |
0.922 |
1.682 |
0.085 |
1.094 |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 6 | 7 | 18 | 7 | 7 |
normalized size | 1 | 1. | 1. | 0.67 | 0.78 | 2. | 0.78 | 0.78 |
time (sec) |
N/A |
0. |
0.001 |
0.001 |
0.927 |
1.739 |
0.052 |
1.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 9 | 11 | 24 | 7 | 11 |
normalized size | 1 | 1. | 1. | 0.9 | 1.1 | 2.4 | 0.7 | 1.1 |
time (sec) |
N/A |
0.003 |
0.004 |
0.005 |
0.925 |
1.88 |
0.112 |
1.101 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 8 | 9 | 18 | 7 | 9 |
normalized size | 1 | 1. | 1. | 1. | 1.12 | 2.25 | 0.88 | 1.12 |
time (sec) |
N/A |
0.003 |
0.001 |
0.002 |
0.933 |
1.862 |
0.06 |
1.071 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 19 | 8 | 9 | 23 | 8 | 9 |
normalized size | 1 | 1. | 1.9 | 0.8 | 0.9 | 2.3 | 0.8 | 0.9 |
time (sec) |
N/A |
0.027 |
0.02 |
0.004 |
0.923 |
1.89 |
2.086 |
1.081 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 16 | 13 | 20 | 46 | 34 | 20 |
normalized size | 1 | 1. | 0.7 | 0.57 | 0.87 | 2. | 1.48 | 0.87 |
time (sec) |
N/A |
0.004 |
0.004 |
0.003 |
0.925 |
1.819 |
0.848 |
1.1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 25 | 10 | 23 | 68 | 17 | 26 |
normalized size | 1 | 1. | 1.92 | 0.77 | 1.77 | 5.23 | 1.31 | 2. |
time (sec) |
N/A |
0.003 |
0.004 |
0. |
1.418 |
1.883 |
0.115 |
1.087 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 18 | 14 | 18 | 50 | 15 | 18 |
normalized size | 1 | 1. | 1. | 0.78 | 1. | 2.78 | 0.83 | 1. |
time (sec) |
N/A |
0.02 |
0.007 |
0.004 |
1.412 |
1.949 |
0.107 |
1.093 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 20 | 0 | 186 | 22 | 26 |
normalized size |
1 |
1. |
1. |
0.65 |
0. |
6. |
0.71 |
0.84 |
time (sec) |
N/A |
0.035 |
0.008 |
0.007 |
0. |
1.932 |
0.151 |
1.085 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 9 | 11 | 30 | 7 | 11 |
normalized size | 1 | 1. | 1. | 1.12 | 1.38 | 3.75 | 0.88 | 1.38 |
time (sec) |
N/A |
0.034 |
0.005 |
0.001 |
0.932 |
1.947 |
0.096 |
1.082 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 13 | 16 | 27 | 8 | 16 |
normalized size | 1 | 1. | 1. | 1.08 | 1.33 | 2.25 | 0.67 | 1.33 |
time (sec) |
N/A |
0.006 |
0.004 |
0.01 |
0.931 |
1.967 |
0.087 |
1.08 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 17 | 22 | 46 | 15 | 22 |
normalized size | 1 | 1. | 1. | 0.85 | 1.1 | 2.3 | 0.75 | 1.1 |
time (sec) |
N/A |
0.019 |
0.002 |
0. |
0.933 |
1.99 |
0.548 |
1.073 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 260 | 41 | 54 | 124 | 46 | 54 |
normalized size | 1 | 1. | 5.31 | 0.84 | 1.1 | 2.53 | 0.94 | 1.1 |
time (sec) |
N/A |
0.036 |
0.109 |
0. |
1.407 |
1.843 |
0.159 |
1.096 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 142 | 41 | 0 | 0 | 54 | 0 |
normalized size | 1 | 1. | 1.23 | 0.36 | 0. | 0. | 0.47 | 0. |
time (sec) |
N/A |
0.056 |
0.293 |
0.089 |
0. |
0. |
5.489 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 17 | 22 | 55 | 20 | 22 |
normalized size | 1 | 1. | 1. | 0.77 | 1. | 2.5 | 0.91 | 1. |
time (sec) |
N/A |
0.01 |
0.014 |
0.01 |
0.931 |
1.83 |
0.295 |
1.079 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 16 | 13 | 20 | 46 | 34 | 20 |
normalized size | 1 | 1. | 0.7 | 0.57 | 0.87 | 2. | 1.48 | 0.87 |
time (sec) |
N/A |
0.004 |
0.003 |
0. |
0.927 |
1.79 |
0.84 |
1.092 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 32 | 92 | 32 | 76 | 0 | 32 |
normalized size | 1 | 1. | 1. | 2.88 | 1. | 2.38 | 0. | 1. |
time (sec) |
N/A |
0.014 |
0.013 |
0. |
0.93 |
1.731 |
0. |
1.076 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 71 | 75 | 108 | 151 | 0 | 82 |
