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
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 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, 58, 59, 60, 62, 63, 64,
65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 79, 82 }
B grade: { 5, 8, 10, 18, 25, 57, 61, 80, 83 }
C grade: { }
F grade: { 75, 78, 81, 84}
2.1.3 Maple
A grade: { 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49,
50, 53, 54, 55, 58, 59, 60, 61, 64, 65, 66, 70, 71, 72 }
B grade: { 27, 69 }
C grade: { 73, 74, 76, 77, 79, 80 }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 62, 63, 67,
68, 75, 78, 81, 82, 83, 84 }
2.1.4 Maxima
A grade: { 2, 4, 5, 6, 7, 9, 11, 14, 22, 34, 53, 58, 59, 61, 72
B grade: { 8, 10, 12, 15, 31, 32, 33, 36, 37, 38, 51, 52, 56, 57 }
C grade: { }
F grade: { 1, 3, 13, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 35, 39, 40, 41, 42, 43, 44, 45, 46, 47,
48, 49, 50, 54, 55, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84
}
2.1.5 FriCAS
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 53,
54, 55, 59, 60, 64, 65, 66, 70, 71, 72, 73, 76, 79, 82 }
B grade: { 3, 10, 12, 15, 18, 25, 27, 58, 61, 69, 74, 77, 80, 83 }
C grade: { 1, 8, 16, 23, 75, 78, 81, 84 }
F grade: { 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 62, 63, 67, 68 }
2.1.6 Sympy
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 17, 19, 21, 22, 24, 26, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 53, 54,
55, 58, 59, 60, 65, 66, 70 }
B grade: { }
C grade: { }
F grade: { 1, 3, 8, 10, 12, 15, 16, 18, 20, 23, 25, 27, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47,
48, 51, 52, 56, 57, 61, 62, 63, 64, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84
}
2.1.7 Giac
A grade: { 2, 4, 5, 6, 7, 9, 11, 13, 14, 17, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50,
53, 54, 55, 59, 60, 64, 65, 66, 69, 70, 71, 72 }
B grade: { 12, 15, 58, 61 }
C grade: { }
F grade: { 1, 3, 8, 10, 16, 18, 23, 25, 31, 32, 33, 36, 37, 38, 41, 42, 43, 46, 47, 48, 51, 52, 56, 57, 62, 63, 67,
68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84 }
2.2 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2)
if the failure was due to an exception being raised, which could indicate a bug in the system. If
the failure was due to integral not being evaluated within the time limit, then it is given just an
F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 159 | 0 | 0 | 1126 | 0 | 0 |
normalized size | 1 | 1. | 1.23 | 0. | 0. | 8.73 | 0. | 0. |
time (sec) |
N/A |
0.15 |
0.259 |
0.15 |
0. |
0.567 |
0. |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.016 |
3.241 |
0.124 |
0. |
0. |
0. |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 118 | 0 | 0 | 757 | 0 | 0 |
normalized size | 1 | 1. | 1.4 | 0. | 0. | 9.01 | 0. | 0. |
time (sec) |
N/A |
0.083 |
0.093 |
0.118 |
0. |
0.547 |
0. |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.016 |
2.541 |
0.115 |
0. |
0. |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 57 | 39 | 42 | 119 | 42 | 41 |
normalized size | 1 | 1. | 2.19 | 1.5 | 1.62 | 4.58 | 1.62 | 1.58 |
time (sec) |
N/A |
0.023 |
0.027 |
0.019 |
0.968 |
0.511 |
2.431 |
1.212 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.017 |
2.318 |
0.087 |
0. |
0. |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.017 |
2.389 |
0.106 |
0. |
0. |
0. |
0. |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
F |
B |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 639 | 0 | 1087 | 1723 | 0 | 0 |
normalized size | 1 | 1. | 2.8 | 0. | 4.77 | 7.56 | 0. | 0. |
time (sec) |
N/A |
0.369 |
3.148 |
0.268 |
1.579 |
0.611 |
0. |
0. |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.023 |
13.661 |
0.238 |
0. |
0. |
0. |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
F |
B |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 268 | 0 | 819 | 1148 | 0 | 0 |
normalized size | 1 | 1. | 2.14 | 0. | 6.55 | 9.18 | 0. | 0. |
time (sec) |
N/A |
0.159 |
4.915 |
0.325 |
1.463 |
0.59 |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.023 |
13.503 |
0.294 |
0. |
0. |
0. |
0. |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 86 | 61 | 132 | 236 | 0 | 113 |
normalized size | 1 | 1. | 1.91 | 1.36 | 2.93 | 5.24 | 0. | 2.51 |
time (sec) |
N/A |
0.051 |
0.397 |
0.03 |
0.958 |
0.505 |
0. |
