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 |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 10 | 12 | 12 | 8 | 12 | 8 |
normalized size | 1 | 1. | 1. | 0.77 | 0.92 | 0.92 | 0.62 | 0.92 | 0.62 |
time (sec) |
N/A |
0.005 |
0.003 |
0.264 |
1.325 |
0.209 |
0.031 |
0.231 |
0.518 |
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 18 | 15 | 26 | 26 | 39 | 26 | 22 |
normalized size | 1 | 1. | 0.67 | 0.56 | 0.96 | 0.96 | 1.44 | 0.96 | 0.81 |
time (sec) |
N/A |
0.015 |
0.006 |
0.004 |
1.354 |
0.218 |
1.489 |
0.214 |
1.479 |
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 21 | 18 | 30 | 30 | 48 | 30 | 29 |
normalized size | 1 | 1. | 0.62 | 0.53 | 0.88 | 0.88 | 1.41 | 0.88 | 0.85 |
time (sec) |
N/A |
0.017 |
0.008 |
0.006 |
1.347 |
0.238 |
2.128 |
0.216 |
1.371 |
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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 |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 18 | 15 | 26 | 19 | 61 | 26 | 22 |
normalized size | 1 | 1. | 0.67 | 0.56 | 0.96 | 0.7 | 2.26 | 0.96 | 0.81 |
time (sec) |
N/A |
0.015 |
0.006 |
0.004 |
1.343 |
0.211 |
1.589 |
0.221 |
1.56 |
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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 |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 13 | 16 | 30 | 22 | 16 | 14 |
normalized size | 1 | 1. | 1. | 0.93 | 1.14 | 2.14 | 1.57 | 1.14 | 1. |
time (sec) |
N/A |
0.006 |
0.007 |
0.172 |
1.343 |
0.219 |
0.132 |
0.222 |
1.235 |
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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 | 13 | 13 | 15 | 11 | 15 | 15 | 8 | 15 | 8 |
normalized size | 1 | 1. | 1.15 | 0.85 | 1.15 | 1.15 | 0.62 | 1.15 | 0.62 |
time (sec) |
N/A |
0.01 |
0.003 |
0.797 |
1.347 |
0.217 |
0.043 |
0.212 |
0.712 |
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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 | 23 | 23 | 16 | 13 | 20 | 23 | 97 | 20 | 19 |
normalized size | 1 | 1. | 0.7 | 0.57 | 0.87 | 1. | 4.22 | 0.87 | 0.83 |
time (sec) |
N/A |
0.012 |
0.005 |
0.004 |
1.348 |
0.207 |
1.447 |
0.217 |
0.988 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 14 | 8 | 14 | 12 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 1.75 | 1. | 1.75 | 1.5 |
time (sec) |
N/A |
0.021 |
0.003 |
0.021 |
1.355 |
0.206 |
0.04 |
0.218 |
1.154 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 13 | 16 | 24 | 29 | 16 | 12 |
normalized size | 1 | 1. | 1. | 0.81 | 1. | 1.5 | 1.81 | 1. | 0.75 |
time (sec) |
N/A |
0.036 |
0.018 |
0.021 |
1.355 |
0.234 |
0.399 |
0.22 |
1.885 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 6 | 6 | 7 | 8 | 8 | 5 | 8 | 5 |
normalized size | 1 | 1. | 1. | 1.17 | 1.33 | 1.33 | 0.83 | 1.33 | 0.83 |
time (sec) |
N/A |
0.027 |
0.005 |
0.325 |
1.353 |
0.223 |
1.018 |
0.22 |
1.521 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 11 | 14 | 16 | 12 | 8 | 14 |
normalized size | 1 | 1. | 1. | 0.92 | 1.17 | 1.33 | 1. | 0.67 | 1.17 |
time (sec) |
N/A |
0.04 |
0.013 |
0.21 |
1.353 |
0.234 |
1.138 |
0.214 |
2.428 |
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 9 | 11 | 11 | 10 | 11 | 10 |
normalized size | 1 | 1. | 1. | 0.9 | 1.1 | 1.1 | 1. | 1.1 | 1. |
time (sec) |
N/A |
0.027 |
0.005 |
0.015 |
1.371 |
0.218 |
0.434 |
0.213 |
2.317 |
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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 |
A |
A |
F(-2) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 10 | 12 | 12 | 0 | 12 | 7 |