normalized size | 1 | 1. | 1.61 | 1.7 | 2.45 | 3.43 | 0. | 1.86 |
time (sec) |
N/A |
0.016 |
0.036 |
0.01 |
1.406 |
1.831 |
0. |
1.105 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 26 | 30 | 59 | 146 | 105 | 39 |
normalized size | 1 | 1. | 0.74 | 0.86 | 1.69 | 4.17 | 3. | 1.11 |
time (sec) |
N/A |
0.009 |
0.024 |
0.004 |
1.425 |
1.835 |
2.606 |
1.083 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 41 | 70 | 153 | 140 | 190 | 111 |
normalized size | 1 | 1. | 0.55 | 0.93 | 2.04 | 1.87 | 2.53 | 1.48 |
time (sec) |
N/A |
0.013 |
0.019 |
0.003 |
0.943 |
1.796 |
11.904 |
1.278 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 26 | 30 | 59 | 146 | 105 | 39 |
normalized size | 1 | 1. | 0.74 | 0.86 | 1.69 | 4.17 | 3. | 1.11 |
time (sec) |
N/A |
0.008 |
0.004 |
0. |
1.419 |
1.87 |
2.568 |
1.099 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
B |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 134 | 262 | 0 | 285 | 0 | 0 |
normalized size |
1 |
1. |
2.63 |
5.14 |
0. |
5.59 |
0. |
0. |
time (sec) |
N/A |
0.029 |
0.029 |
0.022 |
0. |
2.025 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 11 | 14 | 38 | 10 | 14 |
normalized size | 1 | 1. | 1. | 0.79 | 1. | 2.71 | 0.71 | 1. |
time (sec) |
N/A |
0.006 |
0.002 |
0. |
0.925 |
1.985 |
0.057 |
1.137 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 57 | 99 | 149 | 0 | 635 | 0 | 0 |
normalized size |
1 |
1.16 |
2.02 |
3.04 |
0. |
12.96 |
0. |
0. |
time (sec) |
N/A |
0.085 |
0.106 |
0.096 |
0. |
2.998 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 6 | 5 | 12 | 28 | 3 | 41 |
normalized size | 1 | 1. | 0.67 | 0.56 | 1.33 | 3.11 | 0.33 | 4.56 |
time (sec) |
N/A |
0.008 |
0.004 |
0. |
0.918 |
1.945 |
0.179 |
1.109 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 7 | 7 | 8 | 18 | 5 | 8 |
normalized size | 1 | 1. | 0.64 | 0.64 | 0.73 | 1.64 | 0.45 | 0.73 |
time (sec) |
N/A |
0.007 |
0.001 |
0. |
0.929 |
1.931 |
0.074 |
1.092 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 9 | 11 | 18 | 5 | 26 |
normalized size | 1 | 1. | 1. | 1. | 1.22 | 2. | 0.56 | 2.89 |
time (sec) |
N/A |
0.026 |
0.023 |
0.002 |
0.942 |
1.746 |
0.085 |
1.104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 7 | 8 | 15 | 5 | 8 |
normalized size | 1 | 1. | 1. | 1. | 1.14 | 2.14 | 0.71 | 1.14 |
time (sec) |
N/A |
0.032 |
0.005 |
0.001 |
0.938 |
1.975 |
0.081 |
1.067 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 8 | 12 | 30 | 8 | 12 |
normalized size | 1 | 1. | 1. | 0.73 | 1.09 | 2.73 | 0.73 | 1.09 |
time (sec) |
N/A |
0.002 |
0.002 |
0. |
0.927 |
2.029 |
0.231 |
1.085 |
|
|
|
|
|
|
|
|
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|
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|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 8 | 3 | 9 | 2 | 3 |
normalized size | 1 | 1. | 1. | 4. | 1.5 | 4.5 | 1. | 1.5 |
time (sec) |
N/A |
0.01 |
0.004 |
0.002 |
1.013 |
1.869 |
0.736 |
1.076 |
|
|
|
|
|
|
|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 40 | 35 | 46 | 112 | 41 | 47 |
normalized size | 1 | 1. | 0.98 | 0.85 | 1.12 | 2.73 | 1. | 1.15 |
time (sec) |
N/A |
0.022 |
0.009 |
0. |
1.405 |
1.981 |
0.122 |
1.072 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 73 | 75 | 66 | 88 | 230 | 83 | 90 |
normalized size | 1 | 1.55 | 1.6 | 1.4 | 1.87 | 4.89 | 1.77 | 1.91 |
time (sec) |
N/A |
0.105 |
0.013 |
0.004 |
1.417 |
1.842 |
0.233 |
1.069 |
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 21 | 44 | 53 | 62 | 70 | 55 |
normalized size | 1 | 1. | 1. | 2.1 | 2.52 | 2.95 | 3.33 | 2.62 |
