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
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 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 }
B grade: { 3, 24, 53 }
C grade: { 101, 102 }
F grade: { 37 }
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, 27, 28, 29, 30, 31, 32,
33, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 56, 57, 61, 67, 72, 74, 75, 77, 79, 83, 84, 85, 86, 87,
91, 92, 95, 100 }
B grade: { 35, 36, 93, 94, 98, 99 }
C grade: { 26, 39, 55, 58, 59, 60, 62, 63, 82, 88, 89, 90 }
F grade: { 24, 25, 37, 38, 53, 54, 64, 65, 66, 68, 69, 70, 71, 73, 76, 78, 80, 81, 96, 97, 101, 102
}
2.1.4 Maxima
A grade: { 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 27, 28, 29, 30, 31, 32, 33, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 51, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77,
79, 83, 84, 85, 86, 87, 91, 92, 93, 94, 98, 99, 100 }
B grade: { 1, 2, 4, 17, 22, 88, 89, 90, 95 }
C grade: { 34, 35, 36, 50, 52 }
F grade: { 24, 25, 26, 37, 38, 39, 53, 54, 55, 76, 78, 80, 81, 82, 96, 97, 101, 102 }
2.1.5 FriCAS
A grade: { 1, 3, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 40, 42, 44, 46, 47, 48, 50, 52, 56, 57, 67, 72, 74, 75, 77, 79, 83, 87, 88, 90, 91, 92, 93, 94, 95, 98, 99, 100
}
B grade: { 2, 6, 9, 13, 16, 20, 22, 41, 43, 45, 49, 51, 61, 84, 85, 86, 89, 96, 97, 101, 102 }
C grade: { }
F grade: { 37, 38, 39, 53, 54, 55, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 76, 78, 80, 81, 82
}
2.1.6 Sympy
A grade: { 1, 3, 8, 10, 15, 17, 22, 23, 27, 28, 32, 33, 34, 35, 36, 40, 48, 50, 52, 56, 57, 74, 75, 77, 83, 91, 92,
93, 94, 95, 100 }
B grade: { }
C grade: { }
F grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 24, 25, 26, 29, 30, 31, 37, 38, 39, 41, 42, 43, 44,
45, 46, 47, 49, 51, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 79, 80, 81,
82, 84, 85, 86, 87, 88, 89, 90, 96, 97, 98, 99, 101, 102 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 9, 11, 12, 16, 17, 18, 19, 22, 23, 27, 28, 40, 50, 56, 57, 74, 75, 77, 79, 83, 87, 91, 92,
95, 100 }
B grade: { 7, 8, 10, 14, 15, 21, 29, 30, 31, 32, 33, 34, 35, 36, 42, 44, 48, 93, 94, 98, 99 }
C grade: { 88, 89, 90 }
F grade: { 6, 13, 20, 24, 25, 26, 37, 38, 39, 41, 43, 45, 46, 47, 49, 51, 52, 53, 54, 55, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 80, 81, 82, 84, 85, 86, 96, 97, 101, 102
}
2.1.8 Mupad
A grade: { 23, 27, 40, 56, 74, 75, 77, 79, 83, 91, 92 }
B grade: { 1, 3, 8, 10, 15, 17, 22, 28, 33, 34, 35, 36, 48, 50, 52, 57, 95, 100 }
C grade: { }
F grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 18, 19, 20, 21, 24, 25, 26, 29, 30, 31, 32, 37, 38, 39, 41, 42, 43,
44, 45, 46, 47, 49, 51, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 78, 80, 81,
82, 84, 85, 86, 87, 88, 89, 90, 93, 94, 96, 97, 98, 99, 101, 102 }
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 |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 31 | 45 | 81 | 29 | 36 | 47 | 28 |
normalized size | 1 | 1.00 | 0.91 | 1.32 | 2.38 | 0.85 | 1.06 | 1.38 | 0.82 |
time (sec) |
N/A |
0.036 |
0.034 |
0.017 |
0.307 |
0.504 |
0.804 |
0.258 |
0.088 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 67 | 74 | 110 | 190 | 0 | 75 | -1 |
normalized size | 1 | 1.00 | 0.97 | 1.07 | 1.59 | 2.75 | 0.00 | 1.09 | -0.01 |
time (sec) |
N/A |
0.041 |
0.068 |
0.075 |
0.305 |
0.516 |
0.000 |
0.358 |
0.000 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
A |
A |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 31 | 14 | 13 | 13 | 19 | 25 | 13 |
normalized size | 1 | 1.00 | 2.07 | 0.93 | 0.87 | 0.87 | 1.27 | 1.67 | 0.87 |
time (sec) |
N/A |
0.016 |
0.010 |
0.004 |
0.300 |
0.722 |
0.214 |
0.389 |
0.374 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 45 | 40 | 86 | 48 | 0 | 41 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.75 | 1.62 | 0.91 | 0.00 | 0.77 | -0.02 |
time (sec) |
N/A |
0.018 |
0.036 |
0.030 |
0.302 |
0.462 |
0.000 |
0.302 |
0.000 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 23 | 27 | 24 | 39 | 0 | 24 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.08 | 0.96 | 1.56 | 0.00 | 0.96 | -0.04 |
time (sec) |
N/A |
0.035 |
0.014 |
0.020 |
0.373 |
0.484 |
0.000 |
0.311 |
0.000 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 70 | 70 | 54 | 184 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 1.06 | 0.82 | 2.79 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.035 |
0.062 |
0.032 |
0.319 |
0.480 |
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 |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 38 | 58 | 39 | 71 | 0 | 109 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.38 | 0.93 | 1.69 | 0.00 | 2.60 | -0.02 |
