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 }
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, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 55, 56, 57, 61, 62, 63, 64,
65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93
}
B grade: { }
C grade: { }
F grade: { 52, 53, 54, 58, 59, 60, 70, 71, 72 }
2.1.3 Maple
A grade: { 1, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 34, 35, 42, 49, 50, 51,
55, 56, 57, 61, 62, 63, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92,
93 }
B grade: { 2, 3, 10, 11, 19, 46, 47, 48, 52, 53, 54, 58, 59, 60, 77, 78, 83 }
C grade: { }
F grade: { 25, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 43, 44, 45, 70, 71, 72 }
2.1.4 Maxima
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, 32,
33, 34, 35, 39, 40, 41, 42, 49, 50, 51, 55, 56, 57, 61, 62, 63, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79,
80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93 }
B grade: { }
C grade: { }
F grade: { 29, 30, 31, 36, 37, 38, 43, 44, 45, 46, 47, 48, 52, 53, 54, 58, 59, 60, 70, 71, 72 }
2.1.5 FriCAS
A grade: { 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 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, 48, 49, 50, 51, 55, 56, 57, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 78, 79, 80, 81, 83, 84, 85, 86, 87, 90, 91, 92, 93 }
B grade: { 19, 54, 60, 89 }
C grade: { 1, 2, 9, 10, 17, 18, 46, 47, 52, 53, 58, 59, 76, 77, 82, 88 }
F grade: { }
2.1.6 Sympy
A grade: { 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28, 32, 33, 34, 35, 39, 40, 41, 42,
49, 50, 55, 56, 57, 61, 64, 65, 66, 67, 68, 69, 79, 80, 81, 84, 85, 86, 87, 90, 92, 93 }
B grade: { 91 }
C grade: { }
F grade: { 1, 2, 3, 9, 10, 11, 17, 18, 19, 29, 30, 31, 36, 37, 38, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 58, 59,
60, 62, 63, 70, 71, 72, 73, 74, 75, 76, 77, 78, 82, 83, 88, 89 }
2.1.7 Giac
A grade: { 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 28, 35, 42, 49, 50, 51, 55, 56, 57, 61, 62, 63,
67, 68, 69, 73, 74, 75, 79, 80, 81, 85, 86, 87, 91, 92, 93 }
B grade: { 64, 65, 66 }
C grade: { 25, 26, 27, 33, 34, 40, 41 }
F grade: { 1, 2, 3, 9, 10, 11, 17, 18, 19, 29, 30, 31, 32, 36, 37, 38, 39, 43, 44, 45, 46, 47, 48, 52, 53, 54, 58,
59, 60, 70, 71, 72, 76, 77, 78, 82, 83, 84, 88, 89, 90 }
2.1.8 Mupad
A grade: { 5, 6, 13, 14, 21, 22, 50, 51, 56, 57, 62, 63, 67, 68, 69, 73, 74, 75, 80, 81, 86, 87, 92, 93
}
B grade: { 4, 7, 8, 12, 15, 16, 20, 23, 24, 25, 26, 27, 28, 32, 33, 34, 35, 39, 40, 41, 42, 49, 55, 61, 79, 84, 85,
90, 91 }
C grade: { }
F grade: { 1, 2, 3, 9, 10, 11, 17, 18, 19, 29, 30, 31, 36, 37, 38, 43, 44, 45, 46, 47, 48, 52, 53, 54, 58, 59, 60,
64, 65, 66, 70, 71, 72, 76, 77, 78, 82, 83, 88, 89 }
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 |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 112 | 191 | 94 | 120 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 1.74 | 0.85 | 1.09 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.189 |
0.012 |
0.021 |
0.978 |
0.435 |
0.000 |
0.000 |
0.000 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 83 | 166 | 72 | 100 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.98 | 0.86 | 1.19 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.168 |
0.007 |
0.019 |
0.968 |
0.420 |
0.000 |
0.000 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 53 | 133 | 48 | 72 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 2.29 | 0.83 | 1.24 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.099 |
0.003 |
0.018 |
0.969 |
0.455 |
0.000 |
0.000 |
0.000 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 35 | 32 | 24 | 17 | 31 | 24 |
normalized size | 1 | 1.00 | 1.00 | 1.35 | 1.23 | 0.92 | 0.65 | 1.19 | 0.92 |
time (sec) |
N/A |
0.018 |
0.004 |
0.010 |
0.903 |
0.446 |
0.123 |
0.330 |
3.497 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.048 |
0.045 |
0.053 |
0.000 |
0.442 |
0.000 |
0.000 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.045 |
0.131 |
0.047 |
0.000 |
0.458 |
0.000 |
0.000 |