normalized size | 1 | 1. | 1. | 1.11 | 1.33 | 1.33 | 0. | 1.33 | 0.78 |
time (sec) |
N/A |
0.019 |
0.009 |
0.031 |
1.337 |
0.269 |
0. |
0.215 |
1.38 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 32 | 15 | 15 | 10 | 15 | 10 |
normalized size | 1 | 1. | 1. | 2.13 | 1. | 1. | 0.67 | 1. | 0.67 |
time (sec) |
N/A |
0.007 |
0.005 |
0.013 |
1.343 |
0.21 |
0.342 |
0.215 |
0.977 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 16 | 13 | 20 | 20 | 34 | 20 | 19 |
normalized size | 1 | 1. | 0.7 | 0.57 | 0.87 | 0.87 | 1.48 | 0.87 | 0.83 |
time (sec) |
N/A |
0.012 |
0.005 |
0.004 |
1.324 |
0.208 |
1.536 |
0.217 |
1.02 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 10 | 12 | 23 | 8 | 12 | 8 |
normalized size | 1 | 1. | 1. | 0.91 | 1.09 | 2.09 | 0.73 | 1.09 | 0.73 |
time (sec) |
N/A |
0.005 |
0.006 |
0.003 |
1.351 |
0.207 |
1.181 |
0.222 |
0.496 |
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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 |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 27 | 15 | 15 | 27 | 15 | 10 |
normalized size | 1 | 1. | 1. | 1.8 | 1. | 1. | 1.8 | 1. | 0.67 |
time (sec) |
N/A |
0.007 |
0.006 |
0.006 |
1.367 |
0.205 |
0.452 |
0.216 |
0.931 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 12 | 15 | 15 | 12 | 15 | 12 |
normalized size | 1 | 1. | 1. | 0.8 | 1. | 1. | 0.8 | 1. | 0.8 |
time (sec) |
N/A |
0.043 |
0.029 |
0.017 |
1.347 |
0.223 |
0.482 |
0.229 |
2.863 |
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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 |
F |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 37 | 0 | 18 | 31 | 0 | 20 | 26 |
normalized size | 1 | 1. | 1.16 | 0. | 0.56 | 0.97 | 0. | 0.62 | 0.81 |
time (sec) |
N/A |
0.194 |
0.027 |
0.308 |
1.374 |
0.242 |
0. |
0.223 |
5.816 |
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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 |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 14 | 18 | 18 | 14 | 18 | 14 |
normalized size | 1 | 1. | 1. | 0.82 | 1.06 | 1.06 | 0.82 | 1.06 | 0.82 |
time (sec) |
N/A |
0.191 |
0.014 |
0.007 |
1.36 |
0.24 |
0.479 |
0.217 |
4.909 |
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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 |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 13 | 13 | 9 | 16 | 15 | 0 | 15 |
normalized size | 1 | 1. | 0.81 | 0.81 | 0.56 | 1. | 0.94 | 0. | 0.94 |
time (sec) |
N/A |
0.021 |
0.009 |
0.004 |
1.352 |
0.234 |
1.164 |
0. |
2.341 |
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 9 | 11 | 11 | 7 | 11 | 7 |
normalized size | 1 | 1. | 1. | 1.12 | 1.38 | 1.38 | 0.88 | 1.38 | 0.88 |
time (sec) |
N/A |
0.015 |
0.003 |
0.093 |
1.364 |
0.242 |
0.181 |
0.214 |
0.754 |
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 15 | 18 | 20 | 20 | 17 | 20 | 17 |
normalized size | 1 | 1. | 0.88 | 1.06 | 1.18 | 1.18 | 1. | 1.18 | 1. |
time (sec) |
N/A |
0.034 |
0.01 |
0.007 |
1.341 |
0.239 |
0.394 |
0.219 |
1.391 |
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Problem 24 |
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 | 19 | 24 | 27 | 27 | 26 | 27 | 26 |
normalized size | 1 | 1. | 0.83 | 1.04 | 1.17 | 1.17 | 1.13 | 1.17 | 1.13 |
time (sec) |
N/A |
0.053 |
0.012 |
0.01 |
1.335 |
0.24 |
0.87 |
0.216 |
1.922 |
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Problem 25 |
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 | 24 | 24 | 20 | 25 | 28 | 28 | 26 | 28 | 26 |
normalized size | 1 | 1. | 0.83 | 1.04 | 1.17 | 1.17 | 1.08 | 1.17 | 1.08 |
