2 detailed summary tables of results
2.1 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 |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 112 | 109 | 146 | 1 | 148 | 203 | 0 |
normalized size | 1 | 1. | 1. | 0.97 | 1.3 | 0.01 | 1.32 | 1.81 | 0. |
time (sec) |
N/A |
0.414 |
0.09 |
0.008 |
1.363 |
0.186 |
0.153 |
0.21 |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 126 | 126 | 123 | 246 | 219 | 220 | 141 | 281 | 0 |
normalized size | 1 | 1. | 0.98 | 1.95 | 1.74 | 1.75 | 1.12 | 2.23 | 0. |
time (sec) |
N/A |
0.505 |
0.162 |
0.022 |
1.33 |
0.207 |
3.522 |
0.214 |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
A |
A |
A |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 85 | 196 | 140 | 158 | 507 | 0 | 0 |
normalized size | 1 | 1. | 1.01 | 2.33 | 1.67 | 1.88 | 6.04 | 0. | 0. |
time (sec) |
N/A |
0.23 |
0.126 |
0.026 |
1.365 |
0.25 |
33.281 |
0. |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 102 | 179 | 181 | 216 | 0 | 0 | 80 |
normalized size | 1 | 1. | 0.94 | 1.66 | 1.68 | 2. | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.304 |
0.165 |
0.013 |
1.351 |
74.979 |
0. |
0. |
46.099 |
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Problem 5 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
F(-1) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 164 | 164 | 419 | 0 | 0 | 0 | 121 |
normalized size | 1 | 1. | 1.01 | 1.01 | 2.57 | 0. | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.548 |
0.445 |
0.015 |
1.399 |
0. |
0. |
0. |
88.332 |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 20 | 26 | 26 | 20 | 30 | 20 |
normalized size | 1 | 1. | 1. | 0.87 | 1.13 | 1.13 | 0.87 | 1.3 | 0.87 |
time (sec) |
N/A |
0.044 |
0.011 |
0.01 |
1.359 |
0.26 |
0.285 |
0.215 |
5.417 |
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Problem 7 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 33 | 34 | 46 | 72 | 32 | 42 | 34 |
normalized size | 1 | 1. | 0.77 | 0.79 | 1.07 | 1.67 | 0.74 | 0.98 | 0.79 |
time (sec) |
N/A |
0.072 |
0.039 |
0.015 |
1.365 |
0.246 |
0.402 |
0.213 |
9.148 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 197 | 301 | 0 | 1 | 330 | 456 | 252 |
normalized size | 1 | 1. | 0.87 | 1.33 | 0. | 0. | 1.45 | 2.01 | 1.11 |
time (sec) |
N/A |
0.782 |
0.606 |
0.033 |
0. |
0.245 |
117.726 |
0.226 |
60.588 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 131 | 176 | 0 | 1 | 223 | 271 | 160 |
normalized size | 1 | 1. | 0.9 | 1.21 | 0. | 0.01 | 1.53 | 1.86 | 1.1 |
time (sec) |
N/A |
0.341 |
0.317 |
0.016 |
0. |
0.246 |
57.523 |
0.218 |
26.263 |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 81 | 89 | 0 | 1 | 148 | 142 | 80 |
normalized size | 1 | 1. | 1.05 | 1.16 | 0. | 0.01 | 1.92 | 1.84 | 1.04 |
time (sec) |
N/A |
0.114 |
0.214 |
0.017 |
0. |
0.243 |
49.473 |
0.216 |
10.593 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 53 | 46 | 0 | 1 | 110 | 77 | 49 |
normalized size | 1 | 1. | 0.98 | 0.85 | 0. | 0.02 | 2.04 | 1.43 | 0.91 |
time (sec) |
N/A |
0.073 |
0.076 |
0.011 |
0. |
0.225 |
6.313 |
0.216 |
7.956 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 101 | 196 | 0 | 1 | 270 | 151 | 88 |
normalized size | 1 | 1. | 1. | 1.94 | 0. | 0.01 | 2.67 | 1.5 | 0.87 |
time (sec) |
N/A |
0.386 |
0.367 |
0.026 |
0. |
0.301 |
42.442 |
0.218 |
35.831 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 124 | 192 | 0 | 1 | 1467 | 192 | 114 |
normalized size | 1 | 1. | 0.98 | 1.51 | 0. | 0.01 | 11.55 | 1.51 | 0.9 |
time (sec) |
N/A |
0.38 |
0.268 |
0.031 |
0. |
0.337 |
81.722 |
0.218 |
40.712 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 184 | 424 | 0 | 1 | 0 | 405 | 189 |
normalized size | 1 | 1. | 0.88 | 2.04 | 0. | 0. | 0. | 1.95 | 0.91 |
time (sec) |
N/A |
0.833 |
0.572 |
0.028 |
0. |
0.84 |
0. |
0.228 |
86.964 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 226 | 226 | 236 | 301 | 0 | 1 | 330 | 456 | 252 |
normalized size | 1 | 1. | 1.04 | 1.33 | 0. | 0. | 1.46 | 2.02 | 1.12 |
time (sec) |
N/A |
0.756 |
0.615 |
0.016 |
0. |
0.231 |
94.618 |
0.227 |
60.542 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 157 | 176 | 0 | 1 | 223 | 271 | 160 |
normalized size | 1 | 1. | 1.08 | 1.21 | 0. | 0.01 | 1.54 | 1.87 | 1.1 |
time (sec) |
N/A |
0.319 |
0.352 |
0.014 |
0. |
0.229 |
52. |
0.236 |
26.244 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 92 | 89 | 0 | 1 | 148 | 142 | 80 |
normalized size | 1 | 1. | 1.19 | 1.16 | 0. | 0.01 | 1.92 | 1.84 | 1.04 |
time (sec) |
N/A |
0.113 |
0.254 |
0.013 |
0. |
0.23 |
46.486 |
0.215 |
10.185 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 53 | 46 | 0 | 1 | 110 | 77 | 49 |
normalized size | 1 | 1. | 0.98 | 0.85 | 0. | 0.02 | 2.04 | 1.43 | 0.91 |
time (sec) |
N/A |
0.073 |
0.074 |
0.01 |
0. |
0.226 |
6.015 |
0.209 |
7.576 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 101 | 103 | 0 | 1 | 287 | 151 | 88 |
normalized size | 1 | 1. | 1. | 1.02 | 0. | 0.01 | 2.84 | 1.5 | 0.87 |
time (sec) |
N/A |
0.38 |
0.399 |
0.024 |
0. |
0.285 |
37.913 |
0.218 |
34.504 |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 123 | 137 | 0 | 1 | 1409 | 192 | 114 |
normalized size | 1 | 1. | 0.96 | 1.07 | 0. | 0.01 | 11.01 | 1.5 | 0.89 |
time (sec) |
N/A |
0.39 |
0.374 |
0.026 |
0. |
0.342 |
76.5 |
0.222 |
40.923 |
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 180 | 221 | 0 | 1 | 0 | 406 | 189 |
normalized size | 1 | 1. | 0.88 | 1.08 | 0. | 0. | 0. | 1.98 | 0.92 |
time (sec) |
N/A |
0.815 |
0.563 |
0.024 |
0. |
0.938 |
0. |
0.223 |
84.989 |
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Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
C |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 111 | 89 | 132 | 0 | 88 | 484 | 85 | 100 |
normalized size | 1 | 1. | 0.8 | 1.19 | 0. | 0.79 | 4.36 | 0.77 | 0.9 |
time (sec) |
N/A |
0.158 |
0.093 |
0.056 |
0. |
0.226 |
69.764 |
0.229 |
17.424 |
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Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
C |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 81 | 111 | 0 | 77 | 393 | 72 | 78 |
normalized size | 1 | 1. | 0.93 | 1.28 | 0. | 0.89 | 4.52 | 0.83 | 0.9 |
time (sec) |
N/A |
0.123 |
0.075 |
0.021 |
0. |
0.229 |
48.113 |
0.224 |
14.119 |
|
|
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Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 73 | 90 | 0 | 66 | 269 | 54 | 56 |