0.000 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 21 | 37 | 34 | 23 | 17 | 33 | 23 |
normalized size | 1 | 1.00 | 0.81 | 1.42 | 1.31 | 0.88 | 0.65 | 1.27 | 0.88 |
time (sec) |
N/A |
0.021 |
0.017 |
0.010 |
0.884 |
0.431 |
0.127 |
0.337 |
3.474 |
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Problem 8 |
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 | 28 | 28 | 19 | 41 | 34 | 25 | 19 | 33 | 25 |
normalized size | 1 | 1.00 | 0.68 | 1.46 | 1.21 | 0.89 | 0.68 | 1.18 | 0.89 |
time (sec) |
N/A |
0.023 |
0.016 |
0.010 |
0.881 |
0.428 |
0.132 |
0.378 |
0.048 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 158 | 382 | 195 | 330 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 1.76 | 0.90 | 1.52 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.507 |
0.243 |
0.141 |
1.030 |
0.462 |
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 |
B |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 113 | 324 | 149 | 263 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.68 | 1.96 | 0.90 | 1.59 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.399 |
0.244 |
0.114 |
1.022 |
0.478 |
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 |
B |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 85 | 231 | 95 | 176 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.79 | 2.16 | 0.89 | 1.64 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.201 |
0.118 |
0.030 |
1.008 |
0.429 |
0.000 |
0.000 |
0.000 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 40 | 54 | 51 | 60 | 39 | 51 | 66 |
normalized size | 1 | 1.00 | 0.87 | 1.17 | 1.11 | 1.30 | 0.85 | 1.11 | 1.43 |
time (sec) |
N/A |
0.033 |
0.039 |
0.012 |
1.006 |
0.442 |
0.149 |
0.440 |
3.559 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.047 |
0.816 |
0.158 |
0.000 |
0.417 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.044 |
0.636 |
0.174 |
0.000 |
0.442 |
0.000 |
0.000 |
0.000 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 42 | 58 | 55 | 65 | 39 | 54 | 68 |
normalized size | 1 | 1.00 | 0.88 | 1.21 | 1.15 | 1.35 | 0.81 | 1.12 | 1.42 |
time (sec) |
N/A |
0.034 |
0.055 |
0.013 |
1.093 |
0.426 |
0.158 |
0.239 |
0.163 |
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Problem 16 |
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 | 52 | 52 | 35 | 64 | 57 | 73 | 42 | 58 | 76 |
normalized size | 1 | 1.00 | 0.67 | 1.23 | 1.10 | 1.40 | 0.81 | 1.12 | 1.46 |
time (sec) |
N/A |
0.035 |
0.058 |
0.011 |
0.953 |
0.486 |
0.168 |
0.225 |
3.499 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 333 | 333 | 241 | 548 | 303 | 702 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.72 | 1.65 | 0.91 | 2.11 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.078 |
0.254 |
0.167 |
1.084 |
0.447 |
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 |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 203 | 385 | 234 | 521 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 1.58 | 0.96 | 2.14 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.764 |
0.190 |
0.139 |
1.064 |
0.412 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
|
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|
|
Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 159 | 159 | 120 | 393 | 149 | 338 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.75 | 2.47 | 0.94 | 2.13 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.332 |
0.148 |
0.038 |
1.055 |
0.468 |
0.000 |
0.000 |
0.000 |
|
|
|
|
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|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 62 | 74 | 84 | 127 | 76 | 65 | 121 |
normalized size | 1 | 1.00 | 0.90 | 1.07 | 1.22 | 1.84 | 1.10 | 0.94 | 1.75 |
time (sec) |
N/A |
0.042 |
0.062 |
0.012 |
0.913 |
0.432 |
0.188 |
0.217 |
3.745 |
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.045 |
1.004 |
0.187 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.044 |
0.777 |
0.201 |
0.000 |
0.458 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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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 | 72 | 72 | 62 | 79 | 88 | 132 | 78 | 71 | 124 |