time (sec) |
N/A |
0.052 |
0.012 |
0.007 |
1.35 |
0.243 |
0.924 |
0.222 |
1.926 |
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Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 7 | 8 | 8 | 5 | 8 | 0 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 1. | 0.62 | 1. | 0. |
time (sec) |
N/A |
0.011 |
0.002 |
0.003 |
1.34 |
0.235 |
0.036 |
0.218 |
0. |
|
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Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 18 | 18 | 19 | 23 | 24 | 19 | 19 |
normalized size | 1 | 1. | 0.78 | 0.78 | 0.83 | 1. | 1.04 | 0.83 | 0.83 |
time (sec) |
N/A |
0.02 |
0.004 |
0.004 |
1.396 |
0.226 |
0.413 |
0.214 |
1.04 |
|
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Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 11 | 14 | 14 | 10 | 14 | 10 |
normalized size | 1 | 1. | 1. | 0.79 | 1. | 1. | 0.71 | 1. | 0.71 |
time (sec) |
N/A |
0.01 |
0.003 |
0.009 |
1.351 |
0.22 |
0.035 |
0.214 |
0.483 |
|
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Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 15 | 11 | 15 | 15 | 8 | 15 | 8 |
normalized size | 1 | 1. | 1.15 | 0.85 | 1.15 | 1.15 | 0.62 | 1.15 | 0.62 |
time (sec) |
N/A |
0.011 |
0.003 |
0.001 |
1.361 |
0.212 |
0.039 |
0.227 |
0.633 |
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Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 22 | 18 | 22 | 26 | 24 | 22 | 24 |
normalized size | 1 | 1. | 0.92 | 0.75 | 0.92 | 1.08 | 1. | 0.92 | 1. |
time (sec) |
N/A |
0.017 |
0.003 |
0.105 |
1.33 |
0.225 |
0.038 |
0.217 |
0.559 |
|
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Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 23 | 17 | 23 | 23 | 17 | 23 | 17 |
normalized size | 1 | 1. | 1.1 | 0.81 | 1.1 | 1.1 | 0.81 | 1.1 | 0.81 |
time (sec) |
N/A |
0.013 |
0.003 |
0.053 |
1.481 |
0.216 |
0.046 |
0.223 |
0.744 |
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Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 30 | 24 | 32 | 34 | 36 | 30 | 36 |
normalized size | 1 | 1. | 0.88 | 0.71 | 0.94 | 1. | 1.06 | 0.88 | 1.06 |
time (sec) |
N/A |
0.025 |
0.003 |
0.047 |
1.352 |
0.256 |
0.039 |
0.225 |
0.665 |
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Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 25 | 26 | 26 | 36 | 26 | 0 |
normalized size | 1 | 1. | 1. | 1. | 1.04 | 1.04 | 1.44 | 1.04 | 0. |
time (sec) |
N/A |
0.023 |
0.005 |
0.007 |
1.348 |
0.237 |
0.41 |
0.23 |
0. |
|
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Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 31 | 23 | 31 | 31 | 39 | 31 | 32 |
normalized size | 1 | 1. | 0.94 | 0.7 | 0.94 | 0.94 | 1.18 | 0.94 | 0.97 |
time (sec) |
N/A |
0.033 |
0.006 |
0.078 |
1.357 |
0.227 |
0.819 |
0.222 |
1.326 |
|
|
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|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 29 | 37 | 35 | 39 | 56 | 35 | 36 |
normalized size | 1 | 1. | 0.71 | 0.9 | 0.85 | 0.95 | 1.37 | 0.85 | 0.88 |
time (sec) |
N/A |
0.046 |
0.034 |
0.036 |
1.354 |
0.217 |
0.85 |
0.216 |
1.568 |
|
|
|
|
|
|
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|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 11 | 14 | 14 | 10 | 14 | 10 |
normalized size | 1 | 1. | 1. | 0.79 | 1. | 1. | 0.71 | 1. | 0.71 |
time (sec) |
N/A |
0.01 |
0.003 |
0.01 |
1.362 |
0.223 |
0.034 |
0.216 |
0.509 |
|
|
|
|
|
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|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 15 | 11 | 12 | 14 | 8 | 12 | 8 |
