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
}
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, 31, 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: { 37, 38 }
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 }
F grade: { }
2.1.3 Maple
A grade: { 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 37,
43, 44, 45, 46, 47, 48, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76,
77, 83, 84, 85, 86, 91, 92, 93 }
B grade: { 1, 2, 10, 11, 12, 33, 34, 35, 36, 38, 39, 40, 41, 42, 49, 50, 51, 52, 72, 78, 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
}
F grade: { }
2.1.4 Maxima
A grade: { 1, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 22, 24, 25, 26, 27, 28, 29, 30, 31, 36, 40, 41, 43, 45, 46, 47,
48, 49, 50, 51, 53, 54, 55, 56, 79, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93
B grade: { 2, 3, 4, 5, 11, 12, 13, 19, 20, 21, 23, 42, 44, 52, 80, 81, 83 }
C grade: { }
F grade: { 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
}
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,
31, 32, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 60, 62, 79, 80, 81, 82, 83, 84, 85,
86, 87, 88, 89, 90, 91, 92, 93 }
B grade: { 30, 33, 35, 36, 37, 38, 39, 57, 58, 59, 61, 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
}
C grade: { }
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 }
2.1.7 Giac
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,
28, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 54, 55, 56, 79, 80, 81, 82, 83, 85, 86, 87, 88, 92
}
B grade: { 12, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 52, 53, 84, 89, 90, 91, 93 }
C grade: { }
F 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 }
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 |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 82 | 356 | 313 | 193 | 151 | 205 |
normalized size | 1 | 1. | 0.66 | 2.87 | 2.52 | 1.56 | 1.22 | 1.65 |
time (sec) |
N/A |
0.321 |
0.14 |
0.011 |
1.149 |
1.942 |
3.639 |
1.213 |
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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 | 94 | 94 | 65 | 224 | 265 | 151 | 117 | 157 |
normalized size | 1 | 1. | 0.69 | 2.38 | 2.82 | 1.61 | 1.24 | 1.67 |
time (sec) |
N/A |
0.217 |
0.117 |
0.007 |
1.124 |
1.923 |
2.242 |
1.164 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 45 | 122 | 216 | 111 | 82 | 107 |
normalized size | 1 | 1. | 0.7 | 1.91 | 3.38 | 1.73 | 1.28 | 1.67 |
time (sec) |
N/A |
0.114 |
0.088 |
0.008 |
1.13 |
1.919 |
1.95 |
1.224 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 27 | 53 | 92 | 73 | 46 | 62 |
normalized size | 1 | 1. | 0.96 | 1.89 | 3.29 | 2.61 | 1.64 | 2.21 |
time (sec) |
N/A |
0.021 |
0.051 |
0.009 |
1.139 |
1.983 |
0.629 |
1.203 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 39 | 52 | 131 | 142 | 34 | 63 |
normalized size | 1 | 1. | 1.39 | 1.86 | 4.68 | 5.07 | 1.21 | 2.25 |
time (sec) |
N/A |
0.149 |
0.028 |
0.038 |
1.201 |
1.967 |
4.547 |
1.182 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 59 | 77 | 111 | 186 | 0 | 97 |
normalized size | 1 | 1. | 1.26 | 1.64 | 2.36 | 3.96 | 0. | 2.06 |
time (sec) |
N/A |
0.228 |
0.127 |
0.039 |
1.397 |
1.968 |
0. |
1.151 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 78 | 139 | 89 | 278 | 0 | 181 |
normalized size |
1 |
1. |
0.89 |
1.58 |
1.01 |
3.16 |
0. |
2.06 |
time (sec) |
N/A |
0.281 |
0.155 |
0.047 |
1.417 |
1.994 |
0. |
1.152 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 110 | 205 | 105 | 328 | 0 | 269 |
normalized size |
1 |
1. |
0.83 |
1.55 |
0.8 |
2.48 |
0. |
2.04 |
time (sec) |
N/A |
0.34 |
0.272 |
0.053 |