normalized size | 1 | 1. | 1.16 | 1.43 | 0. | 1.05 | 4.27 | 0.86 | 0.89 |
time (sec) |
N/A |
0.093 |
0.07 |
0.017 |
0. |
0.243 |
37.144 |
0.217 |
11.379 |
|
|
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Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 61 | 70 | 0 | 58 | 133 | 38 | 29 |
normalized size | 1 | 1. | 1.65 | 1.89 | 0. | 1.57 | 3.59 | 1.03 | 0.78 |
time (sec) |
N/A |
0.065 |
0.053 |
0.024 |
0. |
0.239 |
18.963 |
0.242 |
7.75 |
|
|
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Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 53 | 69 | 0 | 63 | 71 | 59 | 24 |
normalized size | 1 | 1. | 1.83 | 2.38 | 0. | 2.17 | 2.45 | 2.03 | 0.83 |
time (sec) |
N/A |
0.065 |
0.047 |
0.026 |
0. |
0.229 |
19.516 |
0.221 |
8.282 |
|
|
|
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Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 29 | 25 | 0 | 36 | 107 | 119 | 41 |
normalized size | 1 | 1. | 0.64 | 0.56 | 0. | 0.8 | 2.38 | 2.64 | 0.91 |
time (sec) |
N/A |
0.062 |
0.034 |
0.007 |
0. |
0.221 |
26.098 |
0.217 |
7.654 |
|
|
|
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Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 37 | 33 | 0 | 47 | 189 | 176 | 66 |
normalized size | 1 | 1. | 0.51 | 0.45 | 0. | 0.64 | 2.59 | 2.41 | 0.9 |
time (sec) |
N/A |
0.088 |
0.038 |
0.008 |
0. |
0.224 |
42.515 |
0.225 |
10.504 |
|
|
|
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|
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|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 45 | 41 | 0 | 58 | 274 | 236 | 88 |
normalized size | 1 | 1. | 0.46 | 0.42 | 0. | 0.6 | 2.82 | 2.43 | 0.91 |
time (sec) |
N/A |
0.117 |
0.043 |
0.008 |
0. |
0.226 |
74.305 |
0.226 |
13.297 |
|
|
|
|
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|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 53 | 49 | 0 | 69 | 359 | 293 | 110 |
normalized size | 1 | 1. | 0.44 | 0.4 | 0. | 0.57 | 2.97 | 2.42 | 0.91 |
time (sec) |
N/A |
0.147 |
0.045 |
0.009 |
0. |
0.223 |
150.567 |
0.226 |
16.635 |
|
|
|
|
|
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|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 44 | 28 | 82 | 0 | 58 | 32 |
normalized size | 1 | 1. | 1. | 1.13 | 0.72 | 2.1 | 0. | 1.49 | 0.82 |
time (sec) |
N/A |
0.07 |
0.046 |
0.028 |
1.497 |
0.232 |
0. |
0.217 |
7.143 |
|
|
|
|
|
|
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|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 44 | 28 | 82 | 0 | 58 | 32 |
normalized size | 1 | 1. | 1. | 1.13 | 0.72 | 2.1 | 0. | 1.49 | 0.82 |
time (sec) |
N/A |
0.116 |
0.027 |
0.006 |
1.489 |
0.232 |
0. |
0.217 |
13.226 |
|
|
|
|
|
|
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|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 309 | 624 | 0 | 0 | 0 | 0 | 107 |
normalized size | 1 | 1. | 2.13 | 4.3 | 0. | 0. | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.681 |
2.308 |
0.245 |
0. |
0. |
0. |
0. |
84.363 |
|
|
|
|
|
|
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|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 221 | 221 | 312 | 940 | 0 | 0 | 0 | 0 | 194 |
normalized size | 1 | 1. | 1.41 | 4.25 | 0. | 0. | 0. | 0. | 0.88 |
time (sec) |
N/A |
1.068 |
3.829 |
0.174 |
0. |
0. |
0. |
0. |
134.127 |
|
|
|
|
|
|
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|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 281 | 281 | 135 | 166 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.48 | 0.59 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.877 |
0.425 |
0.097 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 130 | 161 | 0 | 0 | 0 | 0 | 286 |
normalized size | 1 | 1. | 0.53 | 0.66 | 0. | 0. | 0. | 0. | 1.18 |
time (sec) |
N/A |
0.721 |
0.343 |
0.017 |
0. |
0. |
0. |
0. |
94.619 |
|
|
|
|
|
|
|
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|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 125 | 156 | 0 | 0 | 0 | 0 | 226 |
normalized size | 1 | 1. | 0.65 | 0.81 | 0. | 0. | 0. | 0. | 1.17 |
time (sec) |
N/A |
0.463 |
0.33 |
0.017 |
0. |
0. |
0. |
0. |
46.376 |
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 120 | 151 | 0 | 0 | 0 | 0 | 197 |
normalized size | 1 | 1. | 0.74 | 0.93 | 0. | 0. | 0. | 0. | 1.22 |
time (sec) |
N/A |
0.376 |
0.248 |
0.013 |
0. |
0. |
0. |
0. |
34.899 |
|
|
|
|
|
|
|
|
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|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 182 | 182 | 141 | 192 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.77 | 1.05 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.791 |
0.423 |
0.032 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 338 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.79 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.797 |
0.751 |
0.038 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 136 | 488 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.6 | 2.15 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.962 |
0.527 |
0.04 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 263 | 141 | 638 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.54 | 2.43 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.131 |
0.629 |
0.04 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 570 | 570 | 29892 | 3678 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 52.44 | 6.45 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.401 |
19.097 |
0.097 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 243 | 243 | 130 | 161 | 0 | 0 | 0 | 0 | 286 |
normalized size | 1 | 1. | 0.53 | 0.66 | 0. | 0. | 0. | 0. | 1.18 |
time (sec) |
N/A |
0.729 |
0.395 |
0.035 |
0. |
0. |
0. |
0. |
164.158 |
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 125 | 156 | 0 | 0 | 0 | 0 | 226 |
normalized size | 1 | 1. | 0.61 | 0.76 | 0. | 0. | 0. | 0. | 1.1 |
time (sec) |
N/A |
0.59 |
0.358 |
0.018 |
0. |
0. |
0. |
0. |
75.934 |
|
|
|
|
|
|
|
|
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|
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|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 162 | 162 | 120 | 151 | 0 | 0 | 0 | 0 | 196 |
normalized size | 1 | 1. | 0.74 | 0.93 | 0. | 0. | 0. | 0. | 1.21 |
time (sec) |
N/A |
0.398 |
0.271 |
0.016 |