1.182 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
30.345 |
0.221 |
0. |
0. |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
16.789 |
0.237 |
0. |
0. |
0. |
0. |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 167 | 94 | 4783 | 463 | 0 | 285 |
normalized size | 1 | 1. | 1.86 | 1.04 | 53.14 | 5.14 | 0. | 3.17 |
time (sec) |
N/A |
0.076 |
0.089 |
0.023 |
1.399 |
0.498 |
0. |
1.193 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
F |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 488 | 0 | 0 | 3459 | 0 | 0 |
normalized size |
1 |
1. |
1.23 |
0. |
0. |
8.73 |
0. |
0. |
time (sec) |
N/A |
0.946 |
1.155 |
0.319 |
0. |
0.796 |
0. |
0. |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
1.538 |
0.257 |
0. |
0. |
0. |
0. |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
B |
F |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 271 | 271 | 987 | 0 | 0 | 2526 | 0 | 0 |
normalized size |
1 |
1. |
3.64 |
0. |
0. |
9.32 |
0. |
0. |
time (sec) |
N/A |
0.569 |
4.31 |
0.33 |
0. |
0.945 |
0. |
0. |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
1.349 |
0.232 |
0. |
0. |
0. |
0. |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-1) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 66 | 73 | 0 | 560 | 0 | 113 |
normalized size |
1 |
1. |
1.05 |
1.16 |
0. |
8.89 |
0. |
1.79 |
time (sec) |
N/A |
0.118 |
0.175 |
0.063 |
0. |
0.524 |
0. |
1.142 |
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|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
1.073 |
0.095 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.017 |
0.273 |
0.008 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
C |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1124 | 1124 | 2033 | 0 | 0 | 6602 | 0 | 0 |
normalized size |
1 |
1. |
1.81 |
0. |
0. |
5.87 |
0. |
0. |
time (sec) |
N/A |
2.378 |
9.351 |
0.466 |
0. |
1.133 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
15.572 |
0.37 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 616 | 616 | 2446 | 0 | 0 | 4188 | 0 | 0 |
normalized size |
1 |
1. |
3.97 |
0. |
0. |
6.8 |
0. |
0. |
time (sec) |
N/A |
1.201 |
15.315 |
0.53 |
0. |
1.075 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
11.168 |
0.284 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 120 | 120 | 158 | 261 | 0 | 1138 | 0 | 235 |
normalized size |
1 |
1. |
1.32 |
2.17 |
0. |
9.48 |
0. |
1.96 |
time (sec) |
N/A |
0.242 |
0.667 |
0.086 |
0. |
0.572 |
0. |
1.341 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
21.073 |
0.364 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
16.53 |
0.414 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
16.497 |
0.466 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 432 | 432 | 445 | 0 | 2022 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 0. | 4.68 | 0. | 0. | 0. |
time (sec) |
N/A |
0.426 |
0.513 |
0.122 |
1.861 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 316 | 316 | 333 | 0 | 1291 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.05 | 0. | 4.09 | 0. | 0. | 0. |
time (sec) |
N/A |
0.289 |
0.344 |
0.109 |
1.606 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 260 | 0 | 721 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.3 | 0. | 3.6 | 0. | 0. | 0. |
time (sec) |
N/A |
0.178 |
0.377 |
0.11 |
1.383 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.017 |
5.107 |
0.108 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.017 |
6.085 |
0.135 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 695 | 695 | 954 | 0 | 8640 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.37 |
0. |
12.43 |
0. |
0. |
0. |
time (sec) |
N/A |
0.82 |
20.85 |
0.181 |
3.538 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 513 | 513 | 779 | 0 | 5207 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.52 | 0. | 10.15 | 0. | 0. | 0. |
time (sec) |
N/A |
0.612 |
13.711 |
0.199 |
2.279 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 333 | 333 | 449 | 0 | 2624 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.35 | 0. | 7.88 | 0. | 0. | 0. |
time (sec) |
N/A |
0.432 |
8.221 |
0.182 |
1.658 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.021 |
40.841 |
0.181 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
21.59 |
0.191 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1075 | 1075 | 1176 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.493 |
