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 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 23, 25, 29, 31, 33, 36, 38, 42, 45, 47, 49,
50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 72, 73, 74, 79, 80, 81, 83, 85, 86, 87, 88,
89, 90, 91 }
B grade: { 7, 9, 22, 24, 26, 27, 28, 30, 32, 34, 35, 37, 39, 40, 41, 43, 44, 46, 48, 61, 66, 70, 71, 75, 76, 77, 84
}
C grade: { 18, 20, 78 }
F grade: { 82 }
2.1.3 Maple
A grade: { 1, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32,
34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60, 64, 65, 66, 70, 71,
72, 75, 76, 77, 78, 83, 88, 89, 90, 91 }
B grade: { 2, 4, 7, 24, 33, 42, 52, 54, 61, 62, 63, 67, 68, 69, 73, 74 }
C grade: { }
F grade: { 79, 80, 81, 82, 84, 85, 86, 87 }
2.1.4 Maxima
A grade: { 6, 8, 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, 52, 54, 55, 56, 57, 58, 59, 60, 64, 65, 66, 70,
71, 72, 75, 76, 77, 83, 88, 89, 90, 91 }
B grade: { 5, 7, 9, 51, 53, 61, 62, 63, 67, 68, 69, 73, 74, 78 }
C grade: { }
F grade: { 1, 2, 3, 4, 79, 80, 81, 82, 84, 85, 86, 87 }
2.1.5 FriCAS
A grade: { 1, 2, 3, 4, 6, 11, 12, 13, 14, 15, 22, 23, 24, 25, 32, 33, 34, 35, 41, 42, 43, 44, 45, 50, 51, 52, 53,
54, 57, 59, 83, 88, 89, 90, 91 }
B grade: { 5, 7, 8, 9, 10, 16, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 31, 36, 37, 38, 39, 40, 46, 47, 48, 49, 55,
56, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78 }
C grade: { }
F grade: { 79, 80, 81, 82, 84, 85, 86, 87 }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 83, 89, 90, 91 }
B grade: { }
C grade: { }
F grade: { 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, 84, 85, 86, 87, 88
}
2.1.7 Giac
A grade: { 1, 3, 5, 6, 8, 10, 16, 17, 19, 20, 21, 26, 27, 28, 29, 30, 31, 35, 36, 38, 39, 40, 44, 45, 46, 47,
48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 70, 71, 72, 75, 76, 77, 78, 88, 89, 90, 91
}
B grade: { 2, 4, 7, 9, 12, 13, 14, 15, 18, 24, 25, 33, 37, 42, 52, 54, 61, 62, 67, 68, 69, 73, 74 }
C grade: { }
F grade: { 11, 22, 23, 32, 34, 41, 43, 79, 80, 81, 82, 83, 84, 85, 86, 87 }
2.1.8 Mupad
A grade: { 83, 88, 89, 90, 91 }
B 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
}
C grade: { }
F grade: { 79, 80, 81, 82, 84, 85, 86, 87 }
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 |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 67 | 66 | 0 | 39 | 51 | 53 | 49 |
normalized size | 1 | 1.00 | 0.86 | 0.85 | 0.00 | 0.50 | 0.65 | 0.68 | 0.63 |
time (sec) |
N/A |
0.066 |
0.086 |
0.175 |
0.000 |
0.529 |
0.200 |
0.365 |
3.708 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 51 | 81 | 0 | 26 | 37 | 71 | 59 |
normalized size | 1 | 1.00 | 1.76 | 2.79 | 0.00 | 0.90 | 1.28 | 2.45 | 2.03 |
time (sec) |
N/A |
0.137 |
0.021 |
0.172 |
0.000 |
0.456 |
0.191 |
0.342 |
3.865 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 39 | 47 | 0 | 25 | 31 | 41 | 35 |
normalized size | 1 | 1.00 | 0.78 | 0.94 | 0.00 | 0.50 | 0.62 | 0.82 | 0.70 |
time (sec) |
N/A |
0.054 |
0.096 |
0.169 |
0.000 |
0.482 |
0.149 |
0.448 |
3.745 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 33 | 47 | 0 | 14 | 17 | 33 | 39 |
normalized size | 1 | 1.00 | 1.74 | 2.47 | 0.00 | 0.74 | 0.89 | 1.74 | 2.05 |
time (sec) |
N/A |
0.089 |
0.013 |
0.165 |
0.000 |
0.466 |
0.131 |
0.757 |
3.828 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
A |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 31 | 21 | 28 | 25 | 0 | 22 | 20 |
normalized size | 1 | 1.00 | 1.94 | 1.31 | 1.75 | 1.56 | 0.00 | 1.38 | 1.25 |
time (sec) |
N/A |
0.086 |
0.019 |
0.157 |
0.314 |
0.471 |
0.000 |
0.309 |
3.800 |
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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 |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 15 | 20 | 17 | 25 | 0 | 18 | 19 |
normalized size | 1 | 1.00 | 0.83 | 1.11 | 0.94 | 1.39 | 0.00 | 1.00 | 1.06 |
time (sec) |
N/A |
0.033 |
0.019 |
0.174 |
0.315 |
0.465 |
0.000 |
0.316 |
3.738 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
B |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 75 | 42 | 59 | 73 | 0 | 46 | 41 |
normalized size | 1 | 1.00 | 3.12 | 1.75 | 2.46 | 3.04 | 0.00 | 1.92 | 1.71 |
time (sec) |
N/A |
0.132 |
0.022 |
0.177 |
0.318 |
0.471 |
0.000 |
0.303 |
3.729 |
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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 |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 29 | 15 | 12 | 36 | 0 | 12 | 13 |