time (sec) |
N/A |
0.009 |
0.004 |
0.005 |
0.931 |
1.813 |
0.271 |
1.076 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 14 | 18 | 35 | 12 | 18 |
normalized size | 1 | 1. | 1. | 0.82 | 1.06 | 2.06 | 0.71 | 1.06 |
time (sec) |
N/A |
0.004 |
0.001 |
0. |
0.924 |
2.002 |
0.08 |
1.091 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 29 | 34 | 45 | 68 | 32 | 51 |
normalized size | 1 | 1. | 0.72 | 0.85 | 1.12 | 1.7 | 0.8 | 1.27 |
time (sec) |
N/A |
0.024 |
0.012 |
0. |
1.402 |
2.045 |
0.321 |
1.075 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 8 | 9 | 16 | 5 | 9 |
normalized size | 1 | 1. | 1. | 1.14 | 1.29 | 2.29 | 0.71 | 1.29 |
time (sec) |
N/A |
0.001 |
0.001 |
0.002 |
0.925 |
2.021 |
0.071 |
1.084 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 9 | 11 | 22 | 5 | 11 |
normalized size | 1 | 1. | 1. | 1.12 | 1.38 | 2.75 | 0.62 | 1.38 |
time (sec) |
N/A |
0.044 |
0.013 |
0.023 |
0.931 |
1.956 |
0.082 |
1.076 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3 | 3 | 3 | 4 | 4 | 22 | 15 | 4 |
normalized size | 1 | 1. | 1. | 1.33 | 1.33 | 7.33 | 5. | 1.33 |
time (sec) |
N/A |
0.02 |
0.011 |
0.002 |
1.405 |
1.924 |
0.123 |
1.082 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 0 | 9 | 4 | 23 | 2 | 4 |
normalized size | 1 | 1. | 0. | 4.5 | 2. | 11.5 | 1. | 2. |
time (sec) |
N/A |
0.002 |
0.002 |
0. |
1.022 |
1.801 |
0.439 |
1.12 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 15 | 19 | 46 | 15 | 19 |
normalized size | 1 | 1. | 1. | 1.07 | 1.36 | 3.29 | 1.07 | 1.36 |
time (sec) |
N/A |
0.021 |
0.005 |
0.011 |
0.938 |
1.856 |
0.166 |
1.069 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 13 | 16 | 15 | 32 | 8 | 15 |
normalized size | 1 | 1. | 0.76 | 0.94 | 0.88 | 1.88 | 0.47 | 0.88 |
time (sec) |
N/A |
0.031 |
0.01 |
0.001 |
0.932 |
1.878 |
0.081 |
1.099 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 29 | 29 | 32 | 66 | 26 | 32 |
normalized size | 1 | 1. | 0.76 | 0.76 | 0.84 | 1.74 | 0.68 | 0.84 |
time (sec) |
N/A |
0.033 |
0.026 |
0.002 |
0.937 |
1.921 |
0.088 |
1.066 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 8 | 9 | 26 | 7 | 9 |
normalized size | 1 | 1. | 1. | 1.14 | 1.29 | 3.71 | 1. | 1.29 |
time (sec) |
N/A |
0.009 |
0.002 |
0. |
0.935 |
1.905 |
0.167 |
1.061 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 17 | 22 | 55 | 20 | 22 |
normalized size | 1 | 1. | 1. | 0.77 | 1. | 2.5 | 0.91 | 1. |
time (sec) |
N/A |
0.012 |
0.009 |
0. |
0.941 |
2.054 |
0.293 |
1.07 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 8 | 9 | 26 | 7 | 9 |
normalized size | 1 | 1. | 1. | 1.14 | 1.29 | 3.71 | 1. | 1.29 |
time (sec) |
N/A |
0.009 |
0.002 |
0. |
0.932 |
2.008 |
0.161 |
1.06 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 23 | 23 | 61 | 22 | 30 |
normalized size | 1 | 1. | 1. | 0.82 | 0.82 | 2.18 | 0.79 | 1.07 |
time (sec) |
N/A |
0.01 |
0.001 |
0.002 |
0.926 |
1.817 |
0.095 |
1.059 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 10 | 12 | 51 | 8 | 12 |
normalized size | 1 | 1. | 1. | 0.91 | 1.09 | 4.64 | 0.73 | 1.09 |
time (sec) |
N/A |
0.012 |
0.003 |
0.013 |
0.917 |
2.014 |
0.536 |
1.048 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3 | 3 | 3 | 4 | 4 | 22 | 15 | 4 |
normalized size | 1 | 1. | 1. | 1.33 | 1.33 | 7.33 | 5. | 1.33 |
time (sec) |
N/A |
0.019 |
0.008 |
0. |
1.417 |
1.798 |
0.124 |
1.04 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3 | 3 | 3 | 4 | 0 | 26 | 3 | 4 |
normalized size | 1 | 1. | 1. | 1.33 | 0. | 8.67 | 1. | 1.33 |
time (sec) |
N/A |
0.047 |
0.055 |
0.005 |
0. |
2.154 |