2.338 |
0.239 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 807 | 807 | 898 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.11 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.218 |
1.841 |
0.144 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 539 | 539 | 659 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.22 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.972 |
1.593 |
0.108 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.026 |
2.365 |
0.112 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.015 |
0.604 |
0.008 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3205 | 3205 | 3831 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.2 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
4.24 |
14.847 |
0.25 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2385 | 2385 | 2829 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.19 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
3.362 |
14.091 |
0.242 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1565 | 1565 | 1729 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.1 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.699 |
14.463 |
0.181 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
40.582 |
0.161 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
29.079 |
0.181 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 258 | 258 | 286 | 0 | 986 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.11 | 0. | 3.82 | 0. | 0. | 0. |
time (sec) |
N/A |
0.238 |
0.48 |
0.106 |
1.506 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 144 | 144 | 191 | 0 | 500 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.33 | 0. | 3.47 | 0. | 0. | 0. |
time (sec) |
N/A |
0.126 |
3.55 |
0.116 |
1.383 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 52 | 32 | 42 | 130 | 58 | 41 |
normalized size | 1 | 1. | 2. | 1.23 | 1.62 | 5. | 2.23 | 1.58 |
time (sec) |
N/A |
0.022 |
0.093 |
0.024 |
0.986 |
0.515 |
3.848 |
1.496 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.014 |
6.607 |
0.117 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.014 |
6.603 |
0.131 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 421 | 421 | 749 | 0 | 3800 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.78 | 0. | 9.03 | 0. | 0. | 0. |
time (sec) |
N/A |
0.538 |
8.357 |
0.195 |
1.858 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
B |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 241 | 241 | 681 | 0 | 1648 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.83 | 0. | 6.84 | 0. | 0. | 0. |
time (sec) |
N/A |
0.326 |
3.804 |
0.197 |
1.446 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 93 | 62 | 70 | 277 | 90 | 112 |
normalized size | 1 | 1. | 1.98 | 1.32 | 1.49 | 5.89 | 1.91 | 2.38 |
time (sec) |
N/A |
0.053 |
0.443 |
0.039 |
0.986 |
0.525 |
7.742 |
1.52 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
21.113 |
0.19 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.022 |
22.494 |
0.201 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 57 | 24 | 46 | 198 | 0 | 95 |
normalized size | 1 | 1. | 2.38 | 1. | 1.92 | 8.25 | 0. | 3.96 |
time (sec) |
N/A |
0.021 |
0.039 |
0.023 |
0.989 |
0.489 |
0. |
1.313 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 675 | 675 | 757 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.12 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.116 |
1.982 |
0.119 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 407 | 407 | 512 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.26 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.865 |
10.897 |
0.112 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 66 | 68 | 74 | 0 | 630 | 0 | 113 |
normalized size |
1 |
1. |
1.03 |
1.12 |
0. |
9.55 |
0. |
1.71 |
time (sec) |
N/A |
0.105 |
0.218 |
0.086 |
0. |
0.545 |
0. |
1.377 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
3.602 |
0.108 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.025 |
3.618 |
0.105 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1977 | 1977 | 2293 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.16 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.985 |
13.292 |