time (sec) |
N/A |
0.092 |
0.042 |
0.022 |
0.427 |
0.459 |
0.000 |
0.643 |
0.000 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 42 | 55 | 59 | 56 | 78 | 117 | 42 |
normalized size | 1 | 1.00 | 0.82 | 1.08 | 1.16 | 1.10 | 1.53 | 2.29 | 0.82 |
time (sec) |
N/A |
0.050 |
0.104 |
0.055 |
0.329 |
0.480 |
1.550 |
0.545 |
0.103 |
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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 |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 101 | 90 | 95 | 427 | 0 | 97 | -1 |
normalized size | 1 | 1.00 | 1.02 | 0.91 | 0.96 | 4.31 | 0.00 | 0.98 | -0.01 |
time (sec) |
N/A |
0.096 |
0.216 |
0.089 |
0.430 |
0.444 |
0.000 |
0.909 |
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 |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 27 | 34 | 38 | 29 | 60 | 56 | 22 |
normalized size | 1 | 1.00 | 0.87 | 1.10 | 1.23 | 0.94 | 1.94 | 1.81 | 0.71 |
time (sec) |
N/A |
0.027 |
0.023 |
0.013 |
0.333 |
0.522 |
0.438 |
0.791 |
0.379 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 86 | 51 | 56 | 73 | 0 | 58 | -1 |
normalized size | 1 | 1.00 | 1.10 | 0.65 | 0.72 | 0.94 | 0.00 | 0.74 | -0.01 |
time (sec) |
N/A |
0.046 |
0.070 |
0.052 |
0.429 |
0.445 |
0.000 |
0.563 |
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 |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 33 | 34 | 31 | 49 | 0 | 35 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.92 | 0.84 | 1.32 | 0.00 | 0.95 | -0.03 |
time (sec) |
N/A |
0.059 |
0.020 |
0.055 |
0.412 |
0.412 |
0.000 |
0.344 |
0.000 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 94 | 86 | 61 | 396 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.07 | 0.98 | 0.69 | 4.50 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.223 |
0.069 |
0.381 |
0.500 |
0.000 |
0.000 |
0.000 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 46 | 69 | 36 | 90 | 0 | 126 | -1 |
normalized size | 1 | 1.00 | 0.81 | 1.21 | 0.63 | 1.58 | 0.00 | 2.21 | -0.02 |
time (sec) |
N/A |
0.121 |
0.090 |
0.057 |
0.378 |
0.458 |
0.000 |
0.160 |
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 |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 58 | 93 | 100 | 94 | 92 | 183 | 70 |
normalized size | 1 | 1.00 | 0.73 | 1.18 | 1.27 | 1.19 | 1.16 | 2.32 | 0.89 |
time (sec) |
N/A |
0.083 |
0.127 |
0.091 |
0.353 |
0.464 |
2.772 |
0.209 |
0.126 |
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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 |
B |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 184 | 157 | 162 | 904 | 0 | 166 | -1 |
normalized size | 1 | 1.00 | 1.15 | 0.98 | 1.01 | 5.65 | 0.00 | 1.04 | -0.01 |
time (sec) |
N/A |
0.138 |
0.302 |
0.122 |
0.433 |
0.432 |
0.000 |
0.197 |
0.000 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 28 | 62 | 46 | 44 | 56 | 28 |
normalized size | 1 | 1.00 | 1.00 | 0.85 | 1.88 | 1.39 | 1.33 | 1.70 | 0.85 |
time (sec) |
N/A |
0.033 |
0.013 |
0.015 |
0.324 |
0.519 |
0.783 |
0.238 |
0.060 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 136 | 86 | 91 | 112 | 0 | 95 | -1 |
normalized size | 1 | 1.00 | 1.09 | 0.69 | 0.73 | 0.90 | 0.00 | 0.76 | -0.01 |
time (sec) |
N/A |
0.072 |
0.129 |
0.059 |
0.397 |
0.443 |
0.000 |
0.308 |
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 |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 49 | 55 | 50 | 83 | 0 | 50 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.00 | 0.91 | 1.51 | 0.00 | 0.91 | -0.02 |
time (sec) |
N/A |
0.094 |
0.034 |
0.077 |
0.426 |
0.439 |
0.000 |
0.244 |
0.000 |
|
|
|
|
|
|
|
|
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|
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|
Problem 20 |
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 | 136 | 136 | 204 | 149 | 102 | 892 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.50 | 1.10 | 0.75 | 6.56 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.110 |
0.315 |
0.097 |
0.442 |
0.507 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 90 | 120 | 58 | 160 | 0 | 223 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.32 | 0.64 | 1.76 | 0.00 | 2.45 | -0.01 |
time (sec) |
N/A |
0.214 |
0.118 |
0.084 |
0.428 |
0.498 |
0.000 |
0.189 |
0.000 |
|
|
|
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 67 | 52 | 126 | 154 | 94 | 108 | 52 |
normalized size | 1 | 1.00 | 1.00 | 0.78 | 1.88 | 2.30 | 1.40 | 1.61 | 0.78 |
time (sec) |
N/A |
0.047 |
0.025 |
0.119 |
0.424 |
0.415 |
7.686 |
0.230 |
0.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
Problem 23 |
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 | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.020 |
2.506 |
0.052 |
0.000 |
