Chapter 2
detailed summary tables of results
2.1 List of integrals sorted by grade for each CAS
2.1.1 Rubi
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112,
113 }
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 79, 80, 81, 82, 83,
84, 85, 86, 87, 88, 89, 90, 91, 92, 93 }
B grade: { 106, 113 }
C grade: { 31, 37, 38, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 94,
95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112 }
F grade: { }
2.1.3 Maple
A grade: { 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 22, 23, 24, 25, 30, 31, 32, 36, 37, 38, 39, 43,
44, 45, 46, 47, 48, 53, 54, 55, 56, 61, 62, 63, 64, 69, 70, 71, 75, 76, 78, 83, 84, 85, 86, 91, 92, 93
}
B grade: { 1, 2, 10, 11, 12, 18, 19, 20, 21, 26, 27, 28, 29, 33, 34, 35, 40, 41, 42, 49, 50, 51, 52, 57, 58, 59,
60, 65, 66, 67, 68, 72, 73, 74, 77, 79, 80, 81, 82, 87, 88, 89, 90 }
C grade: { 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
}
F grade: { }
2.1.4 Maxima
A grade: { 3, 4, 11, 43
B grade: { 1, 2, 10, 12, 40, 41, 42, 49, 50, 51, 79, 80, 81, 82, 87, 88 }
C grade: { 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 21, 22, 30, 36, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 83, 84, 85, 86,
89, 90, 91, 92, 93 }
F grade: { 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 57, 58, 59, 60, 61, 62, 63, 64,
65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106,
107, 108, 109, 110, 111, 112, 113 }
2.1.5 FriCAS
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, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 79, 80, 81, 82, 83, 84,
85, 86, 87, 88, 89, 90, 91, 92, 93 }
B grade: { 36, 37, 38, 39 }
C grade: { 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 94, 95, 96, 97,
98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113 }
F grade: { }
2.1.6 Sympy
A grade: { 1, 2, 3, 4, 5, 10, 11, 12, 13, 40, 41, 42, 43, 44, 49, 50, 51, 52, 79, 80, 81, 82, 83, 87, 88, 89
}
B grade: { }
C grade: { }
F grade: { 6, 7, 8, 9, 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, 45, 46, 47, 48, 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, 84, 85, 86, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110, 111, 112, 113 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 10, 11, 12, 40, 41, 42, 43, 49, 50, 51, 79, 80, 81, 82, 87, 88 }
B grade: { }
C grade: { 6, 7, 8, 9, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 46, 47, 48, 56, 86
}
F grade: { 5, 13, 14, 32, 33, 34, 35, 37, 38, 39, 44, 45, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 83, 84, 85, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113 }
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 |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 82 | 359 | 413 | 190 | 151 | 116 |
normalized size | 1 | 1. | 0.65 | 2.85 | 3.28 | 1.51 | 1.2 | 0.92 |
time (sec) |
N/A |
0.312 |
0.152 |
0.007 |
1.066 |
1.528 |
2.427 |
1.104 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 65 | 225 | 271 | 149 | 117 | 92 |
normalized size | 1 | 1. | 0.68 | 2.34 | 2.82 | 1.55 | 1.22 | 0.96 |
time (sec) |
N/A |
0.208 |
0.134 |
0.006 |
1.03 |
1.677 |
1.182 |
1.096 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 45 | 121 | 158 | 108 | 82 | 66 |
normalized size | 1 | 1. | 0.69 | 1.86 | 2.43 | 1.66 | 1.26 | 1.02 |
time (sec) |
N/A |
0.105 |
0.101 |
0.004 |
1.017 |
1.616 |
0.604 |
1.107 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 27 | 52 | 72 | 70 | 46 | 42 |
normalized size | 1 | 1. | 0.96 | 1.86 | 2.57 | 2.5 | 1.64 | 1.5 |
time (sec) |
N/A |
0.017 |
0.075 |
0.006 |
0.985 |
1.658 |
0.242 |
1.107 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 40 | 31 | 705 | 158 | 37 | 0 |
normalized size |
1 |
1. |
1.38 |
1.07 |
24.31 |
5.45 |
1.28 |
0. |
time (sec) |
N/A |
0.148 |
0.039 |
0.009 |
1.346 |
1.66 |
5.161 |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 60 | 56 | 146 | 270 | 0 | 768 |
normalized size | 1 | 1. | 1.25 | 1.17 | 3.04 | 5.62 | 0. | 16. |
time (sec) |
N/A |
0.221 |
0.15 |
0.01 |
1.817 |
1.722 |
0. |
1.119 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 76 | 88 | 150 | 351 | 0 | 1075 |
normalized size | 1 | 1. | 0.85 | 0.99 | 1.69 | 3.94 | 0. | 12.08 |
time (sec) |
N/A |
0.27 |
0.281 |
0.013 |
1.961 |
1.647 |
0. |
1.137 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 110 | 117 | 149 | 404 | 0 | 1297 |
normalized size | 1 | 1. | 0.83 | 0.89 | 1.13 | 3.06 | 0. | 9.83 |
time (sec) |
N/A |
0.325 |
0.339 |
0.012 |
2.096 |
1.751 |
0. |