0. |
0. |
0. |
0. |
37.383 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 115 | 146 | 0 | 0 | 0 | 0 | 167 |
normalized size | 1 | 1. | 0.88 | 1.11 | 0. | 0. | 0. | 0. | 1.27 |
time (sec) |
N/A |
0.303 |
0.258 |
0.011 |
0. |
0. |
0. |
0. |
26.75 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 97 | 85 | 0 | 0 | 0 | 0 | 214 |
normalized size | 1 | 1. | 0.64 | 0.56 | 0. | 0. | 0. | 0. | 1.42 |
time (sec) |
N/A |
0.64 |
0.208 |
0.02 |
0. |
0. |
0. |
0. |
39.396 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 338 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.79 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.799 |
0.859 |
0.024 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 137 | 488 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.61 | 2.17 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.962 |
0.664 |
0.025 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 205 | 205 | 125 | 156 | 0 | 0 | 0 | 0 | 257 |
normalized size | 1 | 1. | 0.61 | 0.76 | 0. | 0. | 0. | 0. | 1.25 |
time (sec) |
N/A |
0.594 |
0.304 |
0.037 |
0. |
0. |
0. |
0. |
131.002 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 120 | 151 | 0 | 0 | 0 | 0 | 196 |
normalized size | 1 | 1. | 0.72 | 0.9 | 0. | 0. | 0. | 0. | 1.17 |
time (sec) |
N/A |
0.496 |
0.303 |
0.022 |
0. |
0. |
0. |
0. |
60.279 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 131 | 131 | 115 | 146 | 0 | 0 | 0 | 0 | 170 |
normalized size | 1 | 1. | 0.88 | 1.11 | 0. | 0. | 0. | 0. | 1.3 |
time (sec) |
N/A |
0.329 |
0.237 |
0.02 |
0. |
0. |
0. |
0. |
30.094 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
C |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 111 | 61 | 0 | 0 | 0 | 0 | 65 |
normalized size | 1 | 1. | 2.36 | 1.3 | 0. | 0. | 0. | 0. | 1.38 |
time (sec) |
N/A |
0.101 |
0.732 |
0.018 |
0. |
0. |
0. |
0. |
8.733 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 70 | 62 | 0 | 0 | 0 | 0 | 138 |
normalized size | 1 | 1. | 0.68 | 0.6 | 0. | 0. | 0. | 0. | 1.34 |
time (sec) |
N/A |
0.476 |
0.221 |
0.021 |
0. |
0. |
0. |
0. |
25.564 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 338 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.79 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.798 |
0.876 |
0.026 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 144 | 488 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.64 | 2.17 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.974 |
0.409 |
0.027 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 293 | 293 | 202 | 382 | 0 | 0 | 0 | 0 | 240 |
normalized size | 1 | 1. | 0.69 | 1.3 | 0. | 0. | 0. | 0. | 0.82 |
time (sec) |
N/A |
2.338 |
1.171 |
0.069 |
0. |
0. |
0. |
0. |
104.411 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 449 | 449 | 381 | 968 | 0 | 0 | 0 | 0 | 379 |
normalized size | 1 | 1. | 0.85 | 2.16 | 0. | 0. | 0. | 0. | 0.84 |
time (sec) |
N/A |
2.939 |
10.635 |
0.039 |
0. |
0. |
0. |
0. |
171.238 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 203 | 125 | 156 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.62 | 0.77 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.6 |
0.358 |
0.04 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 120 | 151 | 0 | 0 | 0 | 0 | 197 |
normalized size | 1 | 1. | 0.73 | 0.92 | 0. | 0. | 0. | 0. | 1.19 |
time (sec) |
N/A |
0.489 |
0.323 |
0.024 |
0. |
0. |
0. |
0. |
96.782 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 129 | 129 | 115 | 146 | 0 | 0 | 0 | 0 | 170 |
normalized size | 1 | 1. | 0.89 | 1.13 | 0. | 0. | 0. | 0. | 1.32 |
time (sec) |
N/A |
0.356 |
0.275 |
0.023 |
0. |
0. |
0. |
0. |
44.621 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 187 | 63 | 0 | 0 | 0 | 0 | 141 |
normalized size | 1 | 1. | 1.91 | 0.64 | 0. | 0. | 0. | 0. | 1.44 |
time (sec) |
N/A |
0.252 |
0.725 |
0.021 |
0. |
0. |
0. |
0. |
22.209 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 79 | 39 | 0 | 0 | 0 | 0 | 65 |
normalized size | 1 | 1. | 1.65 | 0.81 | 0. | 0. | 0. | 0. | 1.35 |
time (sec) |
N/A |
0.094 |
0.182 |
0.02 |
0. |
0. |
0. |
0. |
8.99 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 99 | 40 | 0 | 0 | 0 | 0 | 73 |
normalized size | 1 | 1. | 1.94 | 0.78 | 0. | 0. | 0. | 0. | 1.43 |
time (sec) |
N/A |
0.285 |
0.314 |
0.023 |
0. |
0. |
0. |
0. |
10.184 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 132 | 338 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 1.79 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.786 |
0.806 |
0.03 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 225 | 225 | 147 | 488 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.65 | 2.17 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.969 |
0.428 |
0.038 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 137 | 137 | 180 | 552 | 0 | 0 | 0 | 0 | 114 |
normalized size | 1 | 1. | 1.31 | 4.03 | 0. | 0. | 0. | 0. | 0.83 |
time (sec) |
N/A |
0.365 |
0.944 |
0.033 |
0. |
0. |
0. |
0. |
55.414 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 284 | 284 | 319 | 559 | 0 | 0 | 0 | 0 | 241 |
normalized size | 1 | 1. | 1.12 | 1.97 | 0. | 0. | 0. | 0. | 0.85 |
time (sec) |
N/A |
1.034 |
3.031 |
0.058 |
0. |
0. |
0. |
0. |
116.765 |
|
|
|
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Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 225 | 223 | 0 | 0 | 0 | 0 | 129 |
normalized size | 1 | 1. | 1.36 | 1.35 | 0. | 0. | 0. | 0. | 0.78 |
time (sec) |
N/A |
1.593 |
1.271 |
0.041 |
0. |
0. |
0. |
0. |
17.823 |
|
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 1698 | 2842 | 0 | 0 | 0 | 0 | 316 |
normalized size | 1 | 1. | 4.32 | 7.23 | 0. | 0. | 0. | 0. | 0.8 |
time (sec) |
N/A |
2.537 |
14.338 |
0.136 |
0. |
0. |
0. |
0. |
140.58 |
|
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Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 875 | 875 | 12193 | 17330 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 13.93 | 19.81 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
5.195 |
21.638 |
0.372 |
0. |
0. |
0. |
0. |
0. |
|
|
|
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Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 203 | 184 | 0 | 0 | 0 | 0 | 102 |
normalized size | 1 | 1. | 2.74 | 2.49 | 0. | 0. | 0. | 0. | 1.38 |
time (sec) |
N/A |
0.649 |
0.855 |
0.132 |