0.431 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 735 | 0 | 0 | 252 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.43 | 0.00 | 0.00 | 1.18 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.201 |
12.547 |
0.239 |
0.000 |
0.594 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
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 | 135 | 135 | 152 | 0 | 0 | 174 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.13 | 0.00 | 0.00 | 1.29 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.148 |
0.579 |
0.163 |
0.000 |
0.753 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 98 | 77 | 0 | 124 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 0.81 | 0.00 | 1.31 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.153 |
0.100 |
0.000 |
0.452 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.025 |
2.965 |
0.071 |
0.000 |
0.499 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 15 | 15 | 15 | 14 | 13 | 13 | 19 | 25 | 13 |
normalized size | 1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.27 | 1.67 | 0.87 |
time (sec) |
N/A |
0.020 |
0.008 |
0.005 |
0.301 |
0.420 |
0.771 |
0.216 |
0.382 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 70 | 130 | 47 | 93 | 0 | 534 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.67 | 0.60 | 1.19 | 0.00 | 6.85 | -0.01 |
time (sec) |
N/A |
0.143 |
0.067 |
0.056 |
0.367 |
0.417 |
0.000 |
0.394 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 54 | 93 | 44 | 83 | 0 | 313 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.55 | 0.73 | 1.38 | 0.00 | 5.22 | -0.02 |
time (sec) |
N/A |
0.107 |
0.046 |
0.048 |
0.349 |
0.419 |
0.000 |
0.218 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 33 | 56 | 36 | 58 | 0 | 173 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.70 | 1.09 | 1.76 | 0.00 | 5.24 | -0.03 |
time (sec) |
N/A |
0.076 |
0.020 |
0.046 |
0.359 |
0.441 |
0.000 |
0.138 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
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 | 21 | 21 | 21 | 27 | 24 | 39 | 17 | 44 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.29 | 1.14 | 1.86 | 0.81 | 2.10 | -0.05 |
time (sec) |
N/A |
0.032 |
0.010 |
0.043 |
0.394 |
0.396 |
1.029 |
0.408 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 14 | 13 | 15 | 15 | 27 | 13 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.15 | 1.15 | 2.08 | 1.00 |
time (sec) |
N/A |
0.017 |
0.004 |
0.004 |
0.375 |
0.417 |
0.982 |
0.423 |
0.367 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 44 | 48 | 34 | 29 | 95 | 29 |
normalized size | 1 | 1.00 | 1.00 | 1.52 | 1.66 | 1.17 | 1.00 | 3.28 | 1.00 |
time (sec) |
N/A |
0.030 |
0.028 |
0.019 |
0.407 |
0.510 |
1.769 |
0.241 |
0.380 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 39 | 94 | 47 | 43 | 46 | 214 | 67 |
normalized size | 1 | 1.00 | 0.85 | 2.04 | 1.02 | 0.93 | 1.00 | 4.65 | 1.46 |
time (sec) |
N/A |
0.054 |
0.048 |
0.016 |
0.353 |
0.382 |
2.963 |
0.201 |
0.427 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 48 | 165 | 48 | 53 | 61 | 386 | 85 |
normalized size | 1 | 1.00 | 0.77 | 2.66 | 0.77 | 0.85 | 0.98 | 6.23 | 1.37 |
time (sec) |
N/A |
0.080 |
0.065 |
0.017 |
0.388 |
0.385 |
4.899 |
0.188 |
0.442 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F(-1) |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.251 |
180.001 |
0.200 |
0.000 |
0.473 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 88 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.158 |
0.256 |
0.184 |
0.000 |
0.425 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 63 | 70 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.94 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.088 |
0.087 |
0.109 |
0.000 |
0.422 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.024 |
3.418 |
0.086 |
0.000 |
0.449 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
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 | 104 | 104 | 102 | 138 | 62 | 323 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.33 | 0.60 | 3.11 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.090 |
0.112 |
0.079 |
1.339 |
0.435 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 56 | 93 | 44 | 89 | 0 | 353 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.50 | 0.71 | 1.44 | 0.00 | 5.69 | -0.02 |
time (sec) |
N/A |
0.113 |
0.044 |
0.042 |
0.507 |
0.428 |
0.000 |
0.200 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 43 |
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 | 86 | 86 | 84 | 103 | 58 | 267 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.20 | 0.67 | 3.10 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.066 |
0.088 |
0.048 |
0.386 |