1.395 |
1.98 |
0. |
1.148 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 140 | 271 | 111 | 366 | 0 | 359 |
normalized size |
1 |
1. |
0.84 |
1.63 |
0.67 |
2.2 |
0. |
2.16 |
time (sec) |
N/A |
0.406 |
0.318 |
0.062 |
1.399 |
2.021 |
0. |
1.265 |
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Problem 10 |
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 | 184 | 184 | 100 | 463 | 444 | 273 | 228 | 319 |
normalized size | 1 | 1. | 0.54 | 2.52 | 2.41 | 1.48 | 1.24 | 1.73 |
time (sec) |
N/A |
0.346 |
0.242 |
0.007 |
1.184 |
2.019 |
3.531 |
1.177 |
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Problem 11 |
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 | 134 | 134 | 87 | 283 | 371 | 203 | 172 | 231 |
normalized size | 1 | 1. | 0.65 | 2.11 | 2.77 | 1.51 | 1.28 | 1.72 |
time (sec) |
N/A |
0.214 |
0.188 |
0.01 |
1.176 |
2.008 |
2.114 |
1.143 |
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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 |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 56 | 147 | 182 | 140 | 112 | 151 |
normalized size | 1 | 1. | 1.14 | 3. | 3.71 | 2.86 | 2.29 | 3.08 |
time (sec) |
N/A |
0.048 |
0.142 |
0.007 |
1.206 |
1.949 |
1.064 |
1.215 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 51 | 121 | 236 | 221 | 73 | 153 |
normalized size | 1 | 1. | 0.82 | 1.95 | 3.81 | 3.56 | 1.18 | 2.47 |
time (sec) |
N/A |
0.185 |
0.235 |
0.036 |
1.34 |
1.971 |
5.077 |
1.263 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 70 | 70 | 62 | 118 | 184 | 284 | 0 | 161 |
normalized size | 1 | 1. | 0.89 | 1.69 | 2.63 | 4.06 | 0. | 2.3 |
time (sec) |
N/A |
0.247 |
0.23 |
0.049 |
1.393 |
1.994 |
0. |
1.239 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 93 | 181 | 170 | 351 | 0 | 244 |
normalized size | 1 | 1. | 0.77 | 1.5 | 1.4 | 2.9 | 0. | 2.02 |
time (sec) |
N/A |
0.339 |
0.373 |
0.052 |
1.372 |
1.95 |
0. |
1.178 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 154 | 287 | 158 | 431 | 0 | 385 |
normalized size | 1 | 1. | 0.9 | 1.67 | 0.92 | 2.51 | 0. | 2.24 |
time (sec) |
N/A |
0.426 |
0.448 |
0.06 |
1.431 |
2.016 |
0. |
1.152 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 248 | 248 | 206 | 396 | 173 | 510 | 0 | 533 |
normalized size | 1 | 1. | 0.83 | 1.6 | 0.7 | 2.06 | 0. | 2.15 |
time (sec) |
N/A |
0.521 |
0.524 |
0.072 |
1.398 |
1.973 |
0. |
1.115 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 219 | 219 | 159 | 442 | 590 | 481 | 0 | 84 |
normalized size | 1 | 1. | 0.73 | 2.02 | 2.69 | 2.2 | 0. | 0.38 |
time (sec) |
N/A |
0.484 |
0.631 |
0.133 |
1.448 |
2.093 |
0. |
1.149 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
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grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 118 | 292 | 443 | 392 | 0 | 84 |
normalized size | 1 | 1. | 0.79 | 1.95 | 2.95 | 2.61 | 0. | 0.56 |
time (sec) |
N/A |
0.329 |
0.43 |
0.034 |
1.276 |
2.094 |
0. |
1.176 |
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|
|
Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 89 | 184 | 315 | 327 | 0 | 84 |
normalized size | 1 | 1. | 0.89 | 1.84 | 3.15 | 3.27 | 0. | 0.84 |
time (sec) |
N/A |
0.262 |
0.283 |
0.03 |
1.378 |
2.156 |
0. |
1.207 |
|
|
|
|
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 68 | 64 | 114 | 211 | 251 | 0 | 78 |
normalized size | 1 | 1. | 0.94 | 1.68 | 3.1 | 3.69 | 0. | 1.15 |
time (sec) |
N/A |
0.176 |
0.136 |
0.023 |
1.333 |
1.997 |
0. |
1.186 |
|
|
|
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Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 49 | 81 | 77 | 193 | 0 | 76 |