0.418 |
1.064 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 21 | 72 | 51 | 12 | 28 |
normalized size | 1 | 1. | 1. | 1.31 | 4.5 | 3.19 | 0.75 | 1.75 |
time (sec) |
N/A |
0.041 |
0.023 |
0.023 |
1.412 |
2.275 |
0.132 |
1.09 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
B |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 127 | 262 | 0 | 284 | 0 | 0 |
normalized size |
1 |
1. |
2.4 |
4.94 |
0. |
5.36 |
0. |
0. |
time (sec) |
N/A |
0.065 |
0.055 |
0.006 |
0. |
2.626 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 35 | 127 | 93 | 177 | 0 | 112 |
normalized size |
1 |
1. |
2.19 |
7.94 |
5.81 |
11.06 |
0. |
7. |
time (sec) |
N/A |
0.086 |
0.09 |
0.036 |
1.417 |
2.736 |
0. |
1.117 |
|
|
|
|
|
|
|
|
|
|
|
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 35 | 121 | 92 | 76 | 422 | 111 |
normalized size | 1 | 1. | 2.19 | 7.56 | 5.75 | 4.75 | 26.38 | 6.94 |
time (sec) |
N/A |
0.124 |
0.018 |
0.007 |
1.41 |
2.162 |
1.301 |
1.097 |
|
|
|
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Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 35 | 121 | 88 | 76 | 422 | 107 |
normalized size | 1 | 1. | 2.19 | 7.56 | 5.5 | 4.75 | 26.38 | 6.69 |
time (sec) |
N/A |
0.019 |
0.013 |
0.005 |
1.41 |
2.432 |
1.275 |
1.076 |
|
|
|
|
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Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 26 | 30 | 59 | 146 | 105 | 39 |
normalized size | 1 | 1. | 0.74 | 0.86 | 1.69 | 4.17 | 3. | 1.11 |
time (sec) |
N/A |
0.008 |
0.021 |
0. |
1.413 |
2.289 |
2.558 |
1.065 |
|
|
|
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Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 18 | 13 | 16 | 74 | 19 | 16 |
normalized size | 1 | 1. | 1.29 | 0.93 | 1.14 | 5.29 | 1.36 | 1.14 |
time (sec) |
N/A |
0.009 |
0.007 |
0.007 |
1.418 |
2.252 |
0.061 |
1.066 |
|
|
|
|
|
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Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 12 | 15 | 34 | 8 | 15 |
normalized size | 1 | 1. | 1. | 0.92 | 1.15 | 2.62 | 0.62 | 1.15 |
time (sec) |
N/A |
0.005 |
0.004 |
0.001 |
1.403 |
2.098 |
0.081 |
1.06 |
|
|
|
|
|
|
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|
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Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 7 | 7 | 7 | 7 | 8 | 15 | 5 | 8 |
normalized size | 1 | 1. | 1. | 1. | 1.14 | 2.14 | 0.71 | 1.14 |
time (sec) |
N/A |
0.03 |
0.004 |
0. |
0.989 |
2.099 |
0.08 |
1.055 |
|
|
|
|
|
|
|
|
|
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|
|
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|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 20 | 24 | 31 | 55 | 20 | 41 |
normalized size | 1 | 1. | 0.83 | 1. | 1.29 | 2.29 | 0.83 | 1.71 |
time (sec) |
N/A |
0.357 |
0.069 |
0.005 |
1.547 |
2.173 |
0.108 |
1.062 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 9 | 11 | 18 | 7 | 11 |
normalized size | 1 | 1. | 1. | 1. | 1.22 | 2. | 0.78 | 1.22 |
time (sec) |
N/A |
0.003 |
0.003 |
0. |
0.936 |
2.05 |
0.068 |
1.064 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 20 | 32 | 55 | 19 | 26 |
normalized size | 1 | 1. | 1. | 0.8 | 1.28 | 2.2 | 0.76 | 1.04 |
time (sec) |
N/A |
0.045 |
0.002 |
0.002 |
0.927 |
2.145 |
0.085 |
1.051 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 23 | 5 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 2.88 | 0.62 | 1. |
time (sec) |
N/A |
0.003 |
0.003 |
0.002 |
1.409 |
2.189 |
0.087 |
1.065 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 13 | 16 | 36 | 10 | 16 |