0.426 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 39 | 58 | 39 | 63 | 0 | 193 | -1 |
normalized size | 1 | 1.00 | 0.93 | 1.38 | 0.93 | 1.50 | 0.00 | 4.60 | -0.02 |
time (sec) |
N/A |
0.082 |
0.026 |
0.025 |
0.390 |
0.470 |
0.000 |
0.184 |
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 |
A |
A |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 70 | 70 | 71 | 228 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.04 | 1.04 | 1.06 | 3.40 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.044 |
0.067 |
0.048 |
0.360 |
0.560 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 27 | 24 | 39 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.08 | 0.96 | 1.56 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.033 |
0.015 |
0.029 |
0.397 |
0.431 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 50 | 44 | 62 | 52 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 0.77 | 1.09 | 0.91 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.031 |
0.034 |
0.039 |
0.458 |
0.545 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 13 | 17 | 22 | 27 | 13 |
normalized size | 1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.13 | 1.47 | 1.80 | 0.87 |
time (sec) |
N/A |
0.019 |
0.005 |
0.005 |
0.320 |
0.470 |
2.738 |
0.165 |
0.375 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 75 | 75 | 74 | 82 | 62 | 251 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 1.09 | 0.83 | 3.35 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.048 |
0.073 |
0.050 |
0.388 |
0.512 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 34 | 55 | 48 | 40 | 37 | 43 | 58 |
normalized size | 1 | 1.00 | 1.00 | 1.62 | 1.41 | 1.18 | 1.09 | 1.26 | 1.71 |
time (sec) |
N/A |
0.034 |
0.030 |
0.031 |
0.475 |
0.536 |
7.672 |
0.192 |
0.406 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
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 | 93 | 93 | 97 | 117 | 62 | 313 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.04 | 1.26 | 0.67 | 3.37 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.068 |
0.123 |
0.058 |
0.775 |
0.454 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 44 | 73 | 47 | 50 | 51 | 0 | 74 |
normalized size | 1 | 1.00 | 0.94 | 1.55 | 1.00 | 1.06 | 1.09 | 0.00 | 1.57 |
time (sec) |
N/A |
0.059 |
0.050 |
0.048 |
0.375 |
0.472 |
19.216 |
0.000 |
0.436 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 1039 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.221 |
24.294 |
0.197 |
0.000 |
0.537 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 122 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.166 |
0.829 |
0.183 |
0.000 |
0.557 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 84 | 77 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.087 |
0.144 |
0.103 |
0.000 |
0.572 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.024 |
3.397 |
0.079 |
0.000 |
0.515 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 11 | 6 |
normalized size | 1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 1.38 | 0.75 |
time (sec) |
N/A |
0.012 |
0.003 |
0.009 |
0.442 |
0.561 |
0.263 |
0.172 |
0.400 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 88 | 77 | 73 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.03 | 0.97 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.074 |
0.098 |
0.126 |
0.563 |
0.523 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 88 | 69 | 73 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.17 | 0.92 | 0.97 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.041 |
0.085 |
0.089 |
0.508 |
0.414 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 79 | 74 | 61 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.18 | 1.10 | 0.91 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.017 |
0.082 |
0.072 |
0.524 |
0.743 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
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 | 25 | 25 | 23 | 33 | 30 | 55 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.92 | 1.32 | 1.20 | 2.20 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.037 |
0.027 |
0.022 |
0.610 |
0.578 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 68 | 77 | 65 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.08 | 0.92 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.063 |
0.071 |
0.112 |
0.692 |
0.524 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 72 | 77 | 69 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.96 | 1.03 | 0.92 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.062 |
0.076 |
0.053 |
0.668 |
0.439 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 89 | 0 | 82 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.137 |
1.509 |
0.131 |
0.443 |