normalized size | 1 | 1.00 | 1.53 | 0.79 | 0.63 | 1.89 | 0.00 | 0.63 | 0.68 |
time (sec) |
N/A |
0.039 |
0.019 |
0.184 |
0.574 |
0.459 |
0.000 |
0.292 |
3.624 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
B |
A |
B |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 40 | 40 | 139 | 58 | 83 | 121 | 0 | 62 | 57 |
normalized size | 1 | 1.00 | 3.48 | 1.45 | 2.08 | 3.02 | 0.00 | 1.55 | 1.42 |
time (sec) |
N/A |
0.151 |
0.025 |
0.189 |
0.511 |
0.469 |
0.000 |
0.200 |
3.696 |
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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 |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 41 | 28 | 24 | 54 | 0 | 24 | 27 |
normalized size | 1 | 1.00 | 1.11 | 0.76 | 0.65 | 1.46 | 0.00 | 0.65 | 0.73 |
time (sec) |
N/A |
0.047 |
0.020 |
0.186 |
0.415 |
0.449 |
0.000 |
0.323 |
3.601 |
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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 |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 103 | 113 | 91 | 97 | 0 | 0 | 121 |
normalized size | 1 | 1.00 | 1.02 | 1.12 | 0.90 | 0.96 | 0.00 | 0.00 | 1.20 |
time (sec) |
N/A |
0.076 |
0.048 |
0.320 |
0.374 |
0.515 |
0.000 |
0.000 |
3.804 |
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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 |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 82 | 92 | 87 | 74 | 0 | 1066 | 155 |
normalized size | 1 | 1.00 | 0.99 | 1.11 | 1.05 | 0.89 | 0.00 | 12.84 | 1.87 |
time (sec) |
N/A |
0.168 |
0.082 |
0.313 |
0.530 |
0.460 |
0.000 |
0.884 |
3.787 |
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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 |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 71 | 79 | 70 | 74 | 0 | 5350 | 87 |
normalized size | 1 | 1.00 | 1.03 | 1.14 | 1.01 | 1.07 | 0.00 | 77.54 | 1.26 |
time (sec) |
N/A |
0.068 |
0.028 |
0.299 |
0.580 |
0.509 |
0.000 |
31.086 |
3.828 |
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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 |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 56 | 58 | 52 | 47 | 0 | 413 | 50 |
normalized size | 1 | 1.00 | 1.14 | 1.18 | 1.06 | 0.96 | 0.00 | 8.43 | 1.02 |
time (sec) |
N/A |
0.084 |
0.050 |
0.184 |
0.566 |
0.544 |
0.000 |
0.544 |
3.815 |
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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 |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 48 | 45 | 46 | 49 | 0 | 1236 | 53 |
normalized size | 1 | 1.00 | 1.30 | 1.22 | 1.24 | 1.32 | 0.00 | 33.41 | 1.43 |
time (sec) |
N/A |
0.036 |
0.027 |
0.182 |
0.413 |
0.453 |
0.000 |
0.798 |
3.820 |
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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 |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 52 | 42 | 46 | 58 | 0 | 49 | 86 |
normalized size | 1 | 1.00 | 2.00 | 1.62 | 1.77 | 2.23 | 0.00 | 1.88 | 3.31 |
time (sec) |
N/A |
0.029 |
0.018 |
0.280 |
0.539 |
0.523 |
0.000 |
0.489 |
3.745 |
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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 |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 36 | 26 | 25 | 62 | 0 | 35 | 25 |
normalized size | 1 | 1.00 | 1.44 | 1.04 | 1.00 | 2.48 | 0.00 | 1.40 | 1.00 |
time (sec) |
N/A |
0.078 |
0.062 |
0.366 |
0.318 |
0.552 |
0.000 |
0.388 |
3.634 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
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grade |
A |
A |
C |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 60 | 107 | 75 | 83 | 142 | 0 | 118 | 149 |
normalized size | 1 | 1.00 | 1.78 | 1.25 | 1.38 | 2.37 | 0.00 | 1.97 | 2.48 |
time (sec) |
N/A |
0.068 |
0.028 |
0.386 |
0.535 |
0.463 |
0.000 |
0.512 |
3.716 |
|
|
|
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 72 | 60 | 50 | 122 | 0 | 62 | 49 |
normalized size | 1 | 1.00 | 1.26 | 1.05 | 0.88 | 2.14 | 0.00 | 1.09 | 0.86 |
time (sec) |
N/A |
0.088 |
0.255 |
0.377 |
0.522 |
0.521 |
0.000 |
0.502 |
3.672 |
|
|
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 151 | 109 | 123 | 213 | 0 | 177 | 211 |
normalized size | 1 | 1.00 | 1.54 | 1.11 | 1.26 | 2.17 | 0.00 | 1.81 | 2.15 |
time (sec) |
N/A |
0.092 |
0.039 |
0.392 |
0.514 |
0.515 |
0.000 |
2.926 |
3.846 |
|