1.143 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 138 | 145 | 151 | 440 | 0 | 1496 |
normalized size | 1 | 1. | 0.83 | 0.87 | 0.91 | 2.65 | 0. | 9.01 |
time (sec) |
N/A |
0.368 |
0.268 |
0.013 |
2.237 |
1.689 |
0. |
1.158 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 101 | 468 | 548 | 270 | 228 | 173 |
normalized size | 1 | 1. | 0.54 | 2.52 | 2.95 | 1.45 | 1.23 | 0.93 |
time (sec) |
N/A |
0.32 |
0.266 |
0.007 |
1.075 |
1.729 |
2.597 |
1.114 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 87 | 281 | 350 | 200 | 172 | 128 |
normalized size | 1 | 1. | 0.64 | 2.08 | 2.59 | 1.48 | 1.27 | 0.95 |
time (sec) |
N/A |
0.186 |
0.212 |
0.008 |
1.038 |
1.652 |
1.28 |
1.109 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 57 | 148 | 190 | 138 | 112 | 88 |
normalized size | 1 | 1. | 1.14 | 2.96 | 3.8 | 2.76 | 2.24 | 1.76 |
time (sec) |
N/A |
0.042 |
0.172 |
0.007 |
1.008 |
1.65 |
0.656 |
1.107 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 51 | 79 | 108 | 230 | 90 | 0 |
normalized size |
1 |
1. |
0.82 |
1.27 |
1.74 |
3.71 |
1.45 |
0. |
time (sec) |
N/A |
0.183 |
0.288 |
0.01 |
2.091 |
1.65 |
3.755 |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 64 | 74 | 166 | 346 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
1.03 |
2.31 |
4.81 |
0. |
0. |
time (sec) |
N/A |
0.242 |
0.254 |
0.019 |
3.286 |
1.766 |
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 |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 95 | 114 | 252 | 421 | 0 | 1596 |
normalized size | 1 | 1. | 0.79 | 0.94 | 2.08 | 3.48 | 0. | 13.19 |
time (sec) |
N/A |
0.34 |
0.404 |
0.016 |
5.308 |
1.737 |
0. |
1.148 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 154 | 158 | 254 | 497 | 0 | 1890 |
normalized size | 1 | 1. | 0.88 | 0.9 | 1.45 | 2.84 | 0. | 10.8 |
time (sec) |
N/A |
0.41 |
0.532 |
0.015 |
6.147 |
1.772 |
0. |
1.162 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 204 | 201 | 254 | 572 | 0 | 2311 |
normalized size | 1 | 1. | 0.82 | 0.81 | 1.02 | 2.31 | 0. | 9.32 |
time (sec) |
N/A |
0.48 |
0.453 |
0.019 |
7.132 |
1.704 |
0. |
1.163 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 158 | 777 | 0 | 473 | 0 | 911 |
normalized size |
1 |
1. |
0.72 |
3.56 |
0. |
2.17 |
0. |
4.18 |
time (sec) |
N/A |
0.464 |
0.676 |
0.013 |
0. |
1.732 |
0. |
1.16 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 152 | 152 | 117 | 514 | 0 | 385 | 0 | 911 |
normalized size |
1 |
1. |
0.77 |
3.38 |
0. |
2.53 |
0. |
5.99 |
time (sec) |
N/A |
0.306 |
0.596 |
0.012 |
0. |
1.812 |
0. |
1.169 |
|
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 87 | 315 | 0 | 319 | 0 | 911 |
normalized size |
1 |
1. |
0.88 |
3.18 |
0. |
3.22 |
0. |
9.2 |
time (sec) |
N/A |
0.262 |
0.321 |
0.007 |
0. |
1.707 |
0. |
1.165 |
|
|
|
|
|
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|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 63 | 180 | 1048 | 251 | 0 | 849 |
normalized size | 1 | 1. | 0.91 | 2.61 | 15.19 | 3.64 | 0. | 12.3 |
time (sec) |
N/A |
0.166 |
0.191 |
0.009 |
2.484 |
1.701 |
0. |
1.152 |
|
|
|
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|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 49 | 73 | 190 | 201 | 0 | 806 |
normalized size | 1 | 1. | 0.96 | 1.43 | 3.73 | 3.94 | 0. | 15.8 |
time (sec) |
N/A |
0.078 |
0.075 |
0.007 |
1.184 |
1.657 |
0. |
1.168 |
|
|
|
|
|
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|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 63 | 99 | 0 | 306 | 0 | 1131 |
normalized size | 1 | 1. | 0.86 | 1.36 | 0. | 4.19 | 0. | 15.49 |
time (sec) |
N/A |
0.261 |
0.166 |
0.011 |
0. |
1.747 |
0. |
1.203 |
|
|
|
|
|
|
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|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 101 | 144 | 0 | 485 | 0 | 3911 |
normalized size | 1 | 1. | 0.89 | 1.26 | 0. | 4.25 | 0. | 34.31 |
time (sec) |
N/A |
0.35 |
0.409 |
0.014 |
0. |
1.721 |
0. |
1.277 |
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 176 | 202 | 0 | 649 | 0 | 6163 |
normalized size | 1 | 1. | 0.93 | 1.07 | 0. | 3.43 | 0. | 32.61 |
time (sec) |
N/A |
0.491 |
0.649 |
0.013 |
0. |
1.907 |
0. |
1.336 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 233 | 233 | 177 | 1214 | 0 | 794 | 0 | 8586 |
normalized size |
1 |
1. |
0.76 |
5.21 |
0. |
3.41 |
0. |
36.85 |
time (sec) |
N/A |
0.509 |
1.015 |
0.02 |
0. |
1.853 |
0. |
1.435 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 181 | 181 | 153 | 848 | 0 | 718 | 0 | 8586 |
normalized size |
1 |