0.479 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 85 | 0 | 82 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.107 |
1.308 |
0.145 |
0.421 |
0.506 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 81 | 0 | 68 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.065 |
1.113 |
0.095 |
0.418 |
0.485 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 39 | 40 | 37 | 69 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.91 | 0.93 | 0.86 | 1.60 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.064 |
0.035 |
0.140 |
0.401 |
0.535 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 79 | 0 | 74 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.87 | 0.00 | 0.81 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.128 |
1.428 |
0.099 |
0.429 |
0.457 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 161 | 0 | 149 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.195 |
1.538 |
0.164 |
0.499 |
0.446 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 161 | 0 | 149 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.133 |
1.599 |
0.135 |
0.502 |
0.654 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 140 | 0 | 125 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.076 |
1.211 |
0.125 |
0.495 |
0.489 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 52 | 67 | 62 | 115 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.78 | 1.00 | 0.93 | 1.72 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.100 |
0.062 |
0.191 |
0.433 |
0.604 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 154 | 154 | 126 | 0 | 133 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.182 |
1.408 |
0.137 |
0.464 |
0.485 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A |
0.021 |
5.406 |
0.881 |
0.000 |
0.727 |
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 |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
0.025 |
8.076 |
0.743 |
0.000 |
0.651 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 93 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.104 |
0.135 |
0.960 |
0.000 |
0.519 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 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 |
0.051 |
5.895 |
0.880 |
0.000 |
0.587 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 167 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.199 |
0.411 |
0.846 |
0.000 |
0.512 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 | 41 | 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 |
0.060 |
8.447 |
0.790 |
0.000 |
0.521 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 185 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.234 |
2.151 |
0.324 |
0.000 |
0.555 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 117 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.174 |
1.998 |
0.260 |
0.000 |
0.496 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 102 | 115 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.03 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.071 |
0.182 |
0.270 |
0.000 |
0.570 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
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 | 28 | 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 |
0.038 |
24.337 |
0.175 |
0.000 |
0.539 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
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 | 45 | 45 | 46 | 74 | 34 | 139 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.02 | 1.64 | 0.76 | 3.09 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.093 |
0.067 |
0.047 |
0.406 |
0.456 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
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 | 67 | 67 | 54 | 90 | 47 | 182 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 1.34 | 0.70 | 2.72 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.123 |
0.138 |
0.123 |
0.428 |
0.626 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 95 | 152 | 70 | 303 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.84 | 1.35 | 0.62 | 2.68 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.217 |
0.219 |
0.169 |
0.482 |
0.538 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 60 | 54 | 69 | 97 | 0 | 53 | -1 |
normalized size | 1 | 1.00 | 0.85 | 0.76 | 0.97 | 1.37 | 0.00 | 0.75 | -0.01 |
time (sec) |
N/A |
0.045 |
1.577 |
0.076 |
0.395 |
0.725 |
0.000 |
0.146 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 63 | 136 | 817 | 165 | 0 | 137 | -1 |
normalized size | 1 | 1.00 | 0.56 | 1.20 | 7.23 | 1.46 | 0.00 | 1.21 | -0.01 |
time (sec) |
N/A |
0.096 |
0.138 |
0.070 |
0.743 |
0.532 |
0.000 |
0.150 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