normalized size | 1 | 1. | 1.36 | 1. | 1.09 | 1.27 | 0.73 | 1.09 | 0.73 |
time (sec) |
N/A |
0.011 |
0.003 |
0.04 |
1.355 |
0.206 |
0.04 |
0.235 |
0.671 |
|
|
|
|
|
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|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 22 | 18 | 22 | 26 | 24 | 22 | 24 |
normalized size | 1 | 1. | 0.92 | 0.75 | 0.92 | 1.08 | 1. | 0.92 | 1. |
time (sec) |
N/A |
0.019 |
0.003 |
0.062 |
1.358 |
0.246 |
0.039 |
0.237 |
0.591 |
|
|
|
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|
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|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 60 | 69 | 84 | 343 | 180 | 68 | 70 |
normalized size | 1 | 1. | 0.71 | 0.82 | 1. | 4.08 | 2.14 | 0.81 | 0.83 |
time (sec) |
N/A |
0.036 |
0.061 |
0.028 |
1.507 |
0.214 |
6.101 |
0.249 |
2.687 |
|
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|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 25 | 22 | 46 | 134 | 39 | 38 | 31 |
normalized size | 1 | 1. | 0.66 | 0.58 | 1.21 | 3.53 | 1.03 | 1. | 0.82 |
time (sec) |
N/A |
0.035 |
0.01 |
0.007 |
1.511 |
0.195 |
1.686 |
0.235 |
2.363 |
|
|
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|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 172 | 172 | 122 | 168 | 0 | 0 | 31 | 0 | 162 |
normalized size | 1 | 1. | 0.71 | 0.98 | 0. | 0. | 0.18 | 0. | 0.94 |
time (sec) |
N/A |
0.126 |
0.266 |
0.658 |
0. |
0. |
0.9 |
0. |
2.248 |
|
|
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|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 6 | 6 | 7 | 8 | 8 | 7 | 8 | 3 |
normalized size | 1 | 1. | 1. | 1.17 | 1.33 | 1.33 | 1.17 | 1.33 | 0.5 |
time (sec) |
N/A |
0.009 |
0.004 |
0.019 |
1.505 |
0.213 |
0.045 |
0.221 |
0.046 |
|
|
|
|
|
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|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 18 | 13 | 16 | 16 | 19 | 16 | 10 |
normalized size | 1 | 1. | 1.29 | 0.93 | 1.14 | 1.14 | 1.36 | 1.14 | 0.71 |
time (sec) |
N/A |
0.016 |
0.005 |
0.004 |
1.499 |
0.243 |
0.05 |
0.233 |
0.473 |
|
|
|
|
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 8 | 8 | 8 | 12 | 14 | 27 | 8 | 24 | 7 |
normalized size | 1 | 1. | 1. | 1.5 | 1.75 | 3.38 | 1. | 3. | 0.88 |
time (sec) |
N/A |
0.01 |
0.004 |
0.011 |
1.502 |
0.215 |
0.045 |
0.226 |
0.457 |
|
|
|
|
|
|
|
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|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 18 | 14 | 22 | 65 | 19 | 46 | 14 |
normalized size | 1 | 1. | 1.5 | 1.17 | 1.83 | 5.42 | 1.58 | 3.83 | 1.17 |
time (sec) |
N/A |
0.017 |
0.005 |
0.004 |
1.5 |
0.206 |
0.053 |
0.22 |
0.491 |
|
|
|
|
|
|
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|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 26 | 21 | 27 | 24 | 26 | 24 | 20 |
normalized size | 1 | 1. | 1.18 | 0.95 | 1.23 | 1.09 | 1.18 | 1.09 | 0.91 |
time (sec) |
N/A |
0.021 |
0.008 |
0.019 |
1.325 |
0.215 |
0.212 |
0.218 |
1.16 |
|
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 10 | 12 | 93 | 22 | 12 | 8 |
normalized size | 1 | 1. | 1. | 0.77 | 0.92 | 7.15 | 1.69 | 0.92 | 0.62 |
time (sec) |
N/A |
0.005 |
0.004 |
0.005 |
1.355 |
0.203 |
0.215 |
0.22 |
0.739 |
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 11 | 52 | 12 | 1 | 58 | 12 | 7 |
normalized size | 1 | 1. | 0.85 | 4. | 0.92 | 0.08 | 4.46 | 0.92 | 0.54 |
time (sec) |
N/A |
0.007 |
0.003 |
0.026 |
1.369 |
0.194 |
0.038 |
0.228 |
0.719 |
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 16 | 20 | 26 | 26 | 15 | 19 | 15 |