normalized size | 1 | 1. | 0.96 | 1.59 | 1.51 | 3.78 | 0. | 1.49 |
time (sec) |
N/A |
0.08 |
0.061 |
0.019 |
1.316 |
2.086 |
0. |
1.171 |
|
|
|
|
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Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 63 | 108 | 209 | 277 | 0 | 101 |
normalized size | 1 | 1. | 0.86 | 1.48 | 2.86 | 3.79 | 0. | 1.38 |
time (sec) |
N/A |
0.259 |
0.141 |
0.031 |
1.437 |
2.066 |
0. |
1.159 |
|
|
|
|
|
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Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 101 | 172 | 259 | 400 | 0 | 174 |
normalized size | 1 | 1. | 0.89 | 1.52 | 2.29 | 3.54 | 0. | 1.54 |
time (sec) |
N/A |
0.369 |
0.381 |
0.048 |
1.456 |
2.047 |
0. |
1.172 |
|
|
|
|
|
|
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|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 190 | 190 | 178 | 281 | 327 | 591 | 0 | 335 |
normalized size | 1 | 1. | 0.94 | 1.48 | 1.72 | 3.11 | 0. | 1.76 |
time (sec) |
N/A |
0.485 |
0.487 |
0.05 |
1.626 |
2.085 |
0. |
1.205 |
|
|
|
|
|
|
|
|
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|
|
|
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|
Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 231 | 231 | 173 | 431 | 548 | 740 | 0 | 393 |
normalized size | 1 | 1. | 0.75 | 1.87 | 2.37 | 3.2 | 0. | 1.7 |
time (sec) |
N/A |
0.536 |
1.201 |
0.122 |
1.516 |
2.08 |
0. |
1.187 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 156 | 325 | 421 | 663 | 0 | 393 |
normalized size | 1 | 1. | 0.86 | 1.79 | 2.31 | 3.64 | 0. | 2.16 |
time (sec) |
N/A |
0.423 |
0.914 |
0.046 |
1.343 |
2.033 |
0. |
1.186 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 115 | 254 | 319 | 570 | 0 | 387 |
normalized size | 1 | 1. | 0.78 | 1.73 | 2.17 | 3.88 | 0. | 2.63 |
time (sec) |
N/A |
0.375 |
0.692 |
0.039 |
1.348 |
1.992 |
0. |
1.229 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 97 | 215 | 240 | 414 | 0 | 373 |
normalized size | 1 | 1. | 0.78 | 1.72 | 1.92 | 3.31 | 0. | 2.98 |
time (sec) |
N/A |
0.297 |
0.414 |
0.027 |
1.363 |
2.034 |
0. |
1.24 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 65 | 132 | 109 | 316 | 0 | 201 |
normalized size |
1 |
1. |
0.92 |
1.86 |
1.54 |
4.45 |
0. |
2.83 |
time (sec) |
N/A |
0.11 |
0.202 |
0.025 |
1.209 |
2.037 |
0. |
1.211 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 241 | 254 | 306 | 579 | 0 | 439 |
normalized size | 1 | 1. | 1.61 | 1.69 | 2.04 | 3.86 | 0. | 2.93 |
time (sec) |
N/A |
0.4 |
1.05 |
0.05 |
1.432 |
2.151 |
0. |
1.211 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 186 | 186 | 183 | 312 | 0 | 802 | 0 | 576 |
normalized size |
1 |
1. |
0.98 |
1.68 |
0. |
4.31 |
0. |
3.1 |
time (sec) |
N/A |
0.501 |
1.414 |
0.058 |
0. |
2.11 |
0. |
1.286 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 264 | 264 | 236 | 571 | 0 | 1142 | 0 | 1019 |
normalized size | 1 | 1. | 0.89 | 2.16 | 0. | 4.33 | 0. | 3.86 |
time (sec) |
N/A |
0.618 |
1. |
0.117 |
0. |
2.509 |
0. |
1.161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 241 | 241 | 153 | 527 | 0 | 973 | 0 | 1000 |
normalized size | 1 | 1. | 0.63 | 2.19 | 0. | 4.04 | 0. | 4.15 |
time (sec) |
N/A |
0.53 |
0.928 |
0.047 |
0. |
2.473 |
0. |
1.181 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 178 | 178 | 158 | 435 | 0 | 770 | 0 | 714 |
normalized size |
1 |
1. |
0.89 |
2.44 |
0. |
4.33 |
0. |
4.01 |
time (sec) |
N/A |
0.37 |
0.578 |
0.036 |
0. |
2.236 |
0. |
1.234 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 104 | 104 | 88 | 276 | 128 | 518 | 0 | 402 |
normalized size |
1 |
1. |
0.85 |
2.65 |
1.23 |
4.98 |
0. |
3.87 |
time (sec) |
N/A |
0.146 |
0.467 |