0. |
0. |
0. |
0. |
17.292 |
|
|
|
|
|
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Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 203 | 181 | 0 | 0 | 0 | 0 | 107 |
normalized size | 1 | 1. | 2.74 | 2.45 | 0. | 0. | 0. | 0. | 1.45 |
time (sec) |
N/A |
0.755 |
0.128 |
0.034 |
0. |
0. |
0. |
0. |
14.894 |
|
|
|
|
|
|
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Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 218 | 212 | 0 | 0 | 0 | 0 | 121 |
normalized size | 1 | 1. | 2.53 | 2.47 | 0. | 0. | 0. | 0. | 1.41 |
time (sec) |
N/A |
0.657 |
0.817 |
0.134 |
0. |
0. |
0. |
0. |
19.17 |
|
|
|
|
|
|
|
|
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|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 218 | 205 | 0 | 0 | 0 | 0 | 128 |
normalized size | 1 | 1. | 2.53 | 2.38 | 0. | 0. | 0. | 0. | 1.49 |
time (sec) |
N/A |
0.759 |
0.186 |
0.035 |
0. |
0. |
0. |
0. |
15.482 |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 471 | 471 | 350 | 949 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.74 | 2.01 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.626 |
3.742 |
0.148 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 429 | 429 | 345 | 944 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.8 | 2.2 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.445 |
3.711 |
0.028 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 340 | 939 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 2.4 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.258 |
3.631 |
0.026 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 347 | 934 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 2.66 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.116 |
3.38 |
0.046 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 349 | 349 | 330 | 929 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.95 | 2.66 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.131 |
3.328 |
0.057 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 366 | 1221 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.94 | 3.12 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.312 |
3.499 |
0.058 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 251 | 1033 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.76 | 3.13 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.032 |
2.055 |
0.059 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 259 | 1232 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 3.33 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.247 |
2.712 |
0.061 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 429 | 429 | 345 | 944 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.8 | 2.2 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.494 |
3.755 |
0.057 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 340 | 939 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 2.4 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.269 |
3.457 |
0.034 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
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|
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|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 347 | 934 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 2.66 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.126 |
4.345 |
0.029 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 365 | 365 | 318 | 929 | 0 | 0 | 0 | 0 | 396 |
normalized size | 1 | 1. | 0.87 | 2.55 | 0. | 0. | 0. | 0. | 1.08 |
time (sec) |
N/A |
0.834 |
1.906 |
0.033 |
0. |
0. |
0. |
0. |
67.115 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 279 | 279 | 326 | 924 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.17 | 3.31 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.626 |
3.205 |
0.036 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 290 | 290 | 246 | 834 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.85 | 2.88 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.847 |
1.959 |
0.035 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 251 | 1033 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.76 | 3.13 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.043 |
2.004 |
0.039 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 258 | 1232 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 3.33 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.245 |
2.624 |
0.039 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
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Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 391 | 391 | 340 | 939 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.87 | 2.4 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.294 |
3.344 |
0.054 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
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Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 349 | 934 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 2.66 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.138 |
5.131 |
0.033 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
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Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 365 | 365 | 347 | 929 | 0 | 0 | 0 | 0 | 593 |
normalized size | 1 | 1. | 0.95 | 2.55 | 0. | 0. | 0. | 0. | 1.62 |
time (sec) |
N/A |
0.816 |
2.195 |
0.031 |
0. |
0. |
0. |
0. |
85.869 |
|
|
|
|
|
|
|
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Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 170 | 184 | 0 | 0 | 0 | 0 | 294 |
normalized size | 1 | 1. | 1.68 | 1.82 | 0. | 0. | 0. | 0. | 2.91 |
time (sec) |
N/A |
0.199 |
0.548 |
0.038 |
0. |
0. |
0. |
0. |
39.058 |
|
|
|
|
|
|
|
|
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Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 60 | 195 | 237 | 348 | 0 | 0 | 0 | 0 | 396 |
normalized size | 1 | 3.25 | 3.95 | 5.8 | 0. | 0. | 0. | 0. | 6.6 |
time (sec) |
N/A |
0.406 |
1.908 |
0.036 |
0. |
0. |
0. |
0. |
33.807 |
|
|
|
|
|
|
|
|
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|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 290 | 290 | 248 | 834 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.86 | 2.88 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.855 |
2.039 |