normalized size | 1 | 1. | 1. | 0.81 | 1. | 2.25 | 0.62 | 1. |
time (sec) |
N/A |
0.008 |
0.003 |
0.002 |
1.408 |
2.053 |
0.09 |
1.059 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 17 | 22 | 62 | 36 | 22 |
normalized size | 1 | 1. | 1. | 1.21 | 1.57 | 4.43 | 2.57 | 1.57 |
time (sec) |
N/A |
0.015 |
0.003 |
0.01 |
1.407 |
2.281 |
0.384 |
1.053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 26 | 30 | 59 | 146 | 105 | 39 |
normalized size | 1 | 1. | 0.74 | 0.86 | 1.69 | 4.17 | 3. | 1.11 |
time (sec) |
N/A |
0.011 |
0.003 |
0. |
1.413 |
2.105 |
2.556 |
1.062 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 32 | 16 | 20 | 103 | 34 | 28 |
normalized size | 1 | 1. | 1.88 | 0.94 | 1.18 | 6.06 | 2. | 1.65 |
time (sec) |
N/A |
0.005 |
0.007 |
0.004 |
1.41 |
2.169 |
0.526 |
1.071 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 14 | 14 | 15 | 46 | 15 | 15 |
normalized size | 1 | 1. | 0.74 | 0.74 | 0.79 | 2.42 | 0.79 | 0.79 |
time (sec) |
N/A |
0.008 |
0.014 |
0. |
0.928 |
2.231 |
0.28 |
1.046 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 3 | 3 | 11 | 2 | 4 |
normalized size | 1 | 1. | 1. | 1.5 | 1.5 | 5.5 | 1. | 2. |
time (sec) |
N/A |
0. |
0. |
0. |
0.93 |
2.241 |
0.05 |
1.057 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 73 | 31 | 346 | 271 | 0 | 45 |
normalized size | 1 | 1. | 1.62 | 0.69 | 7.69 | 6.02 | 0. | 1. |
time (sec) |
N/A |
0.123 |
0.181 |
0.142 |
1.78 |
2.618 |
0. |
1.104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 11 | 14 | 36 | 10 | 22 |
normalized size | 1 | 1. | 1. | 0.79 | 1. | 2.57 | 0.71 | 1.57 |
time (sec) |
N/A |
0.006 |
0.002 |
0.002 |
0.928 |
2.206 |
0.061 |
1.065 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 14 | 11 | 15 | 31 | 14 | 15 |
normalized size | 1 | 1. | 0.82 | 0.65 | 0.88 | 1.82 | 0.82 | 0.88 |
time (sec) |
N/A |
0.003 |
0.003 |
0.003 |
0.924 |
1.775 |
0.203 |
1.059 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 25 | 20 | 26 | 77 | 0 | 36 |
normalized size | 1 | 1. | 1.09 | 0.87 | 1.13 | 3.35 | 0. | 1.57 |
time (sec) |
N/A |
0.01 |
0.005 |
0.004 |
1.409 |
1.805 |
0. |
1.059 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 38 | 5 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 4.75 | 0.62 | 1. |
time (sec) |
N/A |
0.013 |
0.001 |
0.002 |
0.919 |
2.072 |
0.058 |
1.059 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 6 | 6 | 6 | 7 | 19 | 5 | 7 |
normalized size | 1 | 1. | 1. | 1. | 1.17 | 3.17 | 0.83 | 1.17 |
time (sec) |
N/A |
0.016 |
0.004 |
0. |
0.934 |
2.045 |
0.072 |
1.063 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 11 | 14 | 27 | 8 | 14 |
normalized size | 1 | 1. | 1. | 0.92 | 1.17 | 2.25 | 0.67 | 1.17 |
time (sec) |
N/A |
0.026 |
0.008 |
0.002 |
0.93 |
2.125 |
0.08 |
1.055 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 8 | 9 | 14 | 30 | 7 | 11 |
normalized size | 1 | 1. | 0.67 | 0.75 | 1.17 | 2.5 | 0.58 | 0.92 |
time (sec) |
N/A |
0.009 |
0.008 |
0. |
0.927 |
2.21 |
0.354 |
1.055 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 19 | 7 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 2.38 | 0.88 | 1. |
time (sec) |
N/A |
0.012 |
0.004 |
0. |
0.927 |
1.911 |
0.064 |
1.06 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 14 | 18 | 35 | 12 | 18 |
normalized size | 1 | 1. | 1. | 0.82 | 1.06 | 2.06 | 0.71 | 1.06 |
time (sec) |
N/A |
0.004 |
0.001 |
0. |
0.936 |
1.806 |
0.082 |
1.059 |
|
|
|
|
|
|
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|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 20 | 5 | 8 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 2.5 | 0.62 | 1. |