normalized size | 1 | 1. | 0.89 | 1.11 | 1.44 | 1.44 | 0.83 | 1.06 | 0.83 |
time (sec) |
N/A |
0.009 |
0.006 |
0.01 |
1.36 |
0.19 |
0.103 |
0.215 |
1.139 |
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Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 43 | 32 | 12 | 1 | 31 | 12 | 7 |
normalized size | 1 | 1. | 3.91 | 2.91 | 1.09 | 0.09 | 2.82 | 1.09 | 0.64 |
time (sec) |
N/A |
0.007 |
0.002 |
0.003 |
1.413 |
0.21 |
0.033 |
0.219 |
0.761 |
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Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 140 | 107 | 143 | 1 | 131 | 143 | 36 |
normalized size | 1 | 1. | 2.5 | 1.91 | 2.55 | 0.02 | 2.34 | 2.55 | 0.64 |
time (sec) |
N/A |
0.093 |
0.003 |
0.003 |
1.378 |
0.178 |
0.067 |
0.219 |
7.446 |
|
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Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 4 | 4 | 4 | 5 | 5 | 5 | 3 | 5 | 3 |
normalized size | 1 | 1. | 1. | 1.25 | 1.25 | 1.25 | 0.75 | 1.25 | 0.75 |
time (sec) |
N/A |
0.015 |
0.006 |
0.005 |
1.34 |
0.216 |
1.073 |
0.216 |
1.049 |
|
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Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 46 | 49 | 50 | 50 | 60 | 50 | 60 |
normalized size | 1 | 1. | 0.74 | 0.79 | 0.81 | 0.81 | 0.97 | 0.81 | 0.97 |
time (sec) |
N/A |
0.07 |
0.028 |
0.007 |
1.386 |
0.215 |
3.389 |
0.218 |
2.242 |
|
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Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 9 | 11 | 11 | 7 | 11 | 7 |
normalized size | 1 | 1. | 1. | 0.9 | 1.1 | 1.1 | 0.7 | 1.1 | 0.7 |
time (sec) |
N/A |
0.013 |
0.004 |
0.003 |
1.353 |
0.25 |
0.36 |
0.225 |
0.994 |
|
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Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 49 | 13 | 16 | 16 | 15 | 248 | 15 |
normalized size | 1 | 1. | 3.06 | 0.81 | 1. | 1. | 0.94 | 15.5 | 0.94 |
time (sec) |
N/A |
0.055 |
0.107 |
0.043 |
1.414 |
0.228 |
3.298 |
0.234 |
2.741 |
|
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Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 9 | 11 | 11 | 7 | 12 | 7 |
normalized size | 1 | 1. | 1. | 0.9 | 1.1 | 1.1 | 0.7 | 1.2 | 0.7 |
time (sec) |
N/A |
0.005 |
0.001 |
0. |
1.445 |
0.204 |
0.031 |
0.215 |
0.51 |
|
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Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 16 | 16 | 20 | 15 | 20 | 15 |
normalized size | 1 | 1. | 1. | 1.07 | 1.07 | 1.33 | 1. | 1.33 | 1. |
time (sec) |
N/A |
0.008 |
0.002 |
0.025 |
1.385 |
0.259 |
0.079 |
0.22 |
0.514 |
|
|
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Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 14 | 18 | 18 | 12 | 18 | 0 |
normalized size | 1 | 1. | 1. | 0.82 | 1.06 | 1.06 | 0.71 | 1.06 | 0. |
time (sec) |
N/A |
0.008 |
0.001 |
0.003 |
1.544 |
0.212 |
0.069 |
0.223 |
0. |
|
|
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Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 23 | 23 | 30 | 22 | 30 | 0 |
normalized size | 1 | 1. | 1. | 0.82 | 0.82 | 1.07 | 0.79 | 1.07 | 0. |
time (sec) |
N/A |
0.017 |
0.002 |
0.003 |
1.656 |
0.203 |
0.088 |
0.219 |
0. |
|
|
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Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 4 | 4 | 4 | 5 | 5 | 5 | 3 | 7 | 3 |
normalized size | 1 | 1. | 1. | 1.25 | 1.25 | 1.25 | 0.75 | 1.75 | 0.75 |
time (sec) |
N/A |
0.003 |
0.001 |
0.002 |
1.624 |
0.191 |
0.026 |
0.216 |
0.462 |
|