0.028 |
1.19 |
1.956 |
0. |
1.183 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
B |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 614 | 488 | 0 | 1243 | 0 | 1130 |
normalized size | 1 | 1. | 2.34 | 1.86 | 0. | 4.74 | 0. | 4.31 |
time (sec) |
N/A |
0.561 |
4.592 |
0.055 |
0. |
2.175 |
0. |
1.211 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
B |
F(-2) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 710 | 643 | 0 | 1563 | 0 | 1358 |
normalized size |
1 |
1. |
2.38 |
2.16 |
0. |
5.24 |
0. |
4.56 |
time (sec) |
N/A |
0.69 |
1.44 |
0.073 |
0. |
2.2 |
0. |
1.253 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
B |
F(-1) |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 377 | 377 | 627 | 760 | 0 | 1845 | 0 | 1578 |
normalized size |
1 |
1. |
1.66 |
2.02 |
0. |
4.89 |
0. |
4.19 |
time (sec) |
N/A |
0.821 |
1.807 |
0.082 |
0. |
2.182 |
0. |
1.319 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
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 | 139 | 139 | 92 | 447 | 338 | 212 | 168 | 235 |
normalized size | 1 | 1. | 0.66 | 3.22 | 2.43 | 1.53 | 1.21 | 1.69 |
time (sec) |
N/A |
0.255 |
0.149 |
0.009 |
1.071 |
2.016 |
5.485 |
1.204 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
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 | 109 | 109 | 74 | 298 | 289 | 174 | 134 | 186 |
normalized size | 1 | 1. | 0.68 | 2.73 | 2.65 | 1.6 | 1.23 | 1.71 |
time (sec) |
N/A |
0.187 |
0.129 |
0.009 |
1.03 |
2.026 |
2.615 |
1.198 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 79 | 79 | 57 | 183 | 288 | 132 | 99 | 136 |
normalized size | 1 | 1. | 0.72 | 2.32 | 3.65 | 1.67 | 1.25 | 1.72 |
time (sec) |
N/A |
0.121 |
0.1 |
0.007 |
1.086 |
1.984 |
1.32 |
1.178 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 51 | 51 | 40 | 97 | 116 | 97 | 65 | 95 |
normalized size | 1 | 1. | 0.78 | 1.9 | 2.27 | 1.9 | 1.27 | 1.86 |
time (sec) |
N/A |
0.067 |
0.067 |
0.008 |
1.019 |
1.995 |
0.674 |
1.153 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 55 | 81 | 165 | 188 | 49 | 103 |
normalized size | 1 | 1. | 1.34 | 1.98 | 4.02 | 4.59 | 1.2 | 2.51 |
time (sec) |
N/A |
0.098 |
0.11 |
0.035 |
1.169 |
2.063 |
3.565 |
1.176 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 81 | 108 | 203 | 0 | 108 |
normalized size | 1 | 1. | 1. | 1.93 | 2.57 | 4.83 | 0. | 2.57 |
time (sec) |
N/A |
0.107 |
0.088 |
0.046 |
1.188 |
2.084 |
0. |
1.222 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 80 | 110 | 122 | 254 | 0 | 147 |
normalized size |
1 |
1. |
1.08 |
1.49 |
1.65 |
3.43 |
0. |
1.99 |
time (sec) |
N/A |
0.178 |
0.147 |
0.044 |
1.191 |
2.023 |
0. |
1.16 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 95 | 172 | 99 | 298 | 0 | 230 |
normalized size |
1 |
1. |
0.9 |
1.64 |
0.94 |
2.84 |
0. |
2.19 |
time (sec) |
N/A |
0.234 |
0.225 |
0.059 |
1.213 |
1.98 |
0. |
1.183 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 127 | 238 | 103 | 352 | 0 | 320 |
normalized size |
1 |
1. |
0.85 |
1.6 |
0.69 |
2.36 |
0. |
2.15 |
time (sec) |
N/A |
0.29 |
0.274 |
0.066 |
1.213 |
2.007 |
0. |
1.199 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
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 | 234 | 234 | 138 | 738 | 517 | 336 | 286 | 410 |
normalized size | 1 | 1. | 0.59 | 3.15 | 2.21 | 1.44 | 1.22 | 1.75 |
time (sec) |
N/A |
0.388 |
0.321 |
0.009 |
1.055 |
2.059 |
10.16 |
1.218 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
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 | 184 | 184 | 113 | 513 | 477 | 273 | 226 | 323 |
normalized size | 1 | 1. | 0.61 | 2.79 | 2.59 | 1.48 | 1.23 | 1.76 |
time (sec) |