|
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 104 | 94 | 72 | 174 | 0 | 84 | 70 |
normalized size | 1 | 1.00 | 1.20 | 1.08 | 0.83 | 2.00 | 0.00 | 0.97 | 0.80 |
time (sec) |
N/A |
0.108 |
0.556 |
0.401 |
0.586 |
0.487 |
0.000 |
1.803 |
3.930 |
|
|
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Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 240 | 204 | 128 | 137 | 0 | 0 | 127 |
normalized size | 1 | 1.00 | 2.12 | 1.81 | 1.13 | 1.21 | 0.00 | 0.00 | 1.12 |
time (sec) |
N/A |
0.186 |
3.507 |
0.418 |
0.892 |
0.550 |
0.000 |
0.000 |
3.820 |
|
|
|
|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 152 | 167 | 104 | 126 | 0 | 0 | 174 |
normalized size | 1 | 1.00 | 1.25 | 1.37 | 0.85 | 1.03 | 0.00 | 0.00 | 1.43 |
time (sec) |
N/A |
0.131 |
0.989 |
0.398 |
0.470 |
0.469 |
0.000 |
0.000 |
6.706 |
|
|
|
|
|
|
|
|
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|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 76 | 76 | 162 | 145 | 82 | 101 | 0 | 1061 | 75 |
normalized size | 1 | 1.00 | 2.13 | 1.91 | 1.08 | 1.33 | 0.00 | 13.96 | 0.99 |
time (sec) |
N/A |
0.113 |
2.497 |
0.338 |
0.435 |
0.503 |
0.000 |
2.171 |
3.688 |
|
|
|
|
|
|
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|
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|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 111 | 108 | 67 | 90 | 0 | 2837 | 93 |
normalized size | 1 | 1.00 | 1.63 | 1.59 | 0.99 | 1.32 | 0.00 | 41.72 | 1.37 |
time (sec) |
N/A |
0.074 |
0.469 |
0.311 |
0.366 |
0.515 |
0.000 |
11.780 |
4.042 |
|
|
|
|
|
|
|
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|
|
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|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 97 | 61 | 60 | 102 | 0 | 74 | 125 |
normalized size | 1 | 1.00 | 2.26 | 1.42 | 1.40 | 2.37 | 0.00 | 1.72 | 2.91 |
time (sec) |
N/A |
0.056 |
0.250 |
0.327 |
0.547 |
0.452 |
0.000 |
0.933 |
3.721 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 91 | 43 | 39 | 96 | 0 | 51 | 44 |
normalized size | 1 | 1.00 | 2.17 | 1.02 | 0.93 | 2.29 | 0.00 | 1.21 | 1.05 |
time (sec) |
N/A |
0.047 |
0.579 |
0.472 |
0.468 |
0.464 |
0.000 |
0.870 |
3.641 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 250 | 120 | 122 | 230 | 0 | 172 | 292 |
normalized size | 1 | 1.00 | 2.63 | 1.26 | 1.28 | 2.42 | 0.00 | 1.81 | 3.07 |
time (sec) |
N/A |
0.118 |
1.918 |
0.527 |
0.350 |
0.626 |
0.000 |
1.593 |
3.845 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 127 | 104 | 69 | 174 | 0 | 91 | 72 |
normalized size | 1 | 1.00 | 1.61 | 1.32 | 0.87 | 2.20 | 0.00 | 1.15 | 0.91 |
time (sec) |
N/A |
0.070 |
1.434 |
0.556 |
0.621 |
0.447 |
0.000 |
0.783 |
3.787 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 994 | 183 | 187 | 333 | 0 | 269 | 378 |
normalized size | 1 | 1.00 | 6.02 | 1.11 | 1.13 | 2.02 | 0.00 | 1.63 | 2.29 |
time (sec) |
N/A |
0.160 |
6.219 |
0.431 |
0.466 |
0.513 |
0.000 |
0.811 |
3.909 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 114 | 166 | 104 | 240 | 0 | 131 | 107 |
normalized size | 1 | 1.00 | 0.93 | 1.36 | 0.85 | 1.97 | 0.00 | 1.07 | 0.88 |
time (sec) |
N/A |
0.101 |
1.509 |
0.522 |
0.738 |
0.444 |
0.000 |
0.706 |
4.060 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 771 | 271 | 173 | 188 | 0 | 0 | 291 |
normalized size | 1 | 1.00 | 3.76 | 1.32 | 0.84 | 0.92 | 0.00 | 0.00 | 1.42 |
time (sec) |
N/A |
0.189 |
6.305 |
0.437 |
0.707 |
0.474 |
0.000 |
0.000 |
6.436 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 203 | 226 | 113 | 149 | 0 | 2590 | 151 |
normalized size | 1 | 1.00 | 1.97 | 2.19 | 1.10 | 1.45 | 0.00 | 25.15 | 1.47 |
time (sec) |
N/A |
0.145 |
4.524 |
0.373 |
0.450 |
0.455 |
0.000 |
7.281 |
3.695 |
|
|
|
|
|
|
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|
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|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 637 | 193 | 128 | 144 | 0 | 0 | 193 |
normalized size | 1 | 1.00 | 4.79 | 1.45 | 0.96 | 1.08 | 0.00 | 0.00 | 1.45 |
time (sec) |
N/A |
0.116 |
6.172 |
0.345 |
0.319 |
0.449 |
0.000 |
0.000 |
5.799 |
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
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|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 241 | 125 | 111 | 148 | 0 | 144 | 278 |
normalized size | 1 | 1.00 | 2.80 | 1.45 | 1.29 | 1.72 | 0.00 | 1.67 | 3.23 |
time (sec) |