1. |
0.85 |
4.69 |
0. |
3.97 |
0. |
47.44 |
time (sec) |
N/A |
0.408 |
0.88 |
0.016 |
0. |
1.735 |
0. |
1.428 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 117 | 553 | 0 | 626 | 0 | 8462 |
normalized size |
1 |
1. |
0.79 |
3.71 |
0. |
4.2 |
0. |
56.79 |
time (sec) |
N/A |
0.363 |
0.774 |
0.013 |
0. |
1.819 |
0. |
1.421 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 96 | 315 | 0 | 513 | 0 | 8118 |
normalized size |
1 |
1. |
0.77 |
2.54 |
0. |
4.14 |
0. |
65.47 |
time (sec) |
N/A |
0.285 |
0.437 |
0.012 |
0. |
1.718 |
0. |
1.399 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 66 | 107 | 221 | 301 | 0 | 4131 |
normalized size | 1 | 1. | 0.92 | 1.49 | 3.07 | 4.18 | 0. | 57.38 |
time (sec) |
N/A |
0.097 |
0.22 |
0.009 |
1.376 |
1.737 |
0. |
1.251 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
C |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 641 | 210 | 0 | 682 | 0 | 10037 |
normalized size | 1 | 1. | 4.3 | 1.41 | 0. | 4.58 | 0. | 67.36 |
time (sec) |
N/A |
0.41 |
4.206 |
0.014 |
0. |
1.829 |
0. |
1.463 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 184 | 256 | 0 | 923 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
1.36 |
0. |
4.91 |
0. |
0. |
time (sec) |
N/A |
0.514 |
1.954 |
0.012 |
0. |
1.895 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 265 | 265 | 235 | 1208 | 0 | 1115 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
4.56 |
0. |
4.21 |
0. |
0. |
time (sec) |
N/A |
0.61 |
1.053 |
0.016 |
0. |
1.889 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 241 | 241 | 154 | 779 | 0 | 972 | 0 | 0 |
normalized size |
1 |
1. |
0.64 |
3.23 |
0. |
4.03 |
0. |
0. |
time (sec) |
N/A |
0.535 |
1.187 |
0.013 |
0. |
1.492 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
A |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 179 | 179 | 157 | 419 | 0 | 792 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
2.34 |
0. |
4.42 |
0. |
0. |
time (sec) |
N/A |
0.35 |
0.58 |
0.01 |
0. |
1.337 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
B |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 87 | 145 | 269 | 471 | 0 | 7731 |
normalized size | 1 | 1. | 0.84 | 1.39 | 2.59 | 4.53 | 0. | 74.34 |
time (sec) |
N/A |
0.127 |
0.648 |
0.01 |
1.493 |
1.401 |
0. |
1.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 1749 | 359 | 0 | 1212 | 0 | 0 |
normalized size |
1 |
1. |
6.7 |
1.38 |
0. |
4.64 |
0. |
0. |
time (sec) |
N/A |
0.542 |
11.794 |
0.012 |
0. |
1.66 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 299 | 299 | 2108 | 405 | 0 | 1577 | 0 | 0 |
normalized size |
1 |
1. |
7.05 |
1.35 |
0. |
5.27 |
0. |
0. |
time (sec) |
N/A |
0.668 |
6.004 |
0.012 |
0. |
1.702 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
B |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 630 | 466 | 0 | 1833 | 0 | 0 |
normalized size |
1 |
1. |
1.67 |
1.24 |
0. |
4.86 |
0. |
0. |
time (sec) |
N/A |
0.804 |
2.25 |
0.013 |
0. |
1.829 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 92 | 449 | 502 | 209 | 168 | 131 |
normalized size | 1 | 1. | 0.65 | 3.18 | 3.56 | 1.48 | 1.19 | 0.93 |
time (sec) |
N/A |
0.208 |
0.168 |
0.007 |
1.071 |
1.332 |
5.093 |
1.146 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 75 | 302 | 348 | 171 | 134 | 107 |
normalized size | 1 | 1. | 0.68 | 2.72 | 3.14 | 1.54 | 1.21 | 0.96 |
time (sec) |
N/A |
0.163 |
0.143 |
0.007 |
1.043 |
1.357 |
2.99 |
1.168 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 57 | 181 | 223 | 130 | 99 | 81 |
normalized size | 1 | 1. | 0.71 | 2.26 | 2.79 | 1.62 | 1.24 | 1.01 |
time (sec) |
N/A |
0.102 |
0.112 |
0.006 |
1.027 |
1.341 |
1.431 |
1.095 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
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 | 53 | 53 | 41 | 99 | 123 | 93 | 65 | 57 |
normalized size | 1 | 1. | 0.77 | 1.87 | 2.32 | 1.75 | 1.23 | 1.08 |
time (sec) |
N/A |
0.057 |
0.083 |
0.007 |
1.009 |
1.369 |
0.7 |
1.109 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 54 | 60 | 89 | 200 | 63 | 0 |
normalized size |
1 |
1. |
1.32 |
1.46 |
2.17 |
4.88 |
1.54 |
0. |
time (sec) |
N/A |
0.091 |
0.131 |
0.009 |
1.928 |
1.692 |
4.408 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 44 | 48 | 1265 | 212 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.09 |
28.75 |
4.82 |
0. |
0. |
time (sec) |
N/A |
0.107 |
0.095 |
0.013 |
1.903 |
1.742 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 82 | 73 | 165 | 250 | 0 | 1034 |