normalized size | 1 | 1.00 | 0.86 | 1.10 | 1.22 | 1.83 | 1.08 | 0.99 | 1.72 |
time (sec) |
N/A |
0.044 |
0.093 |
0.014 |
0.900 |
0.435 |
0.199 |
0.207 |
3.651 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 78 | 78 | 54 | 87 | 92 | 140 | 85 | 75 | 132 |
normalized size | 1 | 1.00 | 0.69 | 1.12 | 1.18 | 1.79 | 1.09 | 0.96 | 1.69 |
time (sec) |
N/A |
0.047 |
0.096 |
0.013 |
0.875 |
0.420 |
0.205 |
0.185 |
3.700 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 153 | 153 | 130 | 0 | 294 | 267 | 332 | 5732 | 225 |
normalized size | 1 | 1.00 | 0.85 | 0.00 | 1.92 | 1.75 | 2.17 | 37.46 | 1.47 |
time (sec) |
N/A |
0.238 |
0.278 |
0.079 |
1.351 |
0.452 |
0.278 |
0.576 |
3.815 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 91 | 199 | 178 | 166 | 196 | 2726 | 135 |
normalized size | 1 | 1.00 | 0.79 | 1.73 | 1.55 | 1.44 | 1.70 | 23.70 | 1.17 |
time (sec) |
N/A |
0.154 |
0.169 |
0.050 |
1.256 |
0.457 |
0.220 |
0.442 |
3.672 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 73 | 105 | 88 | 87 | 94 | 1117 | 72 |
normalized size | 1 | 1.00 | 0.95 | 1.36 | 1.14 | 1.13 | 1.22 | 14.51 | 0.94 |
time (sec) |
N/A |
0.076 |
0.167 |
0.038 |
1.078 |
0.495 |
0.170 |
0.374 |
3.595 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 30 | 30 | 30 | 31 | 31 | 37 | 32 | 32 | 31 |
normalized size | 1 | 1.00 | 1.00 | 1.03 | 1.03 | 1.23 | 1.07 | 1.07 | 1.03 |
time (sec) |
N/A |
0.016 |
0.026 |
0.004 |
0.927 |
0.469 |
0.125 |
0.201 |
3.604 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 56 | 0 | 0 | 50 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.74 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.134 |
0.150 |
0.079 |
0.000 |
0.445 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 78 | 0 | 0 | 87 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.174 |
0.278 |
0.077 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 111 | 0 | 0 | 160 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.240 |
0.333 |
0.075 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 322 | 239 | 0 | 604 | 482 | 709 | 0 | 438 |
normalized size | 1 | 1.00 | 0.74 | 0.00 | 1.88 | 1.50 | 2.20 | 0.00 | 1.36 |
time (sec) |
N/A |
0.486 |
0.558 |
0.095 |
1.885 |
0.429 |
0.476 |
0.000 |
3.970 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 239 | 239 | 171 | 0 | 368 | 287 | 439 | 5699 | 267 |
normalized size | 1 | 1.00 | 0.72 | 0.00 | 1.54 | 1.20 | 1.84 | 23.85 | 1.12 |
time (sec) |
N/A |
0.320 |
0.370 |
0.083 |
1.612 |
0.430 |
0.368 |
1.232 |
3.816 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 156 | 117 | 220 | 187 | 139 | 233 | 2312 | 146 |
normalized size | 1 | 1.00 | 0.75 | 1.41 | 1.20 | 0.89 | 1.49 | 14.82 | 0.94 |
time (sec) |
N/A |
0.157 |
0.263 |
0.056 |
1.245 |
0.436 |
0.272 |
0.981 |
3.669 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 67 | 67 | 52 | 90 | 75 | 61 | 94 | 77 | 75 |
normalized size | 1 | 1.00 | 0.78 | 1.34 | 1.12 | 0.91 | 1.40 | 1.15 | 1.12 |
time (sec) |
N/A |
0.037 |
0.038 |
0.022 |
1.194 |
0.429 |
0.177 |
0.489 |
3.719 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 108 | 0 | 0 | 95 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.71 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.254 |
0.315 |
0.088 |
0.000 |
0.424 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 136 | 0 | 0 | 171 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.85 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.341 |
0.685 |
0.077 |
0.000 |
0.418 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 286 | 286 | 217 | 0 | 0 | 314 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.475 |
0.730 |
0.076 |
0.000 |
0.463 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 496 | 341 | 0 | 914 | 708 | 1074 | 0 | 652 |
normalized size | 1 | 1.00 | 0.69 | 0.00 | 1.84 | 1.43 | 2.17 | 0.00 | 1.31 |
time (sec) |
N/A |
0.705 |
0.743 |
0.093 |
2.369 |
0.432 |
0.653 |
0.000 |
4.372 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 366 | 366 | 248 | 0 | 558 | 414 | 653 | 8854 | 399 |
normalized size | 1 | 1.00 | 0.68 | 0.00 | 1.52 | 1.13 | 1.78 | 24.19 | 1.09 |