N/A |
0.086 |
2.289 |
0.347 |
0.327 |
0.530 |
0.000 |
7.583 |
4.209 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 126 | 63 | 56 | 127 | 0 | 70 | 62 |
normalized size | 1 | 1.00 | 1.97 | 0.98 | 0.88 | 1.98 | 0.00 | 1.09 | 0.97 |
time (sec) |
N/A |
0.053 |
1.009 |
0.524 |
0.318 |
0.475 |
0.000 |
1.796 |
3.662 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 897 | 170 | 171 | 299 | 0 | 304 | 581 |
normalized size | 1 | 1.00 | 6.36 | 1.21 | 1.21 | 2.12 | 0.00 | 2.16 | 4.12 |
time (sec) |
N/A |
0.135 |
6.194 |
0.515 |
0.334 |
0.557 |
0.000 |
2.106 |
3.966 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 212 | 141 | 98 | 237 | 0 | 133 | 103 |
normalized size | 1 | 1.00 | 1.88 | 1.25 | 0.87 | 2.10 | 0.00 | 1.18 | 0.91 |
time (sec) |
N/A |
0.086 |
2.247 |
0.545 |
0.457 |
0.456 |
0.000 |
2.512 |
3.719 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 1229 | 254 | 250 | 427 | 0 | 373 | 698 |
normalized size | 1 | 1.00 | 5.37 | 1.11 | 1.09 | 1.86 | 0.00 | 1.63 | 3.05 |
time (sec) |
N/A |
0.208 |
6.217 |
0.484 |
0.514 |
0.566 |
0.000 |
5.326 |
4.038 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 515 | 230 | 142 | 343 | 0 | 189 | 146 |
normalized size | 1 | 1.00 | 3.08 | 1.38 | 0.85 | 2.05 | 0.00 | 1.13 | 0.87 |
time (sec) |
N/A |
0.134 |
1.838 |
0.569 |
0.324 |
0.464 |
0.000 |
1.850 |
3.877 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 275 | 275 | 1017 | 412 | 218 | 224 | 0 | 0 | 319 |
normalized size | 1 | 1.00 | 3.70 | 1.50 | 0.79 | 0.81 | 0.00 | 0.00 | 1.16 |
time (sec) |
N/A |
0.248 |
6.270 |
0.533 |
0.538 |
0.494 |
0.000 |
0.000 |
7.213 |
|
|
|
|
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|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 263 | 368 | 154 | 186 | 0 | 3931 | 161 |
normalized size | 1 | 1.00 | 1.89 | 2.65 | 1.11 | 1.34 | 0.00 | 28.28 | 1.16 |
time (sec) |
N/A |
0.175 |
6.286 |
0.469 |
0.452 |
0.468 |
0.000 |
22.339 |
3.794 |
|
|
|
|
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|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 180 | 180 | 383 | 309 | 166 | 176 | 0 | 0 | 268 |
normalized size | 1 | 1.00 | 2.13 | 1.72 | 0.92 | 0.98 | 0.00 | 0.00 | 1.49 |
time (sec) |
N/A |
0.157 |
5.260 |
0.438 |
0.695 |
0.505 |
0.000 |
0.000 |
7.285 |
|
|
|
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Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 118 | 352 | 214 | 139 | 175 | 0 | 193 | 496 |
normalized size | 1 | 1.00 | 2.98 | 1.81 | 1.18 | 1.48 | 0.00 | 1.64 | 4.20 |
time (sec) |
N/A |
0.114 |
5.000 |
0.464 |
0.681 |
0.514 |
0.000 |
6.001 |
4.144 |
|
|
|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 162 | 90 | 72 | 159 | 0 | 86 | 81 |
normalized size | 1 | 1.00 | 1.95 | 1.08 | 0.87 | 1.92 | 0.00 | 1.04 | 0.98 |
time (sec) |
N/A |
0.058 |
1.207 |
0.537 |
0.417 |
0.453 |
0.000 |
4.038 |
3.663 |
|
|
|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 1128 | 192 | 188 | 346 | 0 | 300 | 670 |
normalized size | 1 | 1.00 | 7.01 | 1.19 | 1.17 | 2.15 | 0.00 | 1.86 | 4.16 |
time (sec) |
N/A |
0.157 |
6.207 |
0.515 |
0.476 |
0.554 |
0.000 |
12.818 |
4.069 |
|
|
|
|
|
|
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|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 188 | 184 | 120 | 267 | 0 | 161 | 132 |
normalized size | 1 | 1.00 | 1.37 | 1.34 | 0.88 | 1.95 | 0.00 | 1.18 | 0.96 |
time (sec) |
N/A |
0.104 |
3.844 |
0.657 |
0.404 |
0.460 |
0.000 |
7.802 |
3.761 |
|
|
|
|
|
|
|
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|
|
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|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 1491 | 317 | 304 | 547 | 0 | 479 | 857 |
normalized size | 1 | 1.00 | 5.44 | 1.16 | 1.11 | 2.00 | 0.00 | 1.75 | 3.13 |
time (sec) |
N/A |
0.241 |
6.302 |
0.504 |
0.633 |
0.685 |
0.000 |
8.970 |
4.171 |
|
|
|
|
|
|
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|
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|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 233 | 301 | 171 | 386 | 0 | 235 | 181 |
normalized size | 1 | 1.00 | 1.20 | 1.55 | 0.88 | 1.99 | 0.00 | 1.21 | 0.93 |
time (sec) |
N/A |
0.157 |
4.012 |
0.594 |
0.629 |
0.479 |
0.000 |
3.636 |
3.827 |
|
|
|
|
|
|
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|
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|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 402 | 402 | 660 | 442 | 387 | 697 | 0 | 647 | 990 |