0.259 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1157 | 1157 | 846 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.73 |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
2.14 |
8.336 |
0.174 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 172 | 263 | 0 | 1312 | 0 | 235 |
normalized size |
1 |
1. |
1.38 |
2.1 |
0. |
10.5 |
0. |
1.88 |
time (sec) |
N/A |
0.215 |
0.755 |
0.121 |
0. |
0.596 |
0. |
1.442 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
26.701 |
0.167 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
F(-1) |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.024 |
28.199 |
0.176 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
0. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.049 |
2.79 |
0.472 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 61 | 158 | 0 | 165 | 0 | 0 |
normalized size |
1 |
1. |
1.36 |
3.51 |
0. |
3.67 |
0. |
0. |
time (sec) |
N/A |
0.05 |
0.126 |
0.346 |
0. |
0.521 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 185 | 739 | 0 | 979 | 0 | 0 |
normalized size |
1 |
1. |
1.31 |
5.24 |
0. |
6.94 |
0. |
0. |
time (sec) |
N/A |
0.109 |
0.219 |
0.658 |
0. |
0.588 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
C |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 0 | 0 | 0 | 1432 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
6.48 |
0. |
0. |
time (sec) |
N/A |
0.184 |
4.007 |
0.711 |
0. |
0.618 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 102 | 275 | 0 | 288 | 0 | 0 |
normalized size |
1 |
1. |
1.27 |
3.44 |
0. |
3.6 |
0. |
0. |
time (sec) |
N/A |
0.092 |
0.698 |
0.334 |
0. |
0.534 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 286 | 674 | 0 | 1415 | 0 | 0 |
normalized size |
1 |
1. |
1.34 |
3.15 |
0. |
6.61 |
0. |
0. |
time (sec) |
N/A |
0.2 |
6.171 |
0.333 |
0. |
0.644 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-2) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 0 | 0 | 0 | 2184 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
5.79 |
0. |
0. |
time (sec) |
N/A |
0.396 |
12.912 |
1.053 |
0. |
0.717 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-1) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 79 | 315 | 0 | 639 | 0 | 0 |
normalized size |
1 |
1. |
0.93 |
3.71 |
0. |
7.52 |
0. |
0. |
time (sec) |
N/A |
0.154 |
0.274 |
0.396 |
0. |
0.557 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F(-1) |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 338 | 338 | 1003 | 1332 | 0 | 2865 | 0 | 0 |
normalized size |
1 |
1. |
2.97 |
3.94 |
0. |
8.48 |
0. |
0. |
time (sec) |
N/A |
0.621 |
5.108 |
0.658 |
0. |
0.953 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 499 | 499 | 0 | 0 | 0 | 3856 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
7.73 |
0. |
0. |
time (sec) |
N/A |
0.941 |
1.97 |
0.733 |
0. |
0.88 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F(-1) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 156 | 176 | 0 | 0 | 1353 | 0 | 0 |
normalized size |
1 |
1. |
1.13 |
0. |
0. |
8.67 |
0. |
0. |
time (sec) |
N/A |
0.286 |
0.959 |
180. |
0. |
0.609 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F(-1) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 778 | 778 | 2839 | 0 | 0 | 5230 | 0 | 0 |
normalized size |
1 |
1. |
3.65 |
0. |
0. |
6.72 |
0. |
0. |
time (sec) |
N/A |
1.302 |
10.357 |
180. |
0. |
1.253 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1417 | 1417 | 0 | 0 | 0 | 8043 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
5.68 |
0. |
0. |
time (sec) |
N/A |
2.442 |
10.602 |
1.539 |
0. |
1.309 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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 [23] had the largest ratio of [ 0.6667
]
|
|
|
|
|
|
|
| Table 2.1Rubi specific breakdown of results for each
integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
10 |
6 |
1. |
16 |
0.375 |
|
|
|
|
|
|
|
2 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
3 |
A |
8 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
4 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
5 |
A |
4 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
6 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
7 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
8 |
A |
15 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
9 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