time (sec) |
N/A |
0.464 |
0.530 |
0.088 |
1.814 |
0.441 |
0.479 |
1.662 |
3.993 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
C |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 236 | 236 | 161 | 0 | 284 | 192 | 350 | 3572 | 219 |
normalized size | 1 | 1.00 | 0.68 | 0.00 | 1.20 | 0.81 | 1.48 | 15.14 | 0.93 |
time (sec) |
N/A |
0.239 |
0.375 |
0.033 |
1.421 |
0.433 |
0.340 |
1.330 |
3.765 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 103 | 103 | 74 | 124 | 115 | 84 | 153 | 102 | 124 |
normalized size | 1 | 1.00 | 0.72 | 1.20 | 1.12 | 0.82 | 1.49 | 0.99 | 1.20 |
time (sec) |
N/A |
0.049 |
0.050 |
0.014 |
1.562 |
0.433 |
0.209 |
0.435 |
3.775 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 160 | 0 | 0 | 140 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.354 |
0.498 |
0.080 |
0.000 |
0.443 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 305 | 305 | 250 | 0 | 0 | 259 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.85 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.491 |
1.325 |
0.077 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 447 | 447 | 325 | 0 | 0 | 475 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.695 |
1.059 |
0.078 |
0.000 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 192 | 192 | 166 | 3075 | 0 | 413 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 16.02 | 0.00 | 2.15 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.326 |
0.112 |
0.091 |
0.000 |
0.437 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 121 | 1677 | 0 | 271 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.83 | 11.57 | 0.00 | 1.87 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.276 |
0.035 |
0.114 |
0.000 |
0.414 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 74 | 679 | 0 | 147 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.76 | 6.93 | 0.00 | 1.50 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.157 |
0.012 |
0.092 |
0.000 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 40 | 40 | 40 | 65 | 66 | 44 | 27 | 74 | 44 |
normalized size | 1 | 1.00 | 1.00 | 1.62 | 1.65 | 1.10 | 0.68 | 1.85 | 1.10 |
time (sec) |
N/A |
0.030 |
0.008 |
0.020 |
1.144 |
0.433 |
0.155 |
0.349 |
3.449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.137 |
0.134 |
0.132 |
0.000 |
0.412 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.128 |
0.385 |
0.155 |
0.000 |
0.427 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 388 | 388 | 0 | 3319 | 0 | 1390 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 8.55 | 0.00 | 3.58 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.867 |
1.814 |
0.085 |
0.000 |
0.462 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 0 | 1650 | 0 | 834 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 5.61 | 0.00 | 2.84 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.671 |
1.183 |
0.077 |
0.000 |
0.440 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 191 | 191 | 0 | 591 | 0 | 400 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 3.09 | 0.00 | 2.09 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.340 |
1.131 |
0.112 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
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 | 74 | 74 | 62 | 99 | 100 | 100 | 66 | 111 | 80 |
normalized size | 1 | 1.00 | 0.84 | 1.34 | 1.35 | 1.35 | 0.89 | 1.50 | 1.08 |
time (sec) |
N/A |
0.049 |
0.061 |
0.022 |
1.190 |
0.423 |
0.190 |
0.415 |
3.445 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.127 |
1.015 |
0.589 |
0.000 |
0.423 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.120 |
1.052 |
0.446 |
0.000 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 594 | 594 | 0 | 4005 | 0 | 2704 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 6.74 | 0.00 | 4.55 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.901 |
1.814 |
0.095 |
0.000 |
0.496 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
C |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 439 | 439 | 0 | 1887 | 0 | 1518 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 4.30 | 0.00 | 3.46 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