N/A |
0.277 |
0.23 |
0.008 |
1.078 |
2.084 |
5.259 |
1.172 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
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 | 136 | 136 | 85 | 332 | 255 | 207 | 172 | 243 |
normalized size | 1 | 1. | 0.62 | 2.44 | 1.88 | 1.52 | 1.26 | 1.79 |
time (sec) |
N/A |
0.181 |
0.179 |
0.008 |
1.039 |
2.181 |
2.954 |
1.175 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
B |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 82 | 226 | 317 | 292 | 121 | 300 |
normalized size | 1 | 1. | 0.75 | 2.05 | 2.88 | 2.65 | 1.1 | 2.73 |
time (sec) |
N/A |
0.189 |
0.361 |
0.05 |
1.187 |
2.477 |
5.733 |
1.201 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 95 | 190 | 242 | 286 | 0 | 266 |
normalized size | 1 | 1. | 1. | 2. | 2.55 | 3.01 | 0. | 2.8 |
time (sec) |
N/A |
0.177 |
0.263 |
0.069 |
1.204 |
2.014 |
0. |
1.199 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 114 | 114 | 97 | 188 | 223 | 359 | 0 | 278 |
normalized size | 1 | 1. | 0.85 | 1.65 | 1.96 | 3.15 | 0. | 2.44 |
time (sec) |
N/A |
0.225 |
0.348 |
0.084 |
1.347 |
1.993 |
0. |
1.22 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 133 | 133 | 114 | 222 | 182 | 381 | 0 | 319 |
normalized size | 1 | 1. | 0.86 | 1.67 | 1.37 | 2.86 | 0. | 2.4 |
time (sec) |
N/A |
0.259 |
0.402 |
0.092 |
1.237 |
2.044 |
0. |
1.158 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 124 | 291 | 188 | 439 | 0 | 397 |
normalized size | 1 | 1. | 0.71 | 1.66 | 1.07 | 2.51 | 0. | 2.27 |
time (sec) |
N/A |
0.36 |
0.439 |
0.116 |
1.277 |
1.974 |
0. |
1.175 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 273 | 273 | 274 | 369 | 0 | 1296 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.35 |
0. |
4.75 |
0. |
0. |
time (sec) |
N/A |
0.729 |
0.419 |
0.189 |
0. |
2.195 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 209 | 209 | 210 | 268 | 0 | 1100 | 0 | 0 |
normalized size | 1 | 1. | 1. | 1.28 | 0. | 5.26 | 0. | 0. |
time (sec) |
N/A |
0.358 |
0.349 |
0.06 |
0. |
2.103 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 213 | 259 | 0 | 1087 | 0 | 0 |
normalized size |
1 |
1. |
0.94 |
1.15 |
0. |
4.81 |
0. |
0. |
time (sec) |
N/A |
0.376 |
0.252 |
0.045 |
0. |
2.169 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 177 | 171 | 200 | 0 | 455 | 0 | 0 |
normalized size | 1 | 1. | 0.97 | 1.13 | 0. | 2.57 | 0. | 0. |
time (sec) |
N/A |
0.254 |
0.175 |
0.032 |
0. |
2.092 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 180 | 212 | 0 | 624 | 0 | 0 |
normalized size |
1 |
1. |
0.85 |
1. |
0. |
2.93 |
0. |
0. |
time (sec) |
N/A |
0.259 |
0.201 |
0.021 |
0. |
2.157 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 187 | 227 | 0 | 545 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 1.15 | 0. | 2.77 | 0. | 0. |
time (sec) |
N/A |
0.372 |
0.31 |
0.043 |
0. |
2.203 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 243 | 288 | 0 | 1323 | 0 | 0 |
normalized size |
1 |
1. |
0.98 |
1.16 |
0. |
5.31 |
0. |
0. |
time (sec) |
N/A |
0.496 |
0.357 |
0.055 |
0. |
2.499 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
B |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 270 | 270 | 257 | 330 | 0 | 1283 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 1.22 | 0. | 4.75 | 0. | 0. |
time (sec) |
N/A |
0.504 |
0.53 |
0.063 |
0. |
2.51 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 449 | 449 | 621 | 532 | 0 | 2488 | 0 | 0 |
normalized size |
1 |
1. |
1.38 |
1.18 |
0. |
5.54 |
0. |
0. |
time (sec) |
N/A |
0.859 |
1.507 |
0.319 |
0. |
2.313 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 582 | 495 | 0 | 2099 | 0 | 0 |
normalized size |