10 |
A |
10 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
11 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
12 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
13 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
14 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
15 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
16 |
A |
13 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
17 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
18 |
A |
11 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
19 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
20 |
A |
5 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
|
21 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
22 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
23 |
A |
31 |
12 |
1. |
18 |
0.667 |
|
|
|
|
|
|
|
24 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
25 |
A |
22 |
10 |
1. |
18 |
0.556 |
|
|
|
|
|
|
|
26 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
27 |
A |
7 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
28 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
29 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
30 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
31 |
A |
20 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
32 |
A |
16 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
33 |
A |
12 |
7 |
1. |
16 |
0.438 |
|
|
|
|
|
|
|
34 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
35 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
36 |
A |
30 |
10 |
1. |
20 |
0.5 |
|
|
|
|
|
|
|
37 |
A |
24 |
10 |
1. |
20 |
0.5 |
|
|
|
|
|
|
|
38 |
A |
18 |
10 |
1. |
18 |
0.556 |
|
|
|
|
|
|
|
39 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
40 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
41 |
A |
23 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
42 |
A |
19 |
9 |
1. |
20 |
0.45 |
|
|
|
|
|
|
|
43 |
A |
15 |
9 |
1. |
18 |
0.5 |
|
|
|
|
|
|
|
44 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
45 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
46 |
A |
61 |
11 |
1. |
20 |
0.55 |
|
|
|
|
|
|
|
47 |
A |
49 |
11 |
1. |
20 |
0.55 |
|
|
|
|
|
|
|
48 |
A |
37 |
11 |
1. |
18 |
0.611 |
|
|
|
|
|
|
|
49 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
50 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
51 |
A |
14 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
52 |
A |
10 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
53 |
A |
4 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
54 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
55 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
56 |
A |
21 |
10 |
1. |
22 |
0.454 |
|
|
|
|
|
|
|
57 |
A |
15 |
11 |
1. |
22 |
0.5 |
|
|
|
|
|
|
|
58 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
59 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
60 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
61 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
62 |
A |
17 |
9 |
1. |
22 |
0.409 |
|
|
|
|
|
|
|
63 |
A |
13 |
8 |
1. |
22 |
0.364 |
|
|
|
|
|
|
|
64 |
A |
5 |
5 |
1. |
22 |
0.227 |
|
|
|
|
|
|
|
65 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
66 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
67 |
A |
43 |
11 |
1. |
22 |
0.5 |
|
|
|
|
|
|
|
68 |
A |
31 |
12 |
1. |
22 |
0.546 |
|
|
|
|
|
|
|
69 |
A |
7 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
70 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
71 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
72 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
73 |
A |
5 |
4 |
1. |
20 |
0.2 |
|
|
|
|
|
|
|
74 |
A |
9 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
75 |
A |
11 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
76 |
A |
6 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
77 |
A |
11 |
8 |
1. |
24 |
0.333 |
|
|
|
|
|
|
|
78 |
A |
16 |
12 |
1. |
24 |
0.5 |
|
|
|
|
|
|
|
79 |
A |
6 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
80 |
A |
12 |
8 |
1. |
24 |
0.333 |
|
|
|
|
|
|
|
|
81 |
A |
14 |
9 |
1. |
24 |
0.375 |
|
|
|
|
|
|
|
82 |
A |
8 |
8 |
1. |
22 |
0.364 |
|
|
|
|
|
|
|
83 |
A |
23 |
11 |
1. |
24 |
0.458 |
|
|
|
|
|
|
|
84 |
A |
32 |
13 |
1. |
24 |
0.542 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|