0.038 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F |
F |
F(-1) |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 721 | 721 | 6667 | 18077 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 9.25 | 25.07 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.724 |
15.973 |
0.19 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 208 | 206 | 4590 | 0 | 0 | 0 | 0 | 178 |
normalized size | 1 | 1.29 | 1.28 | 28.51 | 0. | 0. | 0. | 0. | 1.11 |
time (sec) |
N/A |
0.464 |
8.681 |
0.173 |
0. |
0. |
0. |
0. |
73.525 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 351 | 351 | 347 | 934 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.99 | 2.66 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.098 |
3.231 |
0.053 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 469 | 469 | 347 | 929 | 0 | 0 | 0 | 0 | 806 |
normalized size | 1 | 1. | 0.74 | 1.98 | 0. | 0. | 0. | 0. | 1.72 |
time (sec) |
N/A |
1.116 |
1.894 |
0.034 |
0. |
0. |
0. |
0. |
128.168 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 185 | 182 | 0 | 0 | 0 | 0 | 87 |
normalized size | 1 | 1. | 1.85 | 1.82 | 0. | 0. | 0. | 0. | 0.87 |
time (sec) |
N/A |
0.196 |
0.617 |
0.031 |
0. |
0. |
0. |
0. |
22.319 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 118 | 140 | 0 | 0 | 0 | 0 | 148 |
normalized size | 1 | 1. | 1.66 | 1.97 | 0. | 0. | 0. | 0. | 2.08 |
time (sec) |
N/A |
0.166 |
0.342 |
0.033 |
0. |
0. |
0. |
0. |
16.544 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 195 | 270 | 237 | 635 | 0 | 0 | 0 | 0 | 479 |
normalized size | 1 | 1.38 | 1.22 | 3.26 | 0. | 0. | 0. | 0. | 2.46 |
time (sec) |
N/A |
0.661 |
1.684 |
0.038 |
0. |
0. |
0. |
0. |
58.46 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 288 | 288 | 246 | 834 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.85 | 2.9 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.83 |
1.814 |
0.042 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 968 | 968 | 6638 | 16526 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 6.86 | 17.07 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.838 |
15.33 |
0.119 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 584 | 2465 | 0 | 0 | 0 | 0 | 180 |
normalized size | 1 | 1. | 2.56 | 10.81 | 0. | 0. | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.846 |
9.51 |
0.076 |
0. |
0. |
0. |
0. |
78.027 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 198 | 227 | 270 | 0 | 0 | 0 | 0 | 172 |
normalized size | 1 | 1.23 | 1.41 | 1.68 | 0. | 0. | 0. | 0. | 1.07 |
time (sec) |
N/A |
0.426 |
2.01 |
0.082 |
0. |
0. |
0. |
0. |
99.293 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 429 | 429 | 3247 | 4660 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 7.57 | 10.86 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.171 |
16.114 |
0.138 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
B |
B |
F |
F |
F(-1) |
F |
F |
verified |
N/A |
N/A |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 786 | 0 | 7061 | 21094 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 8.98 | 26.84 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.147 |
22.022 |
0.293 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 319 | 319 | 262 | 0 | 0 | 0 | 0 | 0 | 267 |
normalized size | 1 | 1. | 0.82 | 0. | 0. | 0. | 0. | 0. | 0.84 |
time (sec) |
N/A |
0.719 |
0.885 |
0.171 |
0. |
0. |
0. |
0. |
97.907 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 216 | 216 | 262 | 0 | 0 | 0 | 0 | 0 | 170 |
normalized size | 1 | 1. | 1.21 | 0. | 0. | 0. | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.44 |
0.855 |
0.101 |
0. |
0. |
0. |
0. |
65.192 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 153 | 0 | 0 | 0 | 0 | 0 | 117 |
normalized size | 1 | 1. | 0.97 | 0. | 0. | 0. | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.319 |
0.272 |
0.089 |
0. |
0. |
0. |
0. |
48.135 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 116 | 0 | 0 | 0 | 0 | 0 | 94 |
normalized size | 1 | 1. | 0.94 | 0. | 0. | 0. | 0. | 0. | 0.76 |
time (sec) |
N/A |
0.154 |
0.135 |
0.087 |
0. |
0. |
0. |
0. |
23.404 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 116 | 0 | 0 | 0 | 0 | 0 | 94 |
normalized size | 1 | 1. | 0.94 | 0. | 0. | 0. | 0. | 0. | 0.76 |
time (sec) |
N/A |
0.131 |
0.121 |
0.082 |
0. |
0. |
0. |
0. |
20.365 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 175 | 175 | 177 | 0 | 0 | 0 | 0 | 0 | 129 |
normalized size | 1 | 1. | 1.01 | 0. | 0. | 0. | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.352 |
0.63 |
0.068 |
0. |
0. |
0. |
0. |
49.546 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
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|
|
Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 228 | 0 | 0 | 0 | 0 | 0 | 175 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 0. | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.448 |
1.181 |
0.106 |
0. |
0. |
0. |
0. |
60.913 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 167 | 167 | 241 | 726 | 0 | 1184 | 8218 | 1 | 180 |
normalized size | 1 | 1. | 1.44 | 4.35 | 0. | 7.09 | 49.21 | 0.01 | 1.08 |
time (sec) |
N/A |
0.373 |
0.671 |
0.012 |
0. |
0.249 |
25.948 |
0.218 |
123.205 |
|
|
|
|
|
|
|
|
|
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|
|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 134 | 134 | 317 | 0 | 0 | 0 | 0 | 0 | 119 |
normalized size | 1 | 1. | 2.37 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.246 |
1.54 |
0.075 |
0. |
0. |
0. |
0. |
19.181 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 390 | 0 | 0 | 0 | 0 | 0 | 100 |
normalized size | 1 | 1. | 2.79 | 0. | 0. | 0. | 0. | 0. | 0.71 |
time (sec) |
N/A |
0.247 |
3.04 |
0.087 |
0. |
0. |
0. |
0. |
28.508 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 224 | 224 | 229 | 0 | 0 | 0 | 0 | 0 | 162 |
normalized size | 1 | 1. | 1.02 | 0. | 0. | 0. | 0. | 0. | 0.72 |
time (sec) |
N/A |
0.58 |
0.74 |
0.131 |
0. |
0. |
0. |
0. |
81.298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 309 | 0 | 0 | 0 | 0 | 0 | 104 |
normalized size | 1 | 1. | 2.21 | 0. | 0. | 0. | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.383 |
1.218 |
0.097 |
0. |
0. |
0. |
0. |
39.07 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 335 | 0 | 0 | 0 | 0 | 0 | 257 |
