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
}
B grade: { }
C grade: { }
F grade: { }
2.1.2 Mathematica
A grade: { 8, 10, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 90, 91, 92, 96, 97, 98,
101, 102, 103, 104, 105, 106 }
B grade: { 1, 95 }
C grade: { 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 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, 93, 94, 99, 100 }
F grade: { 89}
2.1.3 Maple
A grade: { 8, 9, 10, 11, 12, 13, 14, 29, 30, 31, 32, 33, 34, 51, 52, 54, 55, 69, 70, 71, 72, 73, 74
}
B grade: { 2, 3, 4, 5, 6, 7, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 35, 36, 37, 38, 39, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 50, 53, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
C grade: { }
F grade: { 1, 88, 89 }
2.1.4 Maxima
A grade: { 92, 93, 94
B grade: { }
C grade: { }
F 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, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
2.1.5 FriCAS
A grade: { 2, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 35, 36, 37, 38, 40, 92 }
B grade: { 3, 4, 5, 6, 7, 27, 39, 90, 91, 93, 94 }
C grade: { }
F grade: { 1, 8, 9, 10, 11, 12, 13, 14, 29, 30, 31, 32, 33, 34, 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, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
2.1.6 Sympy
A grade: { 92 }
B grade: { }
C grade: { }
F 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, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
2.1.7 Giac
A grade: { 92 }
B grade: { 93, 94 }
C grade: { }
F 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, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
}
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 |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 117 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.39 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.028 |
0.307 |
0.388 |
0. |
0. |
0. |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 68 | 388 | 0 | 936 | 0 | 0 |
normalized size |
1 |
1. |
0.59 |
3.34 |
0. |
8.07 |
0. |
0. |
time (sec) |
N/A |
0.157 |
0.181 |
0.041 |
0. |
1.955 |
0. |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 67 | 363 | 0 | 855 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
3.86 |
0. |
9.1 |
0. |
0. |
time (sec) |
N/A |
0.116 |
0.108 |
0.017 |
0. |
2.027 |
0. |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 154 | 337 | 0 | 603 | 0 | 0 |
normalized size |
1 |
1. |
2.17 |
4.75 |
0. |
8.49 |
0. |
0. |
time (sec) |
N/A |
0.078 |
0.283 |
0.018 |
0. |
2.005 |
0. |
0. |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 165 | 327 | 0 | 458 | 0 | 0 |
normalized size |
1 |
1. |
3.37 |
6.67 |
0. |
9.35 |
0. |
0. |
time (sec) |
N/A |
0.044 |
0.212 |
0.028 |
0. |
1.99 |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 191 | 355 | 0 | 803 | 0 | 0 |
normalized size |
1 |
1. |
2.55 |
4.73 |
0. |
10.71 |
0. |
0. |
time (sec) |
N/A |
0.086 |
0.243 |
0.021 |
0. |
2.008 |
0. |
0. |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 99 | 99 | 203 | 374 | 0 | 898 | 0 | 0 |
normalized size |
1 |
1. |
2.05 |
3.78 |
0. |
9.07 |
0. |
0. |
time (sec) |
N/A |
0.135 |
0.431 |
0.02 |
0. |
2.047 |
0. |
0. |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 269 | 269 | 187 | 234 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.7 |
0.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.288 |
1.206 |
0.018 |
0. |
0. |
0. |
0. |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 52 | 213 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.21 |
0.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.235 |
0.37 |
0.021 |
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 |
A |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 244 | 244 | 175 | 204 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
0.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.227 |
0.432 |
0.02 |
0. |
0. |
0. |
0. |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 53 | 186 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.24 |
0.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.2 |
0.243 |
0.024 |
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 |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 236 | 195 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.06 |
0.88 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.208 |
1.783 |
0.02 |
0. |
0. |
0. |
0. |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 247 | 247 | 233 | 216 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
0.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.237 |
1.243 |
0.023 |
0. |
0. |
0. |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 141 | 216 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.57 |
0.87 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.237 |
0.406 |
0.025 |
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 |
C |
B |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 729 | 446 | 0 | 1311 | 0 | 0 |
normalized size |
1 |
1. |
3.92 |
2.4 |
0. |
7.05 |
0. |
0. |
time (sec) |
N/A |
0.3 |
6.096 |
0.025 |
0. |
1.857 |
0. |
0. |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 332 | 419 | 0 | 1206 | 0 | 0 |
normalized size |
1 |
1. |
2.08 |
2.62 |
0. |
7.54 |
0. |
0. |
time (sec) |
N/A |
0.259 |
2.841 |
0.024 |
0. |
1.727 |
0. |
0. |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 315 | 391 | 0 | 900 | 0 | 0 |
normalized size |
1 |
1. |
2.28 |
2.83 |
0. |
6.52 |
0. |
0. |
time (sec) |
N/A |
0.203 |
1.547 |
0.026 |
0. |
1.67 |
0. |
0. |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 292 | 379 | 0 | 863 | 0 | 0 |
normalized size |
1 |
1. |
2.5 |
3.24 |
0. |
7.38 |
0. |
0. |
time (sec) |
N/A |
0.169 |
5.039 |
0.026 |
0. |
1.683 |
0. |
0. |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
C |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 311 | 388 | 0 | 903 | 0 | 0 |
normalized size |
1 |
1. |
2.73 |
3.4 |
0. |
7.92 |
0. |
0. |
time (sec) |
N/A |
0.175 |
2.913 |
0.023 |
0. |
1.686 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 417 | 388 | 0 | 917 | 0 | 0 |
normalized size |
1 |