normalized size | 1 | 1. | 1.11 | 0.99 | 2.23 | 3.38 | 0. | 13.97 |
time (sec) |
N/A |
0.161 |
0.187 |
0.013 |
3.103 |
1.645 |
0. |
1.17 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 106 | 106 | 95 | 102 | 166 | 290 | 0 | 1126 |
normalized size | 1 | 1. | 0.9 | 0.96 | 1.57 | 2.74 | 0. | 10.62 |
time (sec) |
N/A |
0.207 |
0.187 |
0.013 |
3.414 |
1.777 |
0. |
1.198 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 125 | 131 | 163 | 340 | 0 | 1466 |
normalized size | 1 | 1. | 0.84 | 0.88 | 1.09 | 2.28 | 0. | 9.84 |
time (sec) |
N/A |
0.258 |
0.228 |
0.015 |
3.772 |
1.727 |
0. |
1.158 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 236 | 236 | 139 | 746 | 826 | 333 | 286 | 219 |
normalized size | 1 | 1. | 0.59 | 3.16 | 3.5 | 1.41 | 1.21 | 0.93 |
time (sec) |
N/A |
0.327 |
0.393 |
0.007 |
1.176 |
1.571 |
9.837 |
1.131 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 185 | 185 | 113 | 514 | 591 | 270 | 226 | 174 |
normalized size | 1 | 1. | 0.61 | 2.78 | 3.19 | 1.46 | 1.22 | 0.94 |
time (sec) |
N/A |
0.235 |
0.251 |
0.007 |
1.116 |
1.734 |
5.39 |
1.105 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 86 | 336 | 394 | 204 | 172 | 134 |
normalized size | 1 | 1. | 0.62 | 2.43 | 2.86 | 1.48 | 1.25 | 0.97 |
time (sec) |
N/A |
0.163 |
0.198 |
0.007 |
1.054 |
1.772 |
3.037 |
1.105 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 82 | 236 | 157 | 300 | 160 | 0 |
normalized size |
1 |
1. |
0.74 |
2.13 |
1.41 |
2.7 |
1.44 |
0. |
time (sec) |
N/A |
0.172 |
0.405 |
0.013 |
7.84 |
1.671 |
6.393 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 97 | 156 | 131 | 293 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.61 |
1.35 |
3.02 |
0. |
0. |
time (sec) |
N/A |
0.163 |
0.275 |
0.025 |
7.721 |
1.785 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 99 | 124 | 203 | 344 | 0 | 0 |
normalized size |
1 |
1. |
0.87 |
1.09 |
1.78 |
3.02 |
0. |
0. |
time (sec) |
N/A |
0.203 |
0.414 |
0.025 |
16.202 |
1.86 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 114 | 120 | 192 | 363 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
0.9 |
1.43 |
2.71 |
0. |
0. |
time (sec) |
N/A |
0.238 |
0.418 |
0.023 |
11.499 |
1.776 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 122 | 157 | 298 | 409 | 0 | 2021 |
normalized size | 1 | 1. | 0.69 | 0.89 | 1.68 | 2.31 | 0. | 11.42 |
time (sec) |
N/A |
0.333 |
0.458 |
0.022 |
69.44 |
1.734 |
0. |
1.191 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 273 | 273 | 275 | 1656 | 0 | 504 | 0 | 0 |
normalized size |
1 |
1. |
1.01 |
6.07 |
0. |
1.85 |
0. |
0. |
time (sec) |
N/A |
0.73 |
0.484 |
0.052 |
0. |
1.949 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 202 | 1184 | 0 | 406 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
5.67 |
0. |
1.94 |
0. |
0. |
time (sec) |
N/A |
0.348 |
0.415 |
0.036 |
0. |
1.82 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 216 | 798 | 0 | 401 | 0 | 0 |
normalized size |
1 |
1. |
0.95 |
3.52 |
0. |
1.77 |
0. |
0. |
time (sec) |
N/A |
0.365 |
0.362 |
0.026 |
0. |
1.881 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 163 | 494 | 0 | 308 | 0 | 0 |
normalized size |
1 |
1. |
0.92 |
2.79 |
0. |
1.74 |
0. |
0. |
time (sec) |
N/A |
0.248 |
0.223 |
0.016 |
0. |
1.776 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 172 | 229 | 0 | 377 | 0 | 0 |
normalized size | 1 | 1. | 0.81 | 1.08 | 0. | 1.77 | 0. | 0. |
time (sec) |
N/A |
0.239 |
0.223 |
0.013 |
0. |
1.957 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 179 | 200 | 0 | 375 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 1.02 | 0. | 1.9 | 0. | 0. |
time (sec) |
N/A |
0.382 |
0.372 |
0.019 |
0. |
1.782 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 238 | 270 | 0 | 516 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 1.08 | 0. | 2.06 | 0. | 0. |
time (sec) |
N/A |
0.487 |
0.522 |
0.013 |
0. |
1.968 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 247 | 259 | 0 | 517 | 0 | 0 |
normalized size | 1 | 1. | 0.91 | 0.96 | 0. | 1.91 | 0. | 0. |
time (sec) |
N/A |
0.508 |
0.678 |
0.028 |
0. |
1.897 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 450 | 450 | 632 | 3453 | 0 | 714 | 0 | 0 |
normalized size |
1 |
1. |
1.4 |
7.67 |
0. |
1.59 |
0. |
0. |
time (sec) |
N/A |
0.783 |
1.158 |
0.092 |
0. |
1.921 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 583 | 2563 | 0 | 641 | 0 | 0 |
normalized size |
1 |
1. |
1.35 |
5.95 |
0. |
1.49 |
0. |
0. |
time (sec) |
N/A |
0.661 |
0.853 |
0.076 |
0. |