1 |
1. |
1.35 |
1.15 |
0. |
4.87 |
0. |
0. |
time (sec) |
N/A |
0.701 |
0.74 |
0.095 |
0. |
2.153 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 364 | 491 | 0 | 2433 | 0 | 0 |
normalized size |
1 |
1. |
0.88 |
1.18 |
0. |
5.85 |
0. |
0. |
time (sec) |
N/A |
0.611 |
0.992 |
0.068 |
0. |
2.196 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 239 | 239 | 239 | 291 | 0 | 1393 | 0 | 0 |
normalized size |
1 |
1. |
1. |
1.22 |
0. |
5.83 |
0. |
0. |
time (sec) |
N/A |
0.325 |
0.514 |
0.044 |
0. |
2.167 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 590 | 503 | 0 | 2431 | 0 | 0 |
normalized size |
1 |
1. |
1.24 |
1.06 |
0. |
5.11 |
0. |
0. |
time (sec) |
N/A |
0.818 |
0.688 |
0.029 |
0. |
2.274 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 435 | 435 | 363 | 546 | 0 | 2253 | 0 | 0 |
normalized size |
1 |
1. |
0.83 |
1.26 |
0. |
5.18 |
0. |
0. |
time (sec) |
N/A |
0.839 |
4.804 |
0.074 |
0. |
2.297 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 500 | 500 | 675 | 595 | 0 | 2786 | 0 | 0 |
normalized size |
1 |
1. |
1.35 |
1.19 |
0. |
5.57 |
0. |
0. |
time (sec) |
N/A |
1.253 |
1.036 |
0.086 |
0. |
2.337 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 476 | 476 | 648 | 820 | 0 | 3344 | 0 | 0 |
normalized size |
1 |
1. |
1.36 |
1.72 |
0. |
7.03 |
0. |
0. |
time (sec) |
N/A |
1.062 |
1.824 |
0.376 |
0. |
2.408 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 746 | 746 | 932 | 1064 | 0 | 4169 | 0 | 0 |
normalized size |
1 |
1. |
1.25 |
1.43 |
0. |
5.59 |
0. |
0. |
time (sec) |
N/A |
1.1 |
2.509 |
0.108 |
0. |
2.397 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 512 | 512 | 637 | 743 | 0 | 3306 | 0 | 0 |
normalized size |
1 |
1. |
1.24 |
1.45 |
0. |
6.46 |
0. |
0. |
time (sec) |
N/A |
0.831 |
1.712 |
0.069 |
0. |
2.358 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 856 | 856 | 933 | 1064 | 0 | 4342 | 0 | 0 |
normalized size |
1 |
1. |
1.09 |
1.24 |
0. |
5.07 |
0. |
0. |
time (sec) |
N/A |
1.255 |
2.384 |
0.037 |
0. |
2.333 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 730 | 730 | 1558 | 1090 | 0 | 4301 | 0 | 0 |
normalized size |
1 |
1. |
2.13 |
1.49 |
0. |
5.89 |
0. |
0. |
time (sec) |
N/A |
1.682 |
3.262 |
0.105 |
0. |
2.152 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 874 | 874 | 1359 | 1178 | 0 | 4894 | 0 | 0 |
normalized size |
1 |
1. |
1.55 |
1.35 |
0. |
5.6 |
0. |
0. |
time (sec) |
N/A |
2.689 |
3.378 |
0.128 |
0. |
2.172 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 791 | 791 | 998 | 1294 | 0 | 4891 | 0 | 0 |
normalized size |
1 |
1. |
1.26 |
1.64 |
0. |
6.18 |
0. |
0. |
time (sec) |
N/A |
1.868 |
3.717 |
0.152 |
0. |
2.207 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 | 154 | 154 | 100 | 551 | 362 | 240 | 185 | 259 |
normalized size | 1 | 1. | 0.65 | 3.58 | 2.35 | 1.56 | 1.2 | 1.68 |
time (sec) |
N/A |
0.297 |
0.161 |
0.008 |
1.046 |
1.764 |
9.675 |
1.14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 124 | 124 | 84 | 389 | 360 | 200 | 151 | 211 |
normalized size | 1 | 1. | 0.68 | 3.14 | 2.9 | 1.61 | 1.22 | 1.7 |
time (sec) |
N/A |
0.228 |
0.133 |
0.007 |
1.042 |
1.733 |
6.047 |
1.189 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 94 | 94 | 66 | 257 | 265 | 155 | 116 | 161 |
normalized size | 1 | 1. | 0.7 | 2.73 | 2.82 | 1.65 | 1.23 | 1.71 |
time (sec) |
N/A |
0.159 |
0.11 |
0.007 |
1.042 |
1.719 |
3.262 |
1.368 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
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 | 66 | 66 | 49 | 158 | 140 | 119 | 82 | 119 |
normalized size | 1 | 1. | 0.74 | 2.39 | 2.12 | 1.8 | 1.24 | 1.8 |
time (sec) |