normalized size | 1 | 1.00 | 1.64 | 1.10 | 0.96 | 1.73 | 0.00 | 1.61 | 2.46 |
time (sec) |
N/A |
0.306 |
6.266 |
0.535 |
0.401 |
0.709 |
0.000 |
3.187 |
4.035 |
|
|
|
|
|
|
|
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|
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|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 289 | 361 | 658 | 370 | 0 | 464 | 683 |
normalized size | 1 | 1.00 | 1.05 | 1.32 | 2.40 | 1.35 | 0.00 | 1.69 | 2.49 |
time (sec) |
N/A |
0.354 |
3.186 |
0.404 |
0.799 |
0.493 |
0.000 |
2.842 |
6.830 |
|
|
|
|
|
|
|
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|
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|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 249 | 565 | 280 | 216 | 0 | 334 | 313 |
normalized size | 1 | 1.00 | 1.58 | 3.58 | 1.77 | 1.37 | 0.00 | 2.11 | 1.98 |
time (sec) |
N/A |
0.339 |
2.811 |
0.365 |
0.625 |
0.463 |
0.000 |
3.867 |
4.269 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 168 | 168 | 139 | 205 | 364 | 261 | 0 | 241 | 324 |
normalized size | 1 | 1.00 | 0.83 | 1.22 | 2.17 | 1.55 | 0.00 | 1.43 | 1.93 |
time (sec) |
N/A |
0.223 |
0.891 |
0.359 |
0.643 |
0.463 |
0.000 |
0.985 |
6.497 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 170 | 238 | 144 | 122 | 0 | 184 | 147 |
normalized size | 1 | 1.00 | 1.81 | 2.53 | 1.53 | 1.30 | 0.00 | 1.96 | 1.56 |
time (sec) |
N/A |
0.163 |
0.771 |
0.362 |
0.579 |
0.457 |
0.000 |
0.617 |
3.865 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
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|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 79 | 100 | 141 | 185 | 0 | 118 | 110 |
normalized size | 1 | 1.00 | 0.88 | 1.11 | 1.57 | 2.06 | 0.00 | 1.31 | 1.22 |
time (sec) |
N/A |
0.106 |
0.366 |
0.315 |
0.788 |
0.476 |
0.000 |
0.612 |
3.913 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 75 | 65 | 107 | 183 | 0 | 94 | 174 |
normalized size | 1 | 1.00 | 1.14 | 0.98 | 1.62 | 2.77 | 0.00 | 1.42 | 2.64 |
time (sec) |
N/A |
0.129 |
0.108 |
0.364 |
0.471 |
0.483 |
0.000 |
1.619 |
4.092 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 47 | 53 | 47 | 95 | 0 | 60 | 39 |
normalized size | 1 | 1.00 | 0.94 | 1.06 | 0.94 | 1.90 | 0.00 | 1.20 | 0.78 |
time (sec) |
N/A |
0.060 |
0.134 |
0.353 |
0.585 |
0.442 |
0.000 |
0.702 |
3.737 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 179 | 162 | 215 | 270 | 0 | 209 | 764 |
normalized size | 1 | 1.00 | 1.47 | 1.33 | 1.76 | 2.21 | 0.00 | 1.71 | 6.26 |
time (sec) |
N/A |
0.307 |
0.805 |
0.414 |
0.663 |
0.532 |
0.000 |
2.071 |
4.448 |
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 95 | 144 | 97 | 208 | 0 | 144 | 102 |
normalized size | 1 | 1.00 | 0.88 | 1.33 | 0.90 | 1.93 | 0.00 | 1.33 | 0.94 |
time (sec) |
N/A |
0.104 |
0.494 |
0.392 |
0.494 |
0.461 |
0.000 |
2.926 |
3.843 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 169 | 169 | 150 | 273 | 168 | 385 | 0 | 251 | 167 |
normalized size | 1 | 1.00 | 0.89 | 1.62 | 0.99 | 2.28 | 0.00 | 1.49 | 0.99 |
time (sec) |
N/A |
0.151 |
2.102 |
0.409 |
0.540 |
0.469 |
0.000 |
2.932 |
4.329 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 297 | 297 | 603 | 1211 | 799 | 619 | 0 | 735 | 757 |
normalized size | 1 | 1.00 | 2.03 | 4.08 | 2.69 | 2.08 | 0.00 | 2.47 | 2.55 |
time (sec) |
N/A |
0.914 |
6.553 |
0.497 |
0.962 |
0.540 |
0.000 |
1.530 |
5.543 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 373 | 724 | 507 | 444 | 0 | 513 | 481 |
normalized size | 1 | 1.00 | 1.72 | 3.34 | 2.34 | 2.05 | 0.00 | 2.36 | 2.22 |
time (sec) |
N/A |
0.562 |
3.985 |
0.484 |
0.923 |
0.522 |
0.000 |
1.453 |
4.820 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-1) |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 246 | 352 | 293 | 292 | 0 | 263 | 255 |
normalized size | 1 | 1.00 | 1.66 | 2.38 | 1.98 | 1.97 | 0.00 | 1.78 | 1.72 |
time (sec) |
N/A |
0.295 |
3.387 |
0.456 |
0.815 |
0.469 |
0.000 |
0.886 |
4.056 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 109 | 75 | 74 | 293 | 0 | 74 | 79 |
normalized size | 1 | 1.00 | 1.51 | 1.04 | 1.03 | 4.07 | 0.00 | 1.03 | 1.10 |
time (sec) |
N/A |
0.065 |
0.401 |
0.467 |
0.571 |
0.463 |
0.000 |
0.892 |
3.842 |
|
|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 244 | 189 | 144 | 442 | 0 | 203 | 150 |
normalized size | 1 | 1.00 | 1.74 | 1.35 | 1.03 | 3.16 | 0.00 | 1.45 | 1.07 |