1.888 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 583 | 1804 | 0 | 666 | 0 | 0 |
normalized size |
1 |
1. |
1.4 |
4.34 |
0. |
1.6 |
0. |
0. |
time (sec) |
N/A |
0.573 |
0.814 |
0.06 |
0. |
1.882 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 239 | 239 | 309 | 1109 | 0 | 510 | 0 | 0 |
normalized size |
1 |
1. |
1.29 |
4.64 |
0. |
2.13 |
0. |
0. |
time (sec) |
N/A |
0.315 |
0.398 |
0.037 |
0. |
1.821 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 585 | 495 | 0 | 664 | 0 | 0 |
normalized size | 1 | 1. | 1.23 | 1.04 | 0. | 1.39 | 0. | 0. |
time (sec) |
N/A |
0.806 |
0.628 |
0.024 |
0. |
1.838 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 435 | 435 | 650 | 482 | 0 | 753 | 0 | 0 |
normalized size |
1 |
1. |
1.49 |
1.11 |
0. |
1.73 |
0. |
0. |
time (sec) |
N/A |
0.832 |
1.997 |
0.035 |
0. |
1.981 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 501 | 501 | 768 | 769 | 0 | 848 | 0 | 0 |
normalized size |
1 |
1. |
1.53 |
1.53 |
0. |
1.69 |
0. |
0. |
time (sec) |
N/A |
1.313 |
1.097 |
0.029 |
0. |
2.091 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 647 | 3391 | 0 | 1079 | 0 | 0 |
normalized size |
1 |
1. |
1.36 |
7.12 |
0. |
2.27 |
0. |
0. |
time (sec) |
N/A |
1.008 |
1.945 |
0.099 |
0. |
2.096 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 746 | 746 | 927 | 2310 | 0 | 1176 | 0 | 0 |
normalized size |
1 |
1. |
1.24 |
3.1 |
0. |
1.58 |
0. |
0. |
time (sec) |
N/A |
1.135 |
2.727 |
0.085 |
0. |
2.188 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 512 | 512 | 634 | 1374 | 0 | 1040 | 0 | 0 |
normalized size |
1 |
1. |
1.24 |
2.68 |
0. |
2.03 |
0. |
0. |
time (sec) |
N/A |
0.769 |
1.787 |
0.055 |
0. |
2.005 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 856 | 856 | 932 | 602 | 0 | 1233 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
0.7 |
0. |
1.44 |
0. |
0. |
time (sec) |
N/A |
1.181 |
2.429 |
0.032 |
0. |
2.205 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 730 | 730 | 1384 | 584 | 0 | 1455 | 0 | 0 |
normalized size |
1 |
1. |
1.9 |
0.8 |
0. |
1.99 |
0. |
0. |
time (sec) |
N/A |
1.83 |
7.931 |
0.042 |
0. |
2.129 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 875 | 875 | 1673 | 1375 | 0 | 1493 | 0 | 0 |
normalized size |
1 |
1. |
1.91 |
1.57 |
0. |
1.71 |
0. |
0. |
time (sec) |
N/A |
2.846 |
2.864 |
0.051 |
0. |
2.213 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 995 | 701 | 0 | 1685 | 0 | 0 |
normalized size |
1 |
1. |
1.26 |
0.89 |
0. |
2.13 |
0. |
0. |
time (sec) |
N/A |
1.877 |
2.722 |
0.055 |
0. |
2.401 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 156 | 101 | 556 | 606 | 238 | 185 | 143 |
normalized size | 1 | 1. | 0.65 | 3.56 | 3.88 | 1.53 | 1.19 | 0.92 |
time (sec) |
N/A |
0.249 |
0.208 |
0.007 |
1.088 |
1.592 |
7.184 |
1.104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 84 | 392 | 440 | 197 | 151 | 119 |
normalized size | 1 | 1. | 0.67 | 3.11 | 3.49 | 1.56 | 1.2 | 0.94 |
time (sec) |
N/A |
0.191 |
0.164 |
0.007 |
1.042 |
1.655 |
4.131 |
1.107 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 66 | 258 | 302 | 153 | 116 | 93 |
normalized size | 1 | 1. | 0.69 | 2.72 | 3.18 | 1.61 | 1.22 | 0.98 |
time (sec) |
N/A |
0.132 |
0.134 |
0.005 |
1.01 |
1.732 |
2.199 |
1.106 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 50 | 159 | 190 | 116 | 82 | 73 |
normalized size | 1 | 1. | 0.74 | 2.34 | 2.79 | 1.71 | 1.21 | 1.07 |
time (sec) |
N/A |
0.087 |
0.092 |
0.006 |
0.987 |
1.682 |
1.099 |
1.156 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 50 | 112 | 103 | 221 | 85 | 0 |
normalized size |
1 |
1. |
0.88 |
1.96 |
1.81 |
3.88 |
1.49 |
0. |
time (sec) |
N/A |
0.115 |
0.197 |
0.008 |
2.747 |
1.704 |
4.847 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 56 | 79 | 93 | 234 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.41 |
1.66 |
4.18 |
0. |
0. |
time (sec) |
N/A |
0.117 |
0.135 |
0.016 |
2.548 |
1.716 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 66 | 65 | 1554 | 244 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
0.93 |
22.2 |
3.49 |
0. |
0. |
time (sec) |
N/A |
0.127 |
0.155 |
0.015 |
2.057 |
1.719 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
C |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 104 | 87 | 178 | 359 | 0 | 1075 |
normalized size | 1 | 1. | 1.14 | 0.96 | 1.96 | 3.95 | 0. | 11.81 |
time (sec) |
N/A |
0.196 |
0.208 |
0.014 |
4.02 |
1.706 |
0. |
1.155 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 235 | 235 | 139 | 822 | 894 | 355 | 284 | 217 |