N/A |
0.103 |
0.081 |
0.007 |
1.029 |
1.813 |
1.408 |
1.224 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
B |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 49 | 113 | 189 | 211 | 66 | 147 |
normalized size | 1 | 1. | 0.88 | 2.02 | 3.38 | 3.77 | 1.18 | 2.62 |
time (sec) |
N/A |
0.128 |
0.164 |
0.032 |
1.231 |
1.7 |
4.863 |
1.273 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 55 | 110 | 138 | 223 | 0 | 150 |
normalized size | 1 | 1. | 1. | 2. | 2.51 | 4.05 | 0. | 2.73 |
time (sec) |
N/A |
0.129 |
0.131 |
0.054 |
1.159 |
1.822 |
0. |
1.32 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 86 | 114 | 117 | 238 | 0 | 159 |
normalized size |
1 |
1. |
1.25 |
1.65 |
1.7 |
3.45 |
0. |
2.3 |
time (sec) |
N/A |
0.139 |
0.141 |
0.056 |
1.177 |
1.833 |
0. |
1.256 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 91 | 91 | 73 | 143 | 128 | 277 | 0 | 190 |
normalized size |
1 |
1. |
0.8 |
1.57 |
1.41 |
3.04 |
0. |
2.09 |
time (sec) |
N/A |
0.215 |
0.238 |
0.066 |
1.23 |
1.728 |
0. |
1.272 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
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 | 234 | 234 | 139 | 818 | 517 | 358 | 284 | 409 |
normalized size | 1 | 1. | 0.59 | 3.5 | 2.21 | 1.53 | 1.21 | 1.75 |
time (sec) |
N/A |
0.395 |
0.291 |
0.008 |
1.071 |
1.759 |
15.388 |
1.233 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
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 | 186 | 186 | 111 | 592 | 328 | 285 | 226 | 329 |
normalized size | 1 | 1. | 0.6 | 3.18 | 1.76 | 1.53 | 1.22 | 1.77 |
time (sec) |
N/A |
0.287 |
0.22 |
0.009 |
1.046 |
1.741 |
9.363 |
1.381 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 108 | 335 | 390 | 365 | 168 | 447 |
normalized size | 1 | 1. | 0.68 | 2.09 | 2.44 | 2.28 | 1.05 | 2.79 |
time (sec) |
N/A |
0.282 |
0.468 |
0.086 |
1.233 |
1.786 |
11.71 |
1.213 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 143 | 143 | 143 | 296 | 317 | 358 | 0 | 416 |
normalized size | 1 | 1. | 1. | 2.07 | 2.22 | 2.5 | 0. | 2.91 |
time (sec) |
N/A |
0.252 |
0.348 |
0.102 |
1.197 |
1.775 |
0. |
1.261 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 141 | 141 | 136 | 265 | 274 | 351 | 0 | 378 |
normalized size | 1 | 1. | 0.96 | 1.88 | 1.94 | 2.49 | 0. | 2.68 |
time (sec) |
N/A |
0.233 |
0.348 |
0.115 |
1.2 |
1.752 |
0. |
1.336 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 150 | 150 | 135 | 261 | 254 | 412 | 0 | 377 |
normalized size | 1 | 1. | 0.9 | 1.74 | 1.69 | 2.75 | 0. | 2.51 |
time (sec) |
N/A |
0.279 |
0.57 |
0.128 |
1.251 |
1.76 |
0. |
1.335 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
B |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 150 | 292 | 208 | 435 | 0 | 425 |
normalized size | 1 | 1. | 0.9 | 1.75 | 1.25 | 2.6 | 0. | 2.54 |
time (sec) |
N/A |
0.308 |
0.539 |
0.174 |
1.247 |
1.804 |
0. |
1.333 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 373 | 373 | 213 | 925 | 0 | 2627 | 0 | 0 |
normalized size |
1 |
1. |
0.57 |
2.48 |
0. |
7.04 |
0. |
0. |
time (sec) |
N/A |
0.937 |
0.462 |
0.087 |
0. |
2.136 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 358 | 358 | 198 | 671 | 0 | 2591 | 0 | 0 |
normalized size |
1 |
1. |
0.55 |
1.87 |
0. |
7.24 |
0. |
0. |
time (sec) |
N/A |
0.648 |
0.26 |
0.036 |
0. |
2.203 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 283 | 283 | 170 | 423 | 0 | 1322 | 0 | 0 |
normalized size | 1 | 1. | 0.6 | 1.49 | 0. | 4.67 | 0. | 0. |
time (sec) |
N/A |
0.455 |
0.225 |
0.032 |
0. |
1.952 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 345 | 345 | 180 | 280 | 0 | 1773 | 0 | 0 |
normalized size |
1 |
1. |
0.52 |