time (sec) |
N/A |
0.007 |
0.001 |
0. |
0.923 |
1.909 |
0.054 |
1.068 |
|
|
|
|
|
|
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|
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|
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|
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|
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|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 27 | 21 | 30 | 68 | 0 | 27 |
normalized size | 1 | 1. | 1.12 | 0.88 | 1.25 | 2.83 | 0. | 1.12 |
time (sec) |
N/A |
0.009 |
0.032 |
0.006 |
1.415 |
1.802 |
0. |
1.077 |
|
|
|
|
|
|
|
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|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 14 | 18 | 72 | 15 | 18 |
normalized size | 1 | 1. | 1. | 0.7 | 0.9 | 3.6 | 0.75 | 0.9 |
time (sec) |
N/A |
0.023 |
0.005 |
0. |
1.421 |
1.922 |
0.106 |
1.066 |
|
|
|
|
|
|
|
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|
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|
|
|
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|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
B |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 26 | 30 | 59 | 146 | 105 | 39 |
normalized size | 1 | 1. | 0.74 | 0.86 | 1.69 | 4.17 | 3. | 1.11 |
time (sec) |
N/A |
0.009 |
0.003 |
0. |
1.407 |
1.876 |
2.557 |
1.078 |
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 18 | 15 | 19 | 49 | 24 | 19 |
normalized size | 1 | 1. | 0.9 | 0.75 | 0.95 | 2.45 | 1.2 | 0.95 |
time (sec) |
N/A |
0.024 |
0.008 |
0.003 |
1.416 |
1.919 |
0.111 |
1.048 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 27 | 35 | 103 | 31 | 35 |
normalized size | 1 | 1. | 1. | 0.82 | 1.06 | 3.12 | 0.94 | 1.06 |
time (sec) |
N/A |
0.011 |
0.012 |
0. |
1.412 |
1.894 |
0.126 |
1.049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 21 | 20 | 26 | 55 | 15 | 26 |
normalized size | 1 | 1. | 1. | 0.95 | 1.24 | 2.62 | 0.71 | 1.24 |
time (sec) |
N/A |
0.016 |
0. |
0.002 |
0.932 |
1.74 |
0.052 |
1.046 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 25 | 32 | 74 | 19 | 31 |
normalized size | 1 | 1. | 1. | 0.96 | 1.23 | 2.85 | 0.73 | 1.19 |
time (sec) |
N/A |
0.019 |
0. |
0.002 |
0.936 |
1.789 |
0.062 |
1.053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 27 | 26 | 34 | 85 | 22 | 34 |
normalized size | 1 | 1. | 1. | 0.96 | 1.26 | 3.15 | 0.81 | 1.26 |
time (sec) |
N/A |
0.023 |
0. |
0. |
0.928 |
1.865 |
0.055 |
1.053 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 32 | 31 | 41 | 104 | 26 | 39 |
normalized size | 1 | 1. | 1. | 0.97 | 1.28 | 3.25 | 0.81 | 1.22 |
time (sec) |
N/A |
0.026 |
0. |
0.001 |
0.933 |
1.813 |
0.055 |
1.047 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 25 | 24 | 31 | 80 | 20 | 31 |
normalized size | 1 | 1. | 1.04 | 1. | 1.29 | 3.33 | 0.83 | 1.29 |
time (sec) |
N/A |
0.027 |
0. |
0. |
0.931 |
1.875 |
0.053 |
1.242 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 30 | 29 | 38 | 99 | 24 | 36 |
normalized size | 1 | 1. | 1.03 | 1. | 1.31 | 3.41 | 0.83 | 1.24 |
time (sec) |
N/A |
0.032 |
0. |
0. |
0.929 |
1.817 |
0.054 |
1.078 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 18 | 23 | 34 | 15 | 23 |
normalized size | 1 | 1. | 1. | 0.95 | 1.21 | 1.79 | 0.79 | 1.21 |
time (sec) |
N/A |
0.009 |
0. |
0. |
0.93 |
1.807 |
0.051 |
1.049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 24 | 23 | 30 | 42 | 19 | 28 |
normalized size | 1 | 1. | 1. | 0.96 | 1.25 | 1.75 | 0.79 | 1.17 |
time (sec) |
N/A |
0.011 |
0. |
0.002 |
0.937 |
1.817 |
0.053 |