B |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 44 | 66 | 649 | 134 | 0 | 99 | -1 |
normalized size | 1 | 1.00 | 0.81 | 1.22 | 12.02 | 2.48 | 0.00 | 1.83 | -0.02 |
time (sec) |
N/A |
0.053 |
0.028 |
0.043 |
0.675 |
0.552 |
0.000 |
0.148 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
B |
A |
F |
C |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 27 | 36 | 477 | 55 | 0 | 39 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.97 | 12.89 | 1.49 | 0.00 | 1.05 | -0.03 |
time (sec) |
N/A |
0.017 |
0.005 |
0.042 |
0.585 |
0.586 |
0.000 |
0.129 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
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 |
0.036 |
9.983 |
0.063 |
0.000 |
0.531 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.07 |
time (sec) |
N/A |
0.039 |
13.406 |
0.067 |
0.000 |
0.658 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 346 | 346 | 104 | 831 | 486 | 104 | 269 | 914 | -1 |
normalized size | 1 | 1.00 | 0.30 | 2.40 | 1.40 | 0.30 | 0.78 | 2.64 | -0.00 |
time (sec) |
N/A |
0.418 |
1.302 |
0.022 |
0.363 |
0.535 |
1.743 |
0.164 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 72 | 303 | 293 | 68 | 151 | 299 | -1 |
normalized size | 1 | 1.00 | 0.43 | 1.81 | 1.75 | 0.41 | 0.90 | 1.79 | -0.01 |
time (sec) |
N/A |
0.186 |
0.207 |
0.019 |
0.325 |
0.643 |
0.615 |
0.136 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 50 | 63 | 111 | 44 | 65 | 64 | 43 |
normalized size | 1 | 1.00 | 0.93 | 1.17 | 2.06 | 0.81 | 1.20 | 1.19 | 0.80 |
time (sec) |
N/A |
0.046 |
0.063 |
0.008 |
0.320 |
0.591 |
0.475 |
0.136 |
0.441 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 130 | 0 | 0 | 217 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.05 | 0.00 | 0.00 | 1.75 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.287 |
0.989 |
0.032 |
0.000 |
0.582 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 199 | 0 | 0 | 315 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.09 | 0.00 | 0.00 | 1.73 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.361 |
3.092 |
0.030 |
0.000 |
0.487 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 537 | 537 | 378 | 1815 | 642 | 180 | 0 | 2162 | -1 |
normalized size | 1 | 1.00 | 0.70 | 3.38 | 1.20 | 0.34 | 0.00 | 4.03 | -0.00 |
time (sec) |
N/A |
0.697 |
2.902 |
0.020 |
0.331 |
0.489 |
0.000 |
0.207 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 118 | 659 | 371 | 109 | 0 | 706 | -1 |
normalized size | 1 | 1.00 | 0.45 | 2.52 | 1.42 | 0.42 | 0.00 | 2.70 | -0.00 |
time (sec) |
N/A |
0.315 |
0.348 |
0.020 |
0.323 |
0.520 |
0.000 |
0.147 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
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 | 85 | 85 | 65 | 133 | 137 | 58 | 94 | 128 | 75 |
normalized size | 1 | 1.00 | 0.76 | 1.56 | 1.61 | 0.68 | 1.11 | 1.51 | 0.88 |
time (sec) |
N/A |
0.079 |
0.086 |
0.017 |
0.318 |
0.564 |
1.216 |
0.132 |
0.467 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 232 | 232 | 233 | 0 | 0 | 503 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 2.17 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.519 |
0.070 |
0.040 |
0.000 |
0.673 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 329 | 329 | 210 | 0 | 0 | 704 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.64 | 0.00 | 0.00 | 2.14 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.724 |
1.849 |
0.035 |
0.000 |
0.644 |
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 [88] had the largest ratio of
[.7500]
|
|
|
|
|
|
|
| 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 |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
2 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
3 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1.00 |
8 |
0.375 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
6 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
7 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
8 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
9 |
A |
6 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
10 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
11 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
13 |
A |
6 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
14 |
A |
7 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
15 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
16 |
A |
10 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
18 |
A |
8 |
4 |
1.00 |
10 |
0.400 |
|
|
|
|
|
|
|
19 |
A |
8 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
20 |
A |
9 |
5 |
1.00 |
14 |
0.357 |
|
|
|
|
|
|
|
21 |
A |
12 |
6 |
1.00 |
14 |
0.429 |
|
|
|
|
|
|
|
22 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
23 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