normalized size | 1 | 1. | 0.59 | 3.5 | 3.8 | 1.51 | 1.21 | 0.92 |
time (sec) |
N/A |
0.326 |
0.385 |
0.007 |
1.159 |
1.647 |
12.829 |
1.162 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 112 | 599 | 660 | 282 | 226 | 177 |
normalized size | 1 | 1. | 0.6 | 3.19 | 3.51 | 1.5 | 1.2 | 0.94 |
time (sec) |
N/A |
0.242 |
0.315 |
0.007 |
1.076 |
1.708 |
7.544 |
1.15 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 108 | 487 | 198 | 373 | 211 | 0 |
normalized size |
1 |
1. |
0.67 |
3.02 |
1.23 |
2.32 |
1.31 |
0. |
time (sec) |
N/A |
0.256 |
0.512 |
0.017 |
35.687 |
1.748 |
9.354 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 145 | 365 | 174 | 365 | 0 | 0 |
normalized size |
1 |
1. |
1. |
2.52 |
1.2 |
2.52 |
0. |
0. |
time (sec) |
N/A |
0.233 |
0.368 |
0.031 |
41.272 |
1.757 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 142 | 142 | 138 | 251 | 149 | 355 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
1.77 |
1.05 |
2.5 |
0. |
0. |
time (sec) |
N/A |
0.219 |
0.382 |
0.03 |
12.619 |
1.91 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 135 | 196 | 234 | 478 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
1.3 |
1.55 |
3.17 |
0. |
0. |
time (sec) |
N/A |
0.252 |
0.58 |
0.033 |
45.217 |
2.028 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
C |
A |
F |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 148 | 167 | 224 | 502 | 0 | 0 |
normalized size |
1 |
1. |
0.89 |
1. |
1.34 |
3.01 |
0. |
0. |
time (sec) |
N/A |
0.283 |
0.572 |
0.03 |
37.377 |
2.141 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 371 | 371 | 231 | 559 | 0 | 1030 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
1.51 |
0. |
2.78 |
0. |
0. |
time (sec) |
N/A |
0.915 |
0.527 |
0.026 |
0. |
2.416 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 357 | 357 | 216 | 392 | 0 | 1006 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
1.1 |
0. |
2.82 |
0. |
0. |
time (sec) |
N/A |
0.676 |
0.35 |
0.019 |
0. |
2.228 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 186 | 266 | 0 | 747 | 0 | 0 |
normalized size |
1 |
1. |
0.66 |
0.95 |
0. |
2.66 |
0. |
0. |
time (sec) |
N/A |
0.453 |
0.319 |
0.012 |
0. |
2.119 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 343 | 343 | 196 | 176 | 0 | 977 | 0 | 0 |
normalized size |
1 |
1. |
0.57 |
0.51 |
0. |
2.85 |
0. |
0. |
time (sec) |
N/A |
0.413 |
0.301 |
0.01 |
0. |
2.239 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 343 | 343 | 196 | 85 | 0 | 981 | 0 | 0 |
normalized size | 1 | 1. | 0.57 | 0.25 | 0. | 2.86 | 0. | 0. |
time (sec) |
N/A |
0.429 |
0.204 |
0.01 |
0. |
2.257 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 301 | 301 | 206 | 88 | 0 | 815 | 0 | 0 |
normalized size | 1 | 1. | 0.68 | 0.29 | 0. | 2.71 | 0. | 0. |
time (sec) |
N/A |
0.527 |
0.378 |
0.016 |
0. |
2.246 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 380 | 380 | 233 | 116 | 0 | 1152 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0.31 |
0. |
3.03 |
0. |
0. |
time (sec) |
N/A |
0.609 |
0.486 |
0.023 |
0. |
2.424 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 408 | 408 | 253 | 136 | 0 | 1216 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
0.33 |
0. |
2.98 |
0. |
0. |
time (sec) |
N/A |
0.681 |
0.493 |
0.011 |
0. |
2.394 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 714 | 714 | 383 | 1185 | 0 | 1613 | 0 | 0 |
normalized size |
1 |
1. |
0.54 |
1.66 |
0. |
2.26 |
0. |
0. |
time (sec) |
N/A |
1.073 |
0.422 |
0.08 |
0. |
2.479 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 371 | 371 | 214 | 823 | 0 | 1196 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
2.22 |
0. |
3.22 |
0. |
0. |
time (sec) |
N/A |
0.619 |
0.174 |
0.047 |
0. |
2.341 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 691 | 691 | 408 | 508 | 0 | 1520 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
0.74 |
0. |
2.2 |
0. |
0. |
time (sec) |
N/A |
1.297 |
0.211 |
0.033 |
0. |
2.382 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 735 | 735 | 406 | 248 | 0 | 1658 | 0 | 0 |
normalized size |
1 |
1. |
0.55 |
0.34 |
0. |
2.26 |
0. |
0. |
time (sec) |
N/A |
1.341 |
0.212 |
0.02 |
0. |
2.576 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 693 | 693 | 1819 | 233 | 0 | 1493 | 0 | 0 |
normalized size |
1 |
1. |
2.62 |
0.34 |
0. |
2.15 |
0. |
0. |
time (sec) |
N/A |
1.485 |
8.791 |
0.031 |
0. |
2.575 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 712 | 712 | 445 | 283 | 0 | 1713 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