1.05 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 24 | 31 | 85 | 22 | 31 |
normalized size | 1 | 1. | 1. | 0.96 | 1.24 | 3.4 | 0.88 | 1.24 |
time (sec) |
N/A |
0.013 |
0. |
0.002 |
0.931 |
1.881 |
0.053 |
1.06 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 30 | 29 | 38 | 101 | 26 | 36 |
normalized size | 1 | 1. | 1. | 0.97 | 1.27 | 3.37 | 0.87 | 1.2 |
time (sec) |
N/A |
0.015 |
0. |
0. |
0.929 |
1.706 |
0.055 |
1.07 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 28 | 27 | 35 | 53 | 24 | 34 |
normalized size | 1 | 1. | 1.04 | 1. | 1.3 | 1.96 | 0.89 | 1.26 |
time (sec) |
N/A |
0.006 |
0. |
0.001 |
0.926 |
1.812 |
0.054 |
1.057 |
|
|
|
|
|
|
|
|
|
|
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 [ 0.8571
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
3 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
2 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
3 |
A |
2 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
4 |
A |
1 |
1 |
1. |
2 |
0.5 |
|
|
|
|
|
|
|
5 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
6 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
7 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
8 |
A |
1 |
1 |
1. |
6 |
0.167 |
|
|
|
|
|
|
|
9 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
10 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
11 |
A |
1 |
1 |
1. |
6 |
0.167 |
|
|
|
|
|
|
|
12 |
A |
3 |
2 |
1. |
6 |
0.333 |
|
|
|
|
|
|
|
13 |
A |
4 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
14 |
A |
5 |
3 |
1. |
7 |
0.429 |
|
|
|
|
|
|
|
15 |
A |
3 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
16 |
A |
2 |
2 |
1. |
5 |
0.4 |
|
|
|
|
|
|
|
17 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
18 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
20 |
A |
1 |
1 |
1. |
5 |
0.2 |
|
|
|
|
|
|
|
|
21 |
A |
1 |
1 |
1. |
6 |
0.167 |
|
|
|
|
|
|
|
22 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
23 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
24 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
25 |
A |
3 |
3 |
1. |
7 |
0.429 |
|
|
|
|
|
|
|
26 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
27 |
A |
2 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
28 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
29 |
A |
1 |
1 |
1. |
5 |
0.2 |
|
|
|
|
|
|
|
30 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
31 |
A |
7 |
7 |
1. |
11 |
0.636 |
|
|
|
|
|
|
|
32 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
33 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
34 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
35 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
36 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
37 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
38 |
A |
6 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
39 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
40 |
A |
5 |
5 |
1. |
29 |
0.172 |
|
|
|
|
|
|
|
|
41 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
42 |
A |
6 |
6 |
1.16 |
19 |
0.316 |
|
|
|
|
|
|
|
43 |
A |
1 |
1 |
1. |
6 |
0.167 |
|
|
|
|
|
|
|
44 |
A |
2 |
2 |
1. |
5 |
0.4 |
|
|
|
|
|
|
|
45 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
46 |
A |
5 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
47 |
A |
1 |
1 |
1. |
5 |
0.2 |
|
|
|
|
|
|
|
48 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
49 |
A |
6 |
6 |
1. |
9 |
0.667 |
|
|
|
|
|
|
|
50 |
A |
10 |
6 |
1.55 |
7 |
0.857 |
|
|
|
|
|
|
|
51 |
A |
1 |
1 |
1. |
27 |
0.037 |
|
|
|
|
|
|
|
52 |
A |