1.319 |
1.371 |
0.081 |
0.000 |
0.478 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 276 | 276 | 0 | 668 | 0 | 696 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 2.42 | 0.00 | 2.52 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.564 |
0.977 |
0.069 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
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 | 111 | 111 | 84 | 134 | 145 | 190 | 116 | 136 | 142 |
normalized size | 1 | 1.00 | 0.76 | 1.21 | 1.31 | 1.71 | 1.05 | 1.23 | 1.28 |
time (sec) |
N/A |
0.063 |
0.107 |
0.021 |
1.216 |
0.424 |
0.241 |
0.382 |
3.502 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.128 |
1.867 |
0.439 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.121 |
1.490 |
0.712 |
0.000 |
0.433 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 71 | 77 | 82 | 70 | 85 | 132 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 1.15 | 0.99 | 1.20 | 1.86 | -0.01 |
time (sec) |
N/A |
0.088 |
0.102 |
0.018 |
1.173 |
0.434 |
2.135 |
0.337 |
0.000 |
|
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 134 | 144 | 160 | 133 | 184 | 250 | -1 |
normalized size | 1 | 1.00 | 0.92 | 0.99 | 1.10 | 0.92 | 1.27 | 1.72 | -0.01 |
time (sec) |
N/A |
0.185 |
0.324 |
0.017 |
2.485 |
0.425 |
3.213 |
0.418 |
0.000 |
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 196 | 211 | 238 | 196 | 291 | 368 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.94 | 1.06 | 0.88 | 1.30 | 1.64 | -0.00 |
time (sec) |
N/A |
0.264 |
0.797 |
0.018 |
2.415 |
0.419 |
4.360 |
0.527 |
0.000 |
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.040 |
0.683 |
0.088 |
0.000 |
0.420 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.040 |
1.265 |
0.088 |
0.000 |
0.420 |
0.000 |
0.000 |
0.000 |
|
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.039 |
2.365 |
0.099 |
0.000 |
0.442 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
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|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 340 | 340 | 0 | 0 | 0 | 270 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.467 |
0.336 |
0.080 |
0.000 |
0.448 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
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|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 0 | 0 | 0 | 191 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.278 |
0.215 |
0.081 |
0.000 |
0.450 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
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|
|
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|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 0 | 0 | 0 | 111 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.135 |
0.123 |
0.079 |
0.000 |
0.442 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.123 |
0.108 |
0.098 |
0.000 |
0.425 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.120 |
0.137 |
0.463 |
0.000 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A |
0.119 |
0.287 |
0.209 |
0.000 |
0.441 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 115 | 225 | 133 | 134 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.96 | 1.16 | 1.17 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.132 |
0.013 |
0.072 |
0.482 |
0.441 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 85 | 194 | 107 | 108 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.28 | 1.26 | 1.27 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.109 |
0.009 |
0.064 |
0.485 |
0.434 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 154 | 79 | 75 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.85 | 1.46 | 1.39 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.064 |
0.006 |
0.061 |
0.481 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 | 23 | 23 | 23 | 24 | 23 | 23 | 17 | 24 | 23 |
normalized size | 1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.00 | 0.74 | 1.04 | 1.00 |
time (sec) |
N/A |
0.037 |
0.007 |
0.004 |
0.429 |
0.418 |
0.138 |
0.421 |