time (sec) |
N/A |
0.122 |
2.662 |
0.513 |
0.424 |
0.503 |
0.000 |
0.796 |
3.915 |
|
|
|
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Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 219 | 219 | 589 | 343 | 225 | 787 | 0 | 332 | 237 |
normalized size | 1 | 1.00 | 2.69 | 1.57 | 1.03 | 3.59 | 0.00 | 1.52 | 1.08 |
time (sec) |
N/A |
0.198 |
6.249 |
0.518 |
0.602 |
0.527 |
0.000 |
1.009 |
5.015 |
|
|
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Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-2) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 382 | 382 | 683 | 1449 | 1088 | 932 | 0 | 923 | 1068 |
normalized size | 1 | 1.00 | 1.79 | 3.79 | 2.85 | 2.44 | 0.00 | 2.42 | 2.80 |
time (sec) |
N/A |
1.432 |
6.688 |
0.503 |
0.556 |
0.626 |
0.000 |
6.864 |
5.842 |
|
|
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Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-2) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 285 | 285 | 501 | 882 | 744 | 705 | 0 | 588 | 717 |
normalized size | 1 | 1.00 | 1.76 | 3.09 | 2.61 | 2.47 | 0.00 | 2.06 | 2.52 |
time (sec) |
N/A |
0.850 |
6.493 |
0.493 |
0.701 |
0.569 |
0.000 |
3.869 |
5.335 |
|
|
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Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-2) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 316 | 542 | 463 | 526 | 0 | 482 | 433 |
normalized size | 1 | 1.00 | 1.53 | 2.63 | 2.25 | 2.55 | 0.00 | 2.34 | 2.10 |
time (sec) |
N/A |
0.396 |
4.005 |
0.488 |
0.909 |
0.520 |
0.000 |
1.226 |
4.623 |
|
|
|
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|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 241 | 96 | 108 | 565 | 0 | 113 | 99 |
normalized size | 1 | 1.00 | 2.54 | 1.01 | 1.14 | 5.95 | 0.00 | 1.19 | 1.04 |
time (sec) |
N/A |
0.077 |
2.690 |
0.516 |
0.484 |
0.538 |
0.000 |
1.041 |
3.869 |
|
|
|
|
|
|
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|
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|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 456 | 234 | 192 | 811 | 0 | 237 | 200 |
normalized size | 1 | 1.00 | 2.56 | 1.31 | 1.08 | 4.56 | 0.00 | 1.33 | 1.12 |
time (sec) |
N/A |
0.153 |
3.406 |
0.552 |
0.404 |
0.556 |
0.000 |
2.066 |
4.367 |
|
|
|
|
|
|
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|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 265 | 265 | 494 | 410 | 281 | 1018 | 0 | 382 | 297 |
normalized size | 1 | 1.00 | 1.86 | 1.55 | 1.06 | 3.84 | 0.00 | 1.44 | 1.12 |
time (sec) |
N/A |
0.239 |
4.755 |
0.566 |
0.776 |
0.564 |
0.000 |
1.356 |
5.321 |
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-2) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 366 | 366 | 564 | 1215 | 997 | 1053 | 0 | 902 | 962 |
normalized size | 1 | 1.00 | 1.54 | 3.32 | 2.72 | 2.88 | 0.00 | 2.46 | 2.63 |
time (sec) |
N/A |
1.370 |
5.661 |
0.539 |
0.935 |
0.666 |
0.000 |
6.916 |
5.662 |
|
|
|
|
|
|
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|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
B |
F(-2) |
B |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 264 | 264 | 395 | 668 | 662 | 802 | 0 | 642 | 597 |
normalized size | 1 | 1.00 | 1.50 | 2.53 | 2.51 | 3.04 | 0.00 | 2.43 | 2.26 |
time (sec) |
N/A |
0.571 |
3.771 |
0.549 |
0.596 |
0.564 |
0.000 |
3.891 |
5.088 |
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 259 | 117 | 140 | 874 | 0 | 129 | 131 |
normalized size | 1 | 1.00 | 2.23 | 1.01 | 1.21 | 7.53 | 0.00 | 1.11 | 1.13 |
time (sec) |
N/A |
0.088 |
2.217 |
0.531 |
0.380 |
0.544 |
0.000 |
2.575 |
3.976 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 528 | 278 | 228 | 1235 | 0 | 222 | 232 |
normalized size | 1 | 1.00 | 2.58 | 1.36 | 1.11 | 6.02 | 0.00 | 1.08 | 1.13 |
time (sec) |
N/A |
0.173 |
2.079 |
0.588 |
0.558 |
0.601 |
0.000 |
5.001 |
5.058 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 300 | 300 | 673 | 476 | 325 | 1536 | 0 | 428 | 337 |
normalized size | 1 | 1.00 | 2.24 | 1.59 | 1.08 | 5.12 | 0.00 | 1.43 | 1.12 |
time (sec) |
N/A |
0.271 |
1.760 |
0.599 |
0.615 |
0.652 |
0.000 |
1.947 |
5.647 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
B |
B |
F |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 41 | 26 | 50 | 55 | 0 | 44 | 38 |
normalized size | 1 | 1.00 | 1.58 | 1.00 | 1.92 | 2.12 | 0.00 | 1.69 | 1.46 |
time (sec) |
N/A |
0.074 |