1. |
3.56 |
3.32 |
0. |
7.84 |
0. |
0. |
time (sec) |
N/A |
0.188 |
6.116 |
0.03 |
0. |
1.593 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 269 | 409 | 0 | 1170 | 0 | 0 |
normalized size |
1 |
1. |
1.91 |
2.9 |
0. |
8.3 |
0. |
0. |
time (sec) |
N/A |
0.229 |
3.319 |
0.026 |
0. |
1.413 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 174 | 430 | 0 | 1262 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
2.61 |
0. |
7.65 |
0. |
0. |
time (sec) |
N/A |
0.296 |
1.997 |
0.026 |
0. |
1.467 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 110 | 394 | 0 | 1019 | 0 | 0 |
normalized size |
1 |
1. |
0.99 |
3.55 |
0. |
9.18 |
0. |
0. |
time (sec) |
N/A |
0.451 |
0.848 |
0.033 |
0. |
1.401 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 107 | 368 | 0 | 860 | 0 | 0 |
normalized size |
1 |
1. |
1.23 |
4.23 |
0. |
9.89 |
0. |
0. |
time (sec) |
N/A |
0.239 |
3.73 |
0.031 |
0. |
1.497 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 98 | 358 | 0 | 857 | 0 | 0 |
normalized size |
1 |
1. |
1.13 |
4.11 |
0. |
9.85 |
0. |
0. |
time (sec) |
N/A |
0.218 |
0.241 |
0.034 |
0. |
1.413 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 107 | 365 | 0 | 819 | 0 | 0 |
normalized size |
1 |
1. |
1.29 |
4.4 |
0. |
9.87 |
0. |
0. |
time (sec) |
N/A |
0.219 |
0.494 |
0.036 |
0. |
1.43 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 176 | 394 | 0 | 1216 | 0 | 0 |
normalized size |
1 |
1. |
1.59 |
3.55 |
0. |
10.95 |
0. |
0. |
time (sec) |
N/A |
0.452 |
1.953 |
0.034 |
0. |
1.482 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 131 | 416 | 0 | 1295 | 0 | 0 |
normalized size |
1 |
1. |
0.97 |
3.08 |
0. |
9.59 |
0. |
0. |
time (sec) |
N/A |
0.538 |
1.277 |
0.034 |
0. |
1.442 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 224 | 234 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
0.83 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.544 |
1.978 |
0.038 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 279 | 279 | 312 | 234 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.12 |
0.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.564 |
2.752 |
0.034 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 207 | 223 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.74 |
0.8 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.531 |
1.232 |
0.037 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 337 | 222 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.2 |
0.79 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.566 |
0.775 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 306 | 306 | 203 | 255 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.66 |
0.83 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.796 |
1.283 |
0.04 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 467 | 276 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.41 |
0.83 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.075 |
6.324 |
0.039 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 192 | 440 | 0 | 1407 | 0 | 0 |
normalized size |
1 |
1. |
1.17 |
2.68 |
0. |
8.58 |
0. |
0. |
time (sec) |
N/A |
0.617 |
2.072 |
0.042 |
0. |
2.101 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 164 | 164 | 131 | 434 | 0 | 1355 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
2.65 |
0. |
8.26 |
0. |
0. |
time (sec) |
N/A |
0.663 |
1.98 |
0.041 |
0. |
2.041 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 181 | 423 | 0 | 1334 | 0 | 0 |
normalized size |
1 |
1. |
1.12 |
2.63 |
0. |
8.29 |
0. |
0. |
time (sec) |
N/A |
0.592 |
0.817 |
0.042 |
0. |
2.117 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 217 | 426 | 0 | 1300 | 0 | 0 |
normalized size |
1 |
1. |
1.32 |
2.58 |
0. |
7.88 |
0. |
0. |
time (sec) |
N/A |
0.648 |
1.224 |
0.044 |
0. |
1.689 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 156 | 458 | 0 | 1775 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
2.42 |
0. |
9.39 |
0. |
0. |
time (sec) |
N/A |
0.863 |
1.187 |
0.043 |
0. |
1.579 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 215 | 215 | 167 | 482 | 0 | 1850 | 0 | 0 |
normalized size |
1 |
1. |
0.78 |
2.24 |
0. |
8.6 |
0. |
0. |
time (sec) |
N/A |
1.105 |
3.117 |
0.045 |
0. |
1.544 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 223 | 223 | 69 | 356 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.31 |
1.6 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.266 |
0.16 |
0.13 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 61 | 249 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.45 |
1.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.24 |
0.09 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 96 | 265 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.69 |
1.91 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.235 |
0.298 |
0.035 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 98 | 452 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.44 |
2.05 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.209 |
0.243 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 67 | 442 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.31 |
2.07 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.185 |
0.158 |
0.034 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 51 | 249 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.42 |
2.06 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.127 |
0.074 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 65 | 249 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.47 |
1.79 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.193 |
0.127 |
0.048 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 71 | 356 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.31 |
1.58 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.193 |
0.137 |
0.043 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 75 | 265 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.52 |
1.85 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.205 |
0.384 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 216 | 216 | 69 | 444 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.32 |