0.81 |
0. |
5.14 |
0. |
0. |
time (sec) |
N/A |
0.412 |
0.211 |
0.027 |
0. |
2.138 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 345 | 345 | 180 | 143 | 0 | 1770 | 0 | 0 |
normalized size |
1 |
1. |
0.52 |
0.41 |
0. |
5.13 |
0. |
0. |
time (sec) |
N/A |
0.401 |
0.136 |
0.022 |
0. |
2.042 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 303 | 303 | 186 | 138 | 0 | 1412 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
0.46 |
0. |
4.66 |
0. |
0. |
time (sec) |
N/A |
0.523 |
0.268 |
0.036 |
0. |
2.044 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 381 | 381 | 215 | 187 | 0 | 2921 | 0 | 0 |
normalized size |
1 |
1. |
0.56 |
0.49 |
0. |
7.67 |
0. |
0. |
time (sec) |
N/A |
0.6 |
0.407 |
0.047 |
0. |
2.189 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 237 | 240 | 0 | 3071 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
0.59 |
0. |
7.49 |
0. |
0. |
time (sec) |
N/A |
0.639 |
0.377 |
0.054 |
0. |
2.13 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 718 | 718 | 363 | 877 | 0 | 5017 | 0 | 0 |
normalized size |
1 |
1. |
0.51 |
1.22 |
0. |
6.99 |
0. |
0. |
time (sec) |
N/A |
1.081 |
0.336 |
0.15 |
0. |
2.408 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 373 | 373 | 203 | 594 | 0 | 3200 | 0 | 0 |
normalized size |
1 |
1. |
0.54 |
1.59 |
0. |
8.58 |
0. |
0. |
time (sec) |
N/A |
0.601 |
0.16 |
0.044 |
0. |
2.22 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 695 | 695 | 387 | 395 | 0 | 4891 | 0 | 0 |
normalized size |
1 |
1. |
0.56 |
0.57 |
0. |
7.04 |
0. |
0. |
time (sec) |
N/A |
1.324 |
0.188 |
0.037 |
0. |
2.395 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 739 | 739 | 387 | 226 | 0 | 5042 | 0 | 0 |
normalized size |
1 |
1. |
0.52 |
0.31 |
0. |
6.82 |
0. |
0. |
time (sec) |
N/A |
1.323 |
0.194 |
0.026 |
0. |
2.35 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 697 | 697 | 5530 | 338 | 0 | 4420 | 0 | 0 |
normalized size |
1 |
1. |
7.93 |
0.48 |
0. |
6.34 |
0. |
0. |
time (sec) |
N/A |
1.472 |
8.611 |
0.072 |
0. |
2.327 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 784 | 784 | 397 | 2448 | 0 | 6886 | 0 | 0 |
normalized size |
1 |
1. |
0.51 |
3.12 |
0. |
8.78 |
0. |
0. |
time (sec) |
N/A |
1.626 |
0.595 |
0.52 |
0. |
3.099 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1105 | 1105 | 675 | 1927 | 0 | 10106 | 0 | 0 |
normalized size |
1 |
1. |
0.61 |
1.74 |
0. |
9.15 |
0. |
0. |
time (sec) |
N/A |
1.853 |
0.524 |
0.143 |
0. |
3.476 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 776 | 776 | 429 | 1456 | 0 | 6494 | 0 | 0 |
normalized size |
1 |
1. |
0.55 |
1.88 |
0. |
8.37 |
0. |
0. |
time (sec) |
N/A |
2.659 |
0.636 |
0.112 |
0. |
2.639 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 781 | 781 | 423 | 994 | 0 | 6869 | 0 | 0 |
normalized size |
1 |
1. |
0.54 |
1.27 |
0. |
8.8 |
0. |
0. |
time (sec) |
N/A |
1.449 |
0.422 |
0.086 |
0. |
2.537 |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F(-2) |
B |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1147 | 1147 | 669 | 810 | 0 | 10103 | 0 | 0 |
normalized size |
1 |
1. |
0.58 |
0.71 |
0. |
8.81 |
0. |
0. |
time (sec) |
N/A |
3.198 |
0.458 |
0.063 |
0. |
3.085 |
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 [111] had the largest ratio of [ 0.5294
]
|
|
|
|
|
|
|
| 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 |
36 |
8 |
1. |
19 |
0.421 |
|
|
|
|
|
|
|
108 |
A |
47 |
9 |
1. |
19 |
0.474 |
|
|
|
|
|
|
|
109 |
A |
71 |
10 |
1. |
19 |
0.526 |
|
|
|
|
|
|
|
110 |
A |
37 |
9 |
1. |
19 |
0.474 |
|
|
|
|
|
|
|
111 |
A |
89 |
9 |
1. |
17 |
0.529 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|