0.042 |
0.121 |
0.853 |
0.433 |
0.000 |
2.970 |
3.881 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 79 |
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 | 229 | 229 | 205 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.450 |
2.564 |
1.202 |
0.000 |
0.435 |
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 | 179 | 179 | 166 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.268 |
1.208 |
0.941 |
0.000 |
0.434 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
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 | 109 | 109 | 109 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.145 |
0.273 |
1.399 |
0.000 |
0.430 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
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|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 765 | 765 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
4.173 |
13.216 |
1.083 |
0.000 |
0.437 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
2.463 |
3.497 |
1.551 |
0.000 |
0.529 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 435 | 435 | 910 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.803 |
6.598 |
3.519 |
0.000 |
0.454 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 85 |
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 | 276 | 276 | 270 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A |
0.367 |
1.150 |
1.999 |
0.000 |
0.437 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
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|
|
Problem 86 |
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 | 48 | 48 | 48 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A |
0.055 |
0.938 |
0.873 |
0.000 |
0.467 |
0.000 |
0.000 |
0.000 |
|
|
|
|
|
|
|
|
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|
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Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Mupad |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 78 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A |
0.130 |
1.307 |
0.741 |
0.000 |
0.483 |
0.000 |
0.000 |
0.000 |
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Problem 88 |
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 | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
1.979 |
3.215 |
1.869 |
0.000 |
0.443 |
0.000 |
0.000 |
0.000 |
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Problem 89 |
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 |
0.855 |
2.247 |
0.460 |
0.000 |
0.442 |
0.000 |
0.000 |
0.000 |
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Problem 90 |
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 |
0.487 |
1.590 |
0.867 |
0.000 |
0.438 |
0.000 |
0.000 |
0.000 |
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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 | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A |
1.700 |
15.430 |
0.752 |
0.000 |
0.445 |
0.000 |
0.000 |
0.000 |
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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 [5] had the largest ratio of
[.6364]
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| Table 2.1:Rubi specific breakdown of results for each
integral
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|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
5 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
2 |
A |
9 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
3 |
A |
5 |
4 |
1.00 |
13 |
0.308 |
|
|
|
|
|
|
|
4 |
A |
8 |
6 |
1.00 |
11 |
0.546 |
|
|
|
|
|
|
|
5 |
A |
8 |
7 |
1.00 |
11 |
0.636 |
|
|
|
|
|
|
|
6 |
A |
3 |
2 |
1.00 |
13 |
0.154 |
|
|
|
|
|
|
|
7 |
A |
8 |
7 |
1.00 |
13 |
0.538 |
|
|
|
|
|
|
|
8 |
A |
4 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
9 |
A |
9 |
8 |
1.00 |
13 |
0.615 |
|
|
|
|
|
|
|
10 |
A |
4 |
3 |
1.00 |
13 |
0.231 |
|
|
|
|
|
|
|
11 |
A |
8 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
12 |
A |
6 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
13 |
A |
8 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
14 |
A |
5 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
15 |
A |
6 |
5 |
1.00 |
17 |
0.294 |
|
|
|
|
|
|
|
16 |
A |
4 |
2 |
1.00 |
17 |
0.118 |
|
|
|
|
|
|
|
17 |
A |
3 |
1 |
1.00 |
19 |
0.053 |
|
|
|
|
|
|
|
18 |
A |
7 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
19 |
A |
3 |
1 |
1.00 |
19 |
0.053 |
|
|
|