0.4 |
0. |
2.41 |
0. |
0. |
time (sec) |
N/A |
1.602 |
1.103 |
0.033 |
0. |
2.814 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 800 | 800 | 470 | 388 | 0 | 2118 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
0.48 |
0. |
2.65 |
0. |
0. |
time (sec) |
N/A |
1.788 |
1.12 |
0.024 |
0. |
2.861 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 772 | 772 | 457 | 2032 | 0 | 2021 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
2.63 |
0. |
2.62 |
0. |
0. |
time (sec) |
N/A |
2.766 |
0.613 |
0.129 |
0. |
2.703 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 777 | 777 | 449 | 1394 | 0 | 2221 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
1.79 |
0. |
2.86 |
0. |
0. |
time (sec) |
N/A |
1.528 |
0.403 |
0.083 |
0. |
2.721 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-1) |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1141 | 1141 | 698 | 845 | 0 | 2934 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0.74 |
0. |
2.57 |
0. |
0. |
time (sec) |
N/A |
3.116 |
0.552 |
0.059 |
0. |
3.045 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1161 | 1161 | 675 | 392 | 0 | 2813 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
0.34 |
0. |
2.42 |
0. |
0. |
time (sec) |
N/A |
3.368 |
0.431 |
0.031 |
0. |
3.034 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
C |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1163 | 1163 | 2929 | 363 | 0 | 2763 | 0 | 0 |
normalized size |
1 |
1. |
2.52 |
0.31 |
0. |
2.38 |
0. |
0. |
time (sec) |
N/A |
3.893 |
11.69 |
0.051 |
0. |
2.988 |
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 [112] had the largest ratio of [ 0.625
]
|
|
|
|
|
|
|
| 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 |
11 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
2 |
A |
9 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
3 |
A |
7 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
4 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
5 |
A |
6 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
6 |
A |
9 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
7 |
A |
11 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
8 |
A |
13 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
9 |
A |
15 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
10 |
A |
14 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
11 |
A |
11 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
12 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
13 |
A |
8 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
14 |
A |
10 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
15 |
A |
14 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
16 |
A |
17 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
17 |
A |
20 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
18 |
A |
15 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
19 |
A |
11 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
20 |
A |
8 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
|
21 |
A |
6 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
22 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
23 |
A |
8 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
24 |
A |
12 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
25 |
A |
17 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
26 |
A |
15 |
8 |
1. |
17 |
0.471 |
|
|
|
|
|
|
|
27 |
A |
12 |
8 |
1. |
17 |
0.471 |
|
|
|
|
|
|
|
28 |
A |
10 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
29 |
A |
9 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
30 |
A |
4 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
31 |
A |
12 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
32 |
A |
16 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
33 |
A |
15 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
34 |
A |
14 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
35 |
A |
11 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
36 |
A |
5 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
37 |
A |
17 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
38 |
A |
21 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
39 |
A |
26 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
40 |
A |
12 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
|
41 |
A |
10 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
42 |
A |
8 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
43 |
A |
6 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