2.06 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.176 |
0.231 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 247 | 247 | 68 | 363 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.28 |
1.47 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.207 |
0.129 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 155 | 337 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.69 |
1.49 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.172 |
0.281 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 166 | 327 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.8 |
1.57 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.142 |
0.214 |
0.024 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 229 | 229 | 196 | 355 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
1.55 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.194 |
0.349 |
0.02 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 252 | 252 | 196 | 374 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.78 |
1.48 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.258 |
0.746 |
0.021 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 317 | 317 | 224 | 581 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.71 |
1.83 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.334 |
1.982 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 220 | 534 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
1.85 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.275 |
0.57 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 192 | 529 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
1.98 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.249 |
0.873 |
0.028 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 218 | 538 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
2.01 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.258 |
0.307 |
0.023 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 82 | 558 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.28 |
1.92 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.334 |
0.284 |
0.025 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 322 | 85 | 600 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.26 |
1.86 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.428 |
0.356 |
0.027 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 372 | 372 | 251 | 807 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.67 |
2.17 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.564 |
3.086 |
0.032 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 342 | 342 | 247 | 750 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.72 |
2.19 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.477 |
2.593 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 313 | 313 | 216 | 725 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.69 |
2.32 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.425 |
1.016 |
0.031 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 313 | 313 | 193 | 742 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.62 |
2.37 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.42 |
3.311 |
0.03 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 313 | 313 | 104 | 743 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.33 |
2.37 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.458 |
0.358 |
0.028 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 343 | 343 | 108 | 786 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.31 |
2.29 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.561 |
0.614 |
0.075 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 116 | 829 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.31 |
2.2 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.662 |
0.721 |
0.038 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 325 | 325 | 286 | 459 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
1.41 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.66 |
0.835 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 249 | 429 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
1.42 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.379 |
0.57 |
0.036 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 226 | 417 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.75 |
1.38 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.376 |
0.276 |
0.043 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 248 | 423 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.82 |
1.4 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.37 |
0.244 |
0.046 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 325 | 325 | 198 | 459 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
1.41 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.66 |
0.417 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 109 | 481 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.31 |
1.37 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.962 |
0.26 |
0.041 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 437 | 437 | 445 | 805 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.02 |
1.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.108 |
6.155 |
0.056 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 390 | 784 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.99 |
1.99 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.74 |
2.725 |
0.058 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 387 | 387 | 322 | 768 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
1.98 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.677 |
3.181 |
0.047 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 386 | 386 | 401 | 749 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
1.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.646 |
6.09 |
0.052 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 394 | 394 | 300 | 765 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.76 |
1.94 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.738 |