normalized size | 1 | 1. | 1.26 | 0. | 0. | 0. | 0. | 0. | 0.97 |
time (sec) |
N/A |
0.496 |
1.831 |
0.093 |
0. |
0. |
0. |
0. |
152.063 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 245 | 245 | 1043 | 0 | 0 | 0 | 0 | 0 | 224 |
normalized size | 1 | 1. | 4.26 | 0. | 0. | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
0.464 |
6.167 |
0.088 |
0. |
0. |
0. |
0. |
43.049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 235 | 235 | 324 | 0 | 0 | 0 | 0 | 0 | 216 |
normalized size | 1 | 1. | 1.38 | 0. | 0. | 0. | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.395 |
1.317 |
0.087 |
0. |
0. |
0. |
0. |
39.519 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 261 | 261 | 346 | 0 | 0 | 0 | 0 | 0 | 238 |
normalized size | 1 | 1. | 1.33 | 0. | 0. | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
0.567 |
2.152 |
0.077 |
0. |
0. |
0. |
0. |
61.865 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 203 | 205 | 303 | 0 | 0 | 0 | 0 | 0 | 175 |
normalized size | 1 | 1.01 | 1.49 | 0. | 0. | 0. | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.378 |
2.5 |
0.075 |
0. |
0. |
0. |
0. |
33.058 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 633 | 0 | 0 | 0 | 0 | 0 | 240 |
normalized size | 1 | 1. | 2.57 | 0. | 0. | 0. | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.629 |
2.98 |
0.071 |
0. |
0. |
0. |
0. |
40.52 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 362 | 362 | 315 | 894 | 0 | 2240 | 0 | 0 | 337 |
normalized size | 1 | 1. | 0.87 | 2.47 | 0. | 6.19 | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.988 |
1.421 |
0.012 |
0. |
0.261 |
0. |
0. |
127.151 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 507 | 507 | 495 | 2343 | 0 | 4645 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.98 | 4.62 | 0. | 9.16 | 0. | 0. | 0. |
time (sec) |
N/A |
1.454 |
3.337 |
0.016 |
0. |
0.275 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 815 | 803 | 10997 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0.99 | 13.49 | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.051 |
66.911 |
0.082 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 572 | 566 | 10700 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0.99 | 18.71 | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.129 |
8.021 |
0.076 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 363 | 360 | 321 | 906 | 0 | 2171 | 0 | 0 | 337 |
normalized size | 1 | 0.99 | 0.88 | 2.5 | 0. | 5.98 | 0. | 0. | 0.93 |
time (sec) |
N/A |
1.125 |
2.355 |
0.012 |
0. |
0.258 |
0. |
0. |
125.324 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 186 | 201 | 509 | 0 | 1222 | 0 | 0 | 156 |
normalized size | 1 | 0.99 | 1.07 | 2.71 | 0. | 6.5 | 0. | 0. | 0.83 |
time (sec) |
N/A |
0.305 |
0.655 |
0.011 |
0. |
0.256 |
0. |
0. |
45.37 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 177 | 190 | 692 | 0 | 0 | 0 | 0 | 0 | 144 |
normalized size | 1 | 1.07 | 3.91 | 0. | 0. | 0. | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.382 |
1.358 |
0.091 |
0. |
0. |
0. |
0. |
54.903 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 250 | 250 | 551 | 0 | 0 | 0 | 0 | 0 | 199 |
normalized size | 1 | 1. | 2.2 | 0. | 0. | 0. | 0. | 0. | 0.8 |
time (sec) |
N/A |
0.727 |
2.697 |
0.076 |
0. |
0. |
0. |
0. |
158.767 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 530 | 530 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.251 |
12.885 |
0.37 |
0. |
0. |
0. |
0. |
0. |
|
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Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 393 | 393 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.473 |
4.218 |
0.251 |
0. |
0. |
0. |
0. |
0. |
|
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Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 256 | 256 | 0 | 0 | 0 | 0 | 0 | 0 | 201 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.657 |
4.42 |
0.215 |
0. |
0. |
0. |
0. |
164.493 |
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Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 296 | 0 | 0 | 0 | 0 | 0 | 94 |
normalized size | 1 | 1. | 2.41 | 0. | 0. | 0. | 0. | 0. | 0.76 |
time (sec) |
N/A |
0.267 |
0.23 |
0.21 |
0. |
0. |
0. |
0. |
79.022 |
|
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Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.069 |
0.366 |
0.22 |
0. |
0. |
0. |
0. |
0. |
|
|
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Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 268 | 268 | 0 | 0 | 0 | 0 | 0 | 0 | 211 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.718 |
4.66 |
0.22 |
0. |
0. |
0. |
0. |
164.387 |
|
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Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 283 | 283 | 576 | 0 | 0 | 0 | 0 | 0 | 218 |
normalized size | 1 | 1. | 2.04 | 0. | 0. | 0. | 0. | 0. | 0.77 |
time (sec) |
N/A |
0.807 |
2.856 |
0.208 |
0. |
0. |
0. |
0. |
171.238 |
|
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Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 277 | 277 | 487 | 0 | 0 | 0 | 0 | 0 | 214 |
normalized size | 1 | 1. | 1.76 | 0. | 0. | 0. | 0. | 0. | 0.77 |
time (sec) |
N/A |
0.604 |
1.094 |
0.206 |
0. |
0. |
0. |
0. |
106.458 |
|
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Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 263 | 261 | 10558 | 0 | 0 | 0 | 0 | 0 | 212 |
normalized size | 1 | 0.99 | 40.14 | 0. | 0. | 0. | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.675 |
8.867 |
0.221 |
0. |
0. |
0. |
0. |
60.389 |
|
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Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 558 | 558 | 31260 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 56.02 | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.137 |
12.62 |
0.222 |
0. |
0. |
0. |
0. |
0. |
|
|
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Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 57 | 139 | 134 | 306 | 313 | 123 | 68 |
normalized size | 1 | 1. | 0.72 | 1.76 | 1.7 | 3.87 | 3.96 | 1.56 | 0.86 |
time (sec) |
N/A |
0.275 |
0.094 |
0.051 |
1.515 |
0.225 |
108.341 |
0.234 |
26.734 |
|
|
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Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 45 | 117 | 105 | 244 | 282 | 97 | 41 |
normalized size | 1 | 1. | 0.71 | 1.86 | 1.67 | 3.87 | 4.48 | 1.54 | 0.65 |