3.429 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.070 |
0.086 |
0.083 |
0.000 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.069 |
0.068 |
0.080 |
0.000 |
0.428 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 137 | 274 | 134 | 246 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.96 | 0.96 | 1.76 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.248 |
0.161 |
0.053 |
0.524 |
0.423 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 103 | 231 | 106 | 186 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 2.16 | 0.99 | 1.74 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.181 |
0.093 |
0.049 |
0.498 |
0.417 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 54 | 67 | 72 | 74 | 58 | 0 | 63 |
normalized size | 1 | 1.00 | 0.78 | 0.97 | 1.04 | 1.07 | 0.84 | 0.00 | 0.91 |
time (sec) |
N/A |
0.074 |
0.071 |
0.025 |
0.470 |
0.416 |
0.183 |
0.000 |
3.623 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
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 | 25 | 25 | 25 | 26 | 25 | 25 | 26 | 26 | 31 |
normalized size | 1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.00 | 1.04 | 1.04 | 1.24 |
time (sec) |
N/A |
0.035 |
0.021 |
0.002 |
0.429 |
0.428 |
0.123 |
0.316 |
3.463 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.118 |
0.131 |
0.086 |
0.000 |
0.434 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 61 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.118 |
0.161 |
0.088 |
0.000 |
0.432 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
C |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 220 | 501 | 263 | 577 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 1.92 | 1.01 | 2.21 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.504 |
0.323 |
0.083 |
0.525 |
0.465 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 177 | 304 | 214 | 379 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 1.67 | 1.18 | 2.08 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.291 |
0.166 |
0.076 |
0.510 |
0.423 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 98 | 127 | 150 | 148 | 122 | 0 | 155 |
normalized size | 1 | 1.00 | 0.92 | 1.20 | 1.42 | 1.40 | 1.15 | 0.00 | 1.46 |
time (sec) |
N/A |
0.089 |
0.091 |
0.033 |
0.482 |
0.429 |
0.226 |
0.000 |
3.753 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 27 | 26 | 25 | 46 | 53 | 26 | 25 |
normalized size | 1 | 1.00 | 1.00 | 0.96 | 0.93 | 1.70 | 1.96 | 0.96 | 0.93 |
time (sec) |
N/A |
0.035 |
0.027 |
0.004 |
0.429 |
0.407 |
0.153 |
0.325 |
3.633 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.116 |
0.736 |
0.220 |
0.000 |
0.421 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.113 |
0.776 |
0.253 |
0.000 |
0.402 |
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 [19] had the largest ratio of
[.7333]
|
|
|
|
|
|
|
| Table 2.1:Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
6 |
6 |
1.00 |
17 |
0.353 |
|
|
|
|
|
|
|
2 |
A |
5 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
3 |
A |
4 |
4 |
1.00 |
15 |
0.267 |
|
|
|
|
|
|
|
4 |
A |
4 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
5 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
6 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
7 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
8 |
A |
4 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
9 |
A |
13 |
8 |
1.00 |
17 |
0.471 |
|
|
|
|
|
|
|
10 |
A |
11 |
9 |
1.00 |
17 |
0.529 |
|
|
|
|
|
|
|
11 |
A |
10 |
10 |
1.00 |
15 |
0.667 |
|
|
|
|
|
|
|
12 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
13 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
15 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
16 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
17 |
A |
26 |
10 |
1.00 |
17 |
0.588 |
|
|
|
|
|
|
|
18 |
A |
23 |
12 |
1.00 |
17 |
0.706 |
|
|
|
|
|
|
|
19 |
A |
15 |
11 |
1.00 |
15 |
0.733 |
|
|
|
|
|
|
|
20 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
21 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
22 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
23 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