2.757 |
0.051 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 437 | 437 | 244 | 803 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.56 |
1.84 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.095 |
0.595 |
0.056 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 529 | 529 | 556 | 1254 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.05 |
2.37 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.631 |
6.237 |
0.069 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 525 | 1232 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.1 |
2.59 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.23 |
6.153 |
0.052 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 470 | 470 | 488 | 1229 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
2.61 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.295 |
6.183 |
0.054 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 461 | 461 | 518 | 1212 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.12 |
2.63 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.234 |
6.149 |
0.053 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 463 | 463 | 483 | 1187 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.04 |
2.56 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.147 |
6.163 |
0.058 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 411 | 1190 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.86 |
2.5 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.242 |
6.121 |
0.057 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 529 | 529 | 303 | 1245 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.57 |
2.35 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
1.658 |
1.68 |
0.059 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 118 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.71 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.243 |
0.281 |
0.174 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
F |
F |
F |
F |
F(-1) |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0. |
0. |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.272 |
2.768 |
0.898 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 1622 | 0 | 425 | 0 | 0 |
normalized size | 1 | 1. | 1. | 36.04 | 0. | 9.44 | 0. | 0. |
time (sec) |
N/A |
0.065 |
0.074 |
0.079 |
0. |
1.652 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 70 | 1622 | 0 | 424 | 0 | 0 |
normalized size | 1 | 1. | 1.56 | 36.04 | 0. | 9.42 | 0. | 0. |
time (sec) |
N/A |
0.059 |
1.612 |
0.04 |
0. |
1.598 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 67 | 187 | 120 | 184 | 524 | 128 |
normalized size | 1 | 1. | 1.14 | 3.17 | 2.03 | 3.12 | 8.88 | 2.17 |
time (sec) |
N/A |
0.078 |
0.109 |
0.026 |
1.612 |
1.669 |
4.561 |
1.336 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
B |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 144 | 356 | 250 | 748 | 0 | 325 |
normalized size |
1 |
1. |
1.3 |
3.21 |
2.25 |
6.74 |
0. |
2.93 |
time (sec) |
N/A |
0.149 |
1.797 |
0.031 |
1.757 |
1.693 |
0. |
1.383 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
B |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 202 | 559 | 455 | 1191 | 0 | 556 |
normalized size |
1 |
1. |
1.15 |
3.19 |
2.6 |
6.81 |
0. |
3.18 |
time (sec) |
N/A |
0.276 |
4.72 |
0.037 |
1.815 |
1.851 |
0. |
1.424 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 379 | 2405 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
2.02 |
12.79 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.453 |
1.789 |
0.088 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 294 | 1665 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.96 |
11.1 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.333 |
0.951 |
0.057 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 212 | 968 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.74 |
7.93 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.262 |
0.541 |
0.044 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 253 | 1375 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.68 |
9.11 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.278 |
3.88 |
0.049 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 408 | 408 | 178 | 986 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.44 |
2.42 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.511 |
1.793 |
0.052 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 422 | 422 | 158 | 2285 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
0.37 |
5.41 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.418 |
0.996 |
0.05 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 154 | 3976 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.51 |
38.98 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.16 |
0.577 |
0.063 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 226 | 7951 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.64 |
57.62 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.263 |
1.649 |
0.071 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 185 | 185 | 319 | 12836 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.72 |
69.38 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.402 |
3.509 |
0.087 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 146 | 1905 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.43 |
18.68 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.162 |
0.316 |
0.057 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 216 | 2291 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.64 |
17.36 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.248 |
1.405 |
0.056 |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 232 | 3055 | 0 | 0 | 0 | 0 |
normalized size |
1 |
1. |
1.33 |
17.56 |
0. |
0. |
0. |
0. |
time (sec) |
N/A |
0.382 |
5.775 |
0.059 |
0. |
0. |
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 [48] had the largest ratio of [ 0.9091
]
|
|
|
|
|
|
|
| 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 |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
2 |
A |
5 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