time (sec) |
N/A |
0.15 |
0.061 |
0.021 |
1.488 |
0.231 |
55.04 |
0.229 |
15.392 |
|
|
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|
Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 54 | 94 | 89 | 171 | 245 | 0 | 39 |
normalized size | 1 | 1. | 1.12 | 1.96 | 1.85 | 3.56 | 5.1 | 0. | 0.81 |
time (sec) |
N/A |
0.346 |
0.065 |
0.027 |
1.535 |
0.235 |
57.691 |
0. |
30.214 |
|
|
|
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|
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Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 54 | 97 | 89 | 212 | 221 | 0 | 37 |
normalized size | 1 | 1. | 1.12 | 2.02 | 1.85 | 4.42 | 4.6 | 0. | 0.77 |
time (sec) |
N/A |
0.345 |
0.088 |
0.03 |
1.509 |
0.241 |
65.748 |
0. |
27.354 |
|
|
|
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Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 70 | 108 | 132 | 255 | 218 | 0 | 56 |
normalized size | 1 | 1. | 0.99 | 1.52 | 1.86 | 3.59 | 3.07 | 0. | 0.79 |
time (sec) |
N/A |
0.364 |
0.102 |
0.032 |
1.512 |
0.224 |
81.23 |
0. |
27.079 |
|
|
|
|
|
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|
Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 151 | 80 | 137 | 147 | 370 | 308 | 130 | 119 |
normalized size | 1 | 1.74 | 0.92 | 1.57 | 1.69 | 4.25 | 3.54 | 1.49 | 1.37 |
time (sec) |
N/A |
0.288 |
0.133 |
0.031 |
1.347 |
0.233 |
107.586 |
0.246 |
28.533 |
|
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|
Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 135 | 68 | 120 | 142 | 259 | 277 | 104 | 87 |
normalized size | 1 | 2.6 | 1.31 | 2.31 | 2.73 | 4.98 | 5.33 | 2. | 1.67 |
time (sec) |
N/A |
0.181 |
0.087 |
0.022 |
1.324 |
0.222 |
54.632 |
0.257 |
17.098 |
|
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Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 135 | 76 | 93 | 86 | 212 | 240 | 96 | 65 |
normalized size | 1 | 2.45 | 1.38 | 1.69 | 1.56 | 3.85 | 4.36 | 1.75 | 1.18 |
time (sec) |
N/A |
0.36 |
0.108 |
0.027 |
1.473 |
0.234 |
57.202 |
0.225 |
21.179 |
|
|
|
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|
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|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 135 | 76 | 96 | 86 | 178 | 216 | 112 | 48 |
normalized size | 1 | 2.45 | 1.38 | 1.75 | 1.56 | 3.24 | 3.93 | 2.04 | 0.87 |
time (sec) |
N/A |
0.357 |
0.097 |
0.027 |
1.501 |
0.236 |
66.205 |
0.23 |
17.554 |
|
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|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 129 | 64 | 103 | 88 | 238 | 212 | 196 | 88 |
normalized size | 1 | 1.55 | 0.77 | 1.24 | 1.06 | 2.87 | 2.55 | 2.36 | 1.06 |
time (sec) |
N/A |
0.359 |
0.113 |
0.028 |
1.497 |
0.227 |
82.14 |
0.238 |
20.402 |
|
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Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 171 | 75 | 123 | 119 | 297 | 219 | 266 | 119 |
normalized size | 1 | 1.47 | 0.65 | 1.06 | 1.03 | 2.56 | 1.89 | 2.29 | 1.03 |
time (sec) |
N/A |
0.457 |
0.145 |
0.03 |
1.502 |
0.229 |
156.309 |
0.229 |
25.013 |
|
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|
2.2 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 [72] had the largest ratio of [ 0.3429
]
|
|
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|
| Table 1: Rubi specific breakdown of results for each integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size |
|
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
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|
|
1 |
A |
2 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
2 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
3 |
A |
2 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1. |
27 |
0.037 |
|
|
|
|
|
|
|
5 |
A |
2 |
1 |
1. |
29 |
0.034 |
|
|
|
|
|
|
|
6 |
A |
2 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
7 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
8 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
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|
|
|
9 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
10 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
11 |
A |
4 |
4 |
1. |
18 |
0.222 |
|
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|
|
12 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
13 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
14 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
15 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
16 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
17 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
18 |
A |
4 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
19 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
20 |
A |
6 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
|
21 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
22 |
A |
8 |
6 |
1. |
26 |
0.231 |
|
|
|
|
|
|
|
23 |
A |
7 |
6 |
1. |
26 |
0.231 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
25 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
26 |
A |
5 |
5 |
1. |
26 |
0.192 |
|
|
|
|
|
|
|
27 |
A |
3 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
28 |
A |
4 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
29 |
A |
5 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
30 |
A |
6 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
31 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1. |
36 |
0.139 |
|
|
|
|
|
|
|
33 |
A |
3 |
3 |
1. |
45 |
0.067 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1. |
39 |
0.128 |
|
|
|
|
|
|
|
35 |
A |
10 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
36 |
A |
9 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
37 |
A |
8 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
38 |
A |
7 |
7 |
1. |
28 |
0.25 |
|
|
|
|
|
|
|
39 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
40 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
|
41 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
42 |
A |
12 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
43 |
A |
12 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
44 |
A |
9 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
45 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
46 |
A |
7 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
47 |
A |