44 |
A |
7 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
45 |
A |
7 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
46 |
A |
10 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
47 |
A |
12 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
48 |
A |
14 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
49 |
A |
17 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
50 |
A |
14 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
51 |
A |
11 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
52 |
A |
11 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
53 |
A |
10 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
54 |
A |
12 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
55 |
A |
13 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
56 |
A |
17 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
57 |
A |
14 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
58 |
A |
12 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
59 |
A |
11 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
60 |
A |
8 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
|
61 |
A |
8 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
62 |
A |
13 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
63 |
A |
14 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
64 |
A |
18 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
65 |
A |
24 |
9 |
1. |
19 |
0.474 |
|
|
|
|
|
|
|
66 |
A |
20 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
67 |
A |
17 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
68 |
A |
9 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
69 |
A |
18 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
70 |
A |
22 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
71 |
A |
32 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
72 |
A |
27 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
73 |
A |
28 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
74 |
A |
19 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
75 |
A |
28 |
5 |
1. |
16 |
0.312 |
|
|
|
|
|
|
|
76 |
A |
41 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
77 |
A |
60 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
78 |
A |
46 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
79 |
A |
13 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
80 |
A |
11 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
|
81 |
A |
9 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
82 |
A |
7 |
4 |
1. |
14 |
0.286 |
|
|
|
|
|
|
|
83 |
A |
8 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
84 |
A |
8 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
85 |
A |
8 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
86 |
A |
11 |
5 |
1. |
17 |
0.294 |
|
|
|
|
|
|
|
87 |
A |
17 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
88 |
A |
14 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
89 |
A |
14 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
90 |
A |
13 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
91 |
A |
12 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
92 |
A |
14 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
93 |
A |
15 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
94 |
A |
15 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
95 |
A |
14 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
96 |
A |
11 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
97 |
A |
11 |
4 |
1. |
17 |
0.235 |
|
|
|
|
|
|
|
98 |
A |
11 |
4 |
1. |
16 |
0.25 |
|
|
|
|
|
|
|
99 |
A |
16 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
100 |
A |
17 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
|
101 |
A |
18 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
102 |
A |
23 |
6 |
1. |
19 |
0.316 |
|
|
|
|
|
|
|
103 |
A |
12 |
5 |
1. |
19 |
0.263 |
|
|
|
|
|
|
|
104 |
A |
34 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
105 |
A |
36 |
8 |
1. |
16 |
0.5 |
|
|
|
|
|
|
|
106 |
A |
41 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
107 |
A |
47 |
7 |
1. |
19 |
0.368 |
|
|
|
|
|
|
|
108 |
A |
51 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
109 |
A |
71 |
10 |
1. |
19 |
0.526 |
|
|
|
|
|
|
|
110 |
A |
37 |
9 |
1. |
19 |
0.474 |
|
|
|
|
|
|
|
111 |
A |
89 |
9 |
1. |
17 |
0.529 |
|
|
|
|
|
|
|
112 |
A |
99 |
10 |
1. |
16 |
0.625 |
|
|
|
|
|
|
|
113 |
A |
110 |
9 |
1. |
19 |
0.474 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|