3 |
A |
4 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
6 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
7 |
A |
4 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
8 |
A |
16 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
9 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
10 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
11 |
A |
14 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
12 |
A |
13 |
10 |
1. |
25 |
0.4 |
|
|
|
|
|
|
|
13 |
A |
14 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
14 |
A |
14 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
15 |
A |
7 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
16 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
17 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
18 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
19 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
20 |
A |
4 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
|
21 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
22 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
23 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
25 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
26 |
A |
6 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
27 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
28 |
A |
10 |
10 |
1. |
25 |
0.4 |
|
|
|
|
|
|
|
29 |
A |
17 |
14 |
1. |
25 |
0.56 |
|
|
|
|
|
|
|
30 |
A |
18 |
15 |
1. |
25 |
0.6 |
|
|
|
|
|
|
|
31 |
A |
17 |
14 |
1. |
25 |
0.56 |
|
|
|
|
|
|
|
32 |
A |
18 |
15 |
1. |
25 |
0.6 |
|
|
|
|
|
|
|
33 |
A |
18 |
15 |
1. |
25 |
0.6 |
|
|
|
|
|
|
|
34 |
A |
20 |
16 |
1. |
25 |
0.64 |
|
|
|
|
|
|
|
35 |
A |
8 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
36 |
A |
8 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
37 |
A |
8 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
38 |
A |
8 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
39 |
A |
9 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
40 |
A |
10 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
|
41 |
A |
12 |
9 |
1. |
13 |
0.692 |
|
|
|
|
|
|
|
42 |
A |
6 |
5 |
1. |
11 |
0.454 |
|
|
|
|
|
|
|
43 |
A |
8 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
44 |
A |
14 |
9 |
1. |
11 |
0.818 |
|
|
|
|
|
|
|
45 |
A |
12 |
8 |
1. |
13 |
0.615 |
|
|
|
|
|
|
|
46 |
A |
5 |
4 |
1. |
11 |
0.364 |
|
|
|
|
|
|
|
47 |
A |
6 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
48 |
A |
13 |
10 |
1. |
11 |
0.909 |
|
|
|
|
|
|
|
49 |
A |
8 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
50 |
A |
13 |
9 |
1. |
11 |
0.818 |
|
|
|
|
|
|
|
51 |
A |
12 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
52 |
A |
11 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
53 |
A |
10 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
54 |
A |
11 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
55 |
A |
12 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
56 |
A |
13 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
57 |
A |
12 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
58 |
A |
11 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
59 |
A |
11 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
60 |
A |
12 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
|
61 |
A |
13 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
62 |
A |
14 |
10 |
1. |
25 |
0.4 |
|
|
|
|
|
|
|
63 |
A |
13 |
10 |
1. |
25 |
0.4 |
|
|
|
|
|
|
|
64 |
A |
12 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
65 |
A |
12 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
66 |
A |
12 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
67 |
A |
13 |
10 |
1. |
25 |
0.4 |
|
|
|
|
|
|
|
68 |
A |
14 |
10 |
1. |
25 |
0.4 |
|
|
|
|
|
|
|
69 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
70 |
A |
14 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
71 |
A |
14 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
72 |
A |
14 |
11 |
1. |
25 |
0.44 |
|
|
|
|
|
|
|
73 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
74 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
75 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
76 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
77 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
78 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
79 |
A |
15 |
12 |
1. |
25 |
0.48 |
|
|
|
|
|
|
|
80 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
|
81 |
A |
17 |
14 |
1. |
25 |
0.56 |
|
|
|
|
|
|
|
82 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
83 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
84 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
85 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
86 |
A |
16 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
87 |
A |
17 |
13 |
1. |
25 |
0.52 |
|
|
|
|
|
|
|
88 |
A |
5 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
89 |
A |
8 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
90 |
A |
3 |
3 |
1. |
27 |
0.111 |
|
|
|
|
|
|
|
91 |
A |
3 |
3 |
1. |
27 |
0.111 |
|
|
|
|
|
|
|
92 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
93 |
A |
3 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
94 |
A |
4 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
95 |
A |
10 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
96 |
A |
9 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
97 |
A |
8 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
98 |
A |
10 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
99 |
A |
13 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
100 |
A |
13 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
|
101 |
A |
7 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
102 |
A |
8 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
103 |
A |
9 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
104 |
A |
7 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
105 |
A |
8 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
106 |
A |
9 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|