|
|
|
|
20 |
A |
9 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
21 |
A |
3 |
1 |
1.00 |
19 |
0.053 |
|
|
|
|
|
|
|
22 |
A |
8 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
23 |
A |
11 |
7 |
1.00 |
21 |
0.333 |
|
|
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|
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24 |
A |
6 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
25 |
A |
9 |
7 |
1.00 |
19 |
0.368 |
|
|
|
|
|
|
|
26 |
A |
6 |
4 |
1.00 |
19 |
0.210 |
|
|
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|
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27 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
28 |
A |
10 |
7 |
1.00 |
21 |
0.333 |
|
|
|
|
|
|
|
29 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
30 |
A |
13 |
9 |
1.00 |
21 |
0.429 |
|
|
|
|
|
|
|
31 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
32 |
A |
16 |
8 |
1.00 |
21 |
0.381 |
|
|
|
|
|
|
|
33 |
A |
7 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
34 |
A |
13 |
8 |
1.00 |
19 |
0.421 |
|
|
|
|
|
|
|
35 |
A |
8 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
36 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
37 |
A |
12 |
7 |
1.00 |
21 |
0.333 |
|
|
|
|
|
|
|
38 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
39 |
A |
17 |
9 |
1.00 |
21 |
0.429 |
|
|
|
|
|
|
|
40 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
41 |
A |
19 |
8 |
1.00 |
21 |
0.381 |
|
|
|
|
|
|
|
42 |
A |
7 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
43 |
A |
16 |
9 |
1.00 |
19 |
0.474 |
|
|
|
|
|
|
|
44 |
A |
10 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
45 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
46 |
A |
14 |
9 |
1.00 |
21 |
0.429 |
|
|
|
|
|
|
|
47 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
48 |
A |
21 |
9 |
1.00 |
21 |
0.429 |
|
|
|
|
|
|
|
49 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
50 |
A |
25 |
9 |
1.00 |
21 |
0.429 |
|
|
|
|
|
|
|
51 |
A |
13 |
9 |
1.00 |
21 |
0.429 |
|
|
|
|
|
|
|
52 |
A |
8 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
53 |
A |
10 |
9 |
1.00 |
21 |
0.429 |
|
|
|
|
|
|
|
54 |
A |
7 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
55 |
A |
6 |
6 |
1.00 |
19 |
0.316 |
|
|
|
|
|
|
|
56 |
A |
6 |
5 |
1.00 |
19 |
0.263 |
|
|
|
|
|
|
|
57 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
58 |
A |
15 |
11 |
1.00 |
21 |
0.524 |
|
|
|
|
|
|
|
59 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
60 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
61 |
A |
9 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
62 |
A |
8 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
63 |
A |
7 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
64 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
65 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
66 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
67 |
A |
9 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
68 |
A |
8 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
69 |
A |
7 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
70 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
71 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
72 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
73 |
A |
8 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
74 |
A |
7 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
75 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
76 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
77 |
A |
3 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
78 |
A |
6 |
5 |
1.00 |
9 |
0.556 |
|
|
|
|
|
|
|
79 |
A |
8 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
80 |
A |
6 |
5 |
1.00 |
21 |
0.238 |
|
|
|
|
|
|
|
81 |
A |
5 |
4 |
1.00 |
19 |
0.210 |
|
|
|
|
|
|
|
82 |
A |
14 |
6 |
1.00 |
21 |
0.286 |
|
|
|
|
|
|
|
83 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
84 |
A |
7 |
4 |
1.00 |
21 |
0.190 |
|
|
|
|
|
|
|
85 |
A |
6 |
4 |
1.00 |
21 |
0.190 |
|
|
|
|
|
|
|
86 |
A |
2 |
2 |
1.00 |
21 |
0.095 |
|
|
|
|
|
|
|
87 |
A |
4 |
4 |
1.00 |
21 |
0.190 |
|
|
|
|
|
|
|
88 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
89 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
90 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
91 |
A |
0 |
0 |
0.00 |
0 |
0.000 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|