6 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
48 |
A |
9 |
9 |
1. |
35 |
0.257 |
|
|
|
|
|
|
|
49 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
50 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
51 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
52 |
A |
7 |
7 |
1. |
35 |
0.2 |
|
|
|
|
|
|
|
53 |
A |
6 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
54 |
A |
2 |
2 |
1. |
28 |
0.071 |
|
|
|
|
|
|
|
55 |
A |
6 |
6 |
1. |
35 |
0.171 |
|
|
|
|
|
|
|
56 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
57 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
58 |
A |
8 |
6 |
1. |
35 |
0.171 |
|
|
|
|
|
|
|
59 |
A |
11 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
60 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
|
61 | A | 7 | 7 | 1. | 35 | 0.2 |
|
|
|
|
|
|
|
62 |
A |
7 |
7 |
1. |
35 |
0.2 |
|
|
|
|
|
|
|
63 |
A |
5 |
5 |
1. |
33 |
0.152 |
|
|
|
|
|
|
|
64 |
A |
2 |
2 |
1. |
28 |
0.071 |
|
|
|
|
|
|
|
65 |
A |
3 |
3 |
1. |
35 |
0.086 |
|
|
|
|
|
|
|
66 |
A |
10 |
10 |
1. |
35 |
0.286 |
|
|
|
|
|
|
|
67 |
A |
11 |
11 |
1. |
35 |
0.314 |
|
|
|
|
|
|
|
68 |
A |
3 |
3 |
1. |
36 |
0.083 |
|
|
|
|
|
|
|
69 |
A |
6 |
5 |
1. |
33 |
0.152 |
|
|
|
|
|
|
|
70 |
A |
4 |
3 |
1. |
35 |
0.086 |
|
|
|
|
|
|
|
71 |
A |
10 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
72 |
A |
18 |
12 |
1. |
35 |
0.343 |
|
|
|
|
|
|
|
73 |
A |
3 |
3 |
1. |
36 |
0.083 |
|
|
|
|
|
|
|
74 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
75 |
A |
3 |
3 |
1. |
40 |
0.075 |
|
|
|
|
|
|
|
76 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
77 |
A |
13 |
11 |
1. |
37 |
0.297 |
|
|
|
|
|
|
|
78 |
A |
12 |
11 |
1. |
37 |
0.297 |
|
|
|
|
|
|
|
79 |
A |
11 |
11 |
1. |
37 |
0.297 |
|
|
|
|
|
|
|
80 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
|
81 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
82 |
A |
11 |
11 |
1. |
37 |
0.297 |
|
|
|
|
|
|
|
83 |
A |
9 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
84 |
A |
10 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
85 |
A |
12 |
11 |
1. |
37 |
0.297 |
|
|
|
|
|
|
|
86 |
A |
11 |
11 |
1. |
37 |
0.297 |
|
|
|
|
|
|
|
87 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
88 |
A |
9 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
89 |
A |
7 |
7 |
1. |
37 |
0.189 |
|
|
|
|
|
|
|
90 |
A |
8 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
91 |
A |
9 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
92 |
A |
10 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
93 |
A |
11 |
11 |
1. |
37 |
0.297 |
|
|
|
|
|
|
|
94 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
95 |
A |
9 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
96 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
97 |
B |
5 |
5 |
3.25 |
37 |
0.135 |
|
|
|
|
|
|
|
98 |
A |
8 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
99 |
A |
7 |
7 |
1. |
37 |
0.189 |
|
|
|
|
|
|
|
100 |
A |
2 |
2 |
1.29 |
37 |
0.054 |
|
|
|
|
|
|
|
|
101 |
A |
10 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
102 |
A |
12 |
10 |
1. |
37 |
0.27 |
|
|
|
|
|
|
|
103 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
104 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
105 |
A |
8 |
7 |
1.38 |
37 |
0.189 |
|
|
|
|
|
|
|
106 |
A |
8 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
107 |
A |
10 |
8 |
1. |
37 |
0.216 |
|
|
|
|
|
|
|
108 |
A |
2 |
2 |
1. |
37 |
0.054 |
|
|
|
|
|
|
|
109 |
A |
2 |
2 |
1.23 |
37 |
0.054 |
|
|
|
|
|
|
|
110 |
A |
5 |
5 |
1. |
37 |
0.135 |
|
|
|
|
|
|
|
111 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
112 |
A |
8 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
113 |
A |
6 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
114 |
A |
4 |
2 |
1. |
25 |
0.08 |
|
|
|
|
|
|
|
115 |
A |
3 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
116 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
117 |
A |
5 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
118 |
A |
6 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
119 |
A |
2 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
120 |
A |
2 |
2 |
1. |
25 |
0.08 |
|
|
|
|
|
|
|
|
121 | A | 3 | 2 | 1. | 27 | 0.074 |
|
|
|
|
|
|
|
122 |
A |
5 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
123 |
A |
6 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
124 |
A |
3 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
125 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
126 |
A |
3 |
3 |
1. |
27 |
0.111 |
|
|
|
|
|
|
|
127 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
128 |
A |
3 |
3 |
1.01 |
29 |
0.103 |
|
|
|
|
|
|
|
129 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
130 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
131 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
132 |
A |
10 |
9 |
0.99 |
31 |
0.29 |
|
|
|
|
|
|
|
133 |
A |
9 |
8 |
0.99 |
31 |
0.258 |
|
|
|
|
|
|
|
134 |
A |
3 |
3 |
0.99 |
29 |
0.103 |
|
|
|
|
|
|
|
135 |
A |
3 |
3 |
0.99 |
24 |
0.125 |
|
|
|
|
|
|
|
136 |
A |
5 |
5 |
1.07 |
27 |
0.185 |
|
|
|
|
|
|
|
137 |
A |
7 |
4 |
1. |
29 |
0.138 |
|
|
|
|
|
|
|
138 |
A |
31 |
5 |
1. |
29 |
0.172 |
|
|
|
|
|
|
|
139 |
A |
15 |
5 |
1. |
29 |
0.172 |
|
|
|
|
|
|
|
140 |
A |
7 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
|
141 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
142 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
143 |
A |
7 |
4 |
1. |
33 |
0.121 |
|
|
|
|
|
|
|
144 |
A |
7 |
4 |
1. |
34 |
0.118 |
|
|
|
|
|
|
|
145 |
A |
5 |
5 |
1. |
34 |
0.147 |
|
|
|
|
|
|
|
146 |
A |
3 |
3 |
0.99 |
34 |
0.088 |
|
|
|
|
|
|
|
147 |
A |
4 |
3 |
1. |
34 |
0.088 |
|
|
|
|
|
|
|
148 |
A |
4 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
149 |
A |
4 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
150 |
A |
7 |
7 |
1. |
33 |
0.212 |
|
|
|
|
|
|
|
151 |
A |
7 |
7 |
1. |
33 |
0.212 |
|
|
|
|
|
|
|
152 |
A |
6 |
6 |
1. |
33 |
0.182 |
|
|
|
|
|
|
|
153 |
A |
5 |
5 |
1.74 |
30 |
0.167 |
|
|
|
|
|
|
|
154 |
B |
5 |
5 |
2.6 |
29 |
0.172 |
|
|
|
|
|
|
|
155 |
B |
8 |
8 |
2.45 |
32 |
0.25 |
|
|
|
|
|
|
|
156 |
B |
8 |
8 |
2.45 |
32 |
0.25 |
|
|
|
|
|
|
|
157 |
A |
6 |
6 |
1.55 |
32 |
0.188 |
|
|
|
|
|
|
|
158 |
A |
7 |
7 |
1.47 |
32 |
0.219 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|