24 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
|
|
|
|
|
|
|
25 |
A |
6 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
26 |
A |
5 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
27 |
A |
4 |
3 |
1.00 |
21 |
0.143 |
|
|
|
|
|
|
|
28 |
A |
2 |
1 |
1.00 |
15 |
0.067 |
|
|
|
|
|
|
|
29 |
A |
4 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
30 |
A |
5 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
31 |
A |
6 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
32 |
A |
10 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
33 |
A |
8 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
34 |
A |
6 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
35 |
A |
4 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
36 |
A |
6 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
37 |
A |
8 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
38 |
A |
10 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
39 |
A |
14 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
40 |
A |
11 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
41 |
A |
8 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
42 |
A |
4 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
43 |
A |
8 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
44 |
A |
11 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
45 |
A |
14 |
4 |
1.00 |
25 |
0.160 |
|
|
|
|
|
|
|
46 |
A |
6 |
6 |
1.00 |
25 |
0.240 |
|
|
|
|
|
|
|
47 |
A |
5 |
5 |
1.00 |
25 |
0.200 |
|
|
|
|
|
|
|
48 |
A |
4 |
4 |
1.00 |
23 |
0.174 |
|
|
|
|
|
|
|
49 |
A |
5 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
51 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
52 |
A |
13 |
8 |
1.00 |
25 |
0.320 |
|
|
|
|
|
|
|
53 |
A |
11 |
9 |
1.00 |
25 |
0.360 |
|
|
|
|
|
|
|
54 |
A |
11 |
11 |
1.00 |
23 |
0.478 |
|
|
|
|
|
|
|
55 |
A |
4 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
56 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
57 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
58 |
A |
26 |
10 |
1.00 |
25 |
0.400 |
|
|
|
|
|
|
|
59 |
A |
24 |
13 |
1.00 |
25 |
0.520 |
|
|
|
|
|
|
|
60 |
A |
17 |
12 |
1.00 |
23 |
0.522 |
|
|
|
|
|
|
|
61 |
A |
4 |
3 |
1.00 |
17 |
0.176 |
|
|
|
|
|
|
|
62 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
63 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
64 |
A |
5 |
4 |
1.00 |
17 |
0.235 |
|
|
|
|
|
|
|
65 |
A |
8 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
66 |
A |
11 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
67 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
68 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
69 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
70 |
A |
8 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
71 |
A |
6 |
3 |
1.00 |
25 |
0.120 |
|
|
|
|
|
|
|
72 |
A |
4 |
3 |
1.00 |
23 |
0.130 |
|
|
|
|
|
|
|
73 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
74 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
75 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
76 |
A |
5 |
5 |
1.00 |
24 |
0.208 |
|
|
|
|
|
|
|
77 |
A |
4 |
4 |
1.00 |
24 |
0.167 |
|
|
|
|
|
|
|
78 |
A |
3 |
3 |
1.00 |
22 |
0.136 |
|
|
|
|
|
|
|
79 |
A |
2 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
80 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
81 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
82 |
A |
6 |
6 |
1.00 |
24 |
0.250 |
|
|
|
|
|
|
|
83 |
A |
5 |
5 |
1.00 |
24 |
0.208 |
|
|
|
|
|
|
|
84 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
85 |
A |
2 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
86 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
87 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
88 |
A |
12 |
9 |
1.00 |
24 |
0.375 |
|
|
|
|
|
|
|
89 |
A |
11 |
10 |
1.00 |
24 |
0.417 |
|
|
|
|
|
|
|
90 |
A |
4 |
3 |
1.00 |
22 |
0.136 |
|
|
|
|
|
|
|
91 |
A |
2 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
92 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
93 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|