24 |
A |
8 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
25 |
A |
5 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
26 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
27 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
28 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
29 |
A |
7 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
30 |
A |
6 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
31 |
A |
5 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
32 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
33 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
34 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
35 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
36 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
37 |
A |
9 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
38 |
A |
6 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
39 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
41 |
A |
7 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
42 |
A |
6 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
43 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
44 |
A |
5 |
5 |
1.00 |
10 |
0.500 |
|
|
|
|
|
|
|
45 |
A |
5 |
5 |
1.00 |
8 |
0.625 |
|
|
|
|
|
|
|
46 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
47 |
A |
4 |
4 |
1.00 |
12 |
0.333 |
|
|
|
|
|
|
|
48 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
49 |
A |
5 |
5 |
1.00 |
12 |
0.417 |
|
|
|
|
|
|
|
50 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
51 |
A |
6 |
6 |
1.00 |
12 |
0.500 |
|
|
|
|
|
|
|
52 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
53 |
A |
9 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
54 |
A |
6 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
55 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
56 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
57 |
A |
2 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
58 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
59 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
|
|
|
|
|
|
|
60 |
A |
3 |
2 |
1.00 |
8 |
0.250 |
|
|
|
|
|
|
|
61 |
A |
3 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
62 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
63 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
|
|
|
|
|
|
|
64 |
A |
5 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
65 |
A |
5 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
66 |
A |
5 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
67 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
68 |
A |
5 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
69 |
A |
8 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
70 |
A |
8 |
3 |
1.00 |
12 |
0.250 |
|
|
|
|
|
|
|
71 |
A |
8 |
3 |
1.00 |
10 |
0.300 |
|
|
|
|
|
|
|
72 |
A |
8 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
73 |
A |
8 |
3 |
1.00 |
14 |
0.214 |
|
|
|
|
|
|
|
74 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
75 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
76 |
A |
3 |
3 |
1.00 |
20 |
0.150 |
|
|
|
|
|
|
|
77 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
78 |
A |
5 |
5 |
1.00 |
22 |
0.227 |
|
|
|
|
|
|
|
79 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
80 |
A |
8 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
81 |
A |
5 |
3 |
1.00 |
16 |
0.188 |
|
|
|
|
|
|
|
82 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
|
|
|
|
|
|
|
83 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
84 |
A |
5 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
85 |
A |
7 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
86 |
A |
12 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
87 |
A |
4 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
88 |
A |
12 |
9 |
1.00 |
12 |
0.750 |
|
|
|
|
|
|
|
89 |
A |
8 |
7 |
1.00 |
10 |
0.700 |
|
|
|
|
|
|
|
90 |
A |
4 |
4 |
1.00 |
8 |
0.500 |
|
|
|
|
|
|
|
91 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
92 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
93 |
A |
16 |
4 |
1.00 |
18 |
0.222 |
|
|
|
|
|
|
|
94 |
A |
10 |
4 |
1.00 |
16 |
0.250 |
|
|
|
|
|
|
|
95 |
A |
4 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
96 |
A |
10 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
97 |
A |
11 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
98 |
A |
23 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
99 |
A |
13 |
5 |
1.00 |
16 |
0.312 |
|
|
|
|
|
|
|
100 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
|
|
|
|
|
|
|
101 |
A |
13 |
5 |
1.00 |
18 |
0.278 |
|
|
|
|
|
|
|
102 |
A |
14 |
6 |
1.00 |
18 |
0.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|