1 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
53 |
A |
4 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
54 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
55 |
A |
7 |
4 |
1. |
9 |
0.444 |
|
|
|
|
|
|
|
56 |
A |
2 |
1 |
1. |
12 |
0.083 |
|
|
|
|
|
|
|
57 |
A |
1 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
58 |
A |
6 |
4 |
1. |
7 |
0.571 |
|
|
|
|
|
|
|
59 |
A |
4 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
60 |
A |
6 |
3 |
1. |
9 |
0.333 |
|
|
|
|
|
|
|
|
61 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
62 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
63 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
64 |
A |
2 |
2 |
1. |
6 |
0.333 |
|
|
|
|
|
|
|
65 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
66 |
A |
2 |
1 |
1. |
12 |
0.083 |
|
|
|
|
|
|
|
67 |
A |
2 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
68 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
69 |
A |
6 |
6 |
1. |
30 |
0.2 |
|
|
|
|
|
|
|
70 |
A |
5 |
5 |
1. |
39 |
0.128 |
|
|
|
|
|
|
|
71 |
A |
6 |
5 |
1. |
45 |
0.111 |
|
|
|
|
|
|
|
72 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
73 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
74 |
A |
3 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
75 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
76 |
A |
5 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
77 |
A |
10 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
78 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
79 |
A |
5 |
5 |
1. |
8 |
0.625 |
|
|
|
|
|
|
|
80 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
|
81 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
82 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
83 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
84 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
85 |
A |
1 |
1 |
1. |
6 |
0.167 |
|
|
|
|
|
|
|
86 |
A |
1 |
1 |
1. |
3 |
0.333 |
|
|
|
|
|
|
|
87 |
A |
4 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
88 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
89 |
A |
2 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
90 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
91 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
92 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
93 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
94 |
A |
1 |
1 |
1. |
8 |
0.125 |
|
|
|
|
|
|
|
95 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
96 |
A |
1 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
97 |
A |
2 |
2 |
1. |
5 |
0.4 |
|
|
|
|
|
|
|
98 |
A |
3 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
99 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
100 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
|
101 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
102 |
A |
3 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
103 |
A |
1 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
104 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
105 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
106 |
A |
1 |
1 |
1. |
31 |
0.032 |
|
|
|
|
|
|
|
107 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
108 |
A |
1 |
1 |
1. |
29 |
0.034 |
|
|
|
|
|
|
|
109 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
110 |
A |
1 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
111 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
112 |
A |
1 |
1 |
1. |
29 |
0.034 |
|
|
|
|
|
|
|
113 |
A |
1 |
1 |
1. |
27 |
0.037 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|