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Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3 | 3 | 3 | 4 | 4 | 15 | 3 | 15 | 3 |
normalized size | 1 | 1. | 1. | 1.33 | 1.33 | 5. | 1. | 5. | 1. |
time (sec) |
N/A |
0.005 |
0.003 |
0.001 |
1.62 |
0.219 |
0.044 |
0.217 |
0.03 |
|
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|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 21 | 36 | 0 | 43 | 0 | 0 | 22 |
normalized size | 1 | 1. | 0.75 | 1.29 | 0. | 1.54 | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.02 |
0.014 |
0.083 |
0. |
0.219 |
0. |
0. |
1.616 |
|
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Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 23 | 23 | 30 | 26 | 30 | 26 |
normalized size | 1 | 1. | 1. | 0.82 | 0.82 | 1.07 | 0.93 | 1.07 | 0.93 |
time (sec) |
N/A |
0.031 |
0.004 |
0.001 |
1.416 |
0.206 |
0.091 |
0.235 |
1.928 |
|
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|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 3 | 3 | 3 | 4 | 4 | 4 | 3 | 5 | 3 |
normalized size | 1 | 1. | 1. | 1.33 | 1.33 | 1.33 | 1. | 1.67 | 1. |
time (sec) |
N/A |
0.018 |
0.001 |
0. |
1.43 |
0.218 |
0.079 |
0.238 |
1.118 |
|
|
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Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 11 | 14 | 14 | 8 | 14 | 8 |
normalized size | 1 | 1. | 1. | 0.92 | 1.17 | 1.17 | 0.67 | 1.17 | 0.67 |
time (sec) |
N/A |
0.026 |
0.003 |
0.002 |
1.448 |
0.207 |
0.08 |
0.24 |
1.463 |
|
|
|
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|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 16 | 18 | 23 | 16 | 20 | 23 | 24 |
normalized size | 1 | 1. | 0.7 | 0.78 | 1. | 0.7 | 0.87 | 1. | 1.04 |
time (sec) |
N/A |
0.065 |
0.008 |
0.009 |
1.502 |
0.203 |
1.435 |
0.235 |
5.066 |
|
|
|
|
|
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|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 32 | 31 | 42 | 37 | 42 | 37 |
normalized size | 1 | 1. | 1. | 0.82 | 0.79 | 1.08 | 0.95 | 1.08 | 0.95 |
time (sec) |
N/A |
0.049 |
0.004 |
0.003 |
1.564 |
0.205 |
0.113 |
0.215 |
2.806 |
|
|
|
|
|
|
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|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 9 | 9 | 9 | 7 | 8 | 8 | 5 | 8 | 5 |
normalized size | 1 | 1. | 1. | 0.78 | 0.89 | 0.89 | 0.56 | 0.89 | 0.56 |
time (sec) |
N/A |
0.02 |
0.003 |
0.004 |
1.548 |
0.208 |
0.063 |
0.222 |
1.384 |
|
|
|
|
|
|
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|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 12 | 16 | 15 | 10 | 15 | 10 |
normalized size | 1 | 1. | 1. | 0.86 | 1.14 | 1.07 | 0.71 | 1.07 | 0.71 |
time (sec) |
N/A |
0.02 |
0.005 |
0.006 |
1.483 |
0.207 |
0.153 |
0.216 |
1.321 |
|
|
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Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 8 | 9 | 9 | 7 | 9 | 7 |
normalized size | 1 | 1. | 1. | 0.8 | 0.9 | 0.9 | 0.7 | 0.9 | 0.7 |
time (sec) |
N/A |
0.016 |
0.008 |
0.01 |
1.419 |
0.214 |
0.355 |
0.223 |
1.671 |
|
|
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 14 | 14 | 15 | 18 | 15 | 15 | 15 |
normalized size | 1 | 1. | 0.74 | 0.74 | 0.79 | 0.95 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A |
0.014 |
0.016 |
0.029 |
1.377 |
0.21 |
0.349 |
0.218 |
1.173 |
|
|
|
|
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Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 12 | 14 | 12 | 18 | 15 | 12 | 15 |
normalized size | 1 | 1. | 0.63 | 0.74 | 0.63 | 0.95 | 0.79 | 0.63 | 0.79 |
time (sec) |
N/A |
0.014 |
0.007 |
0.007 |
1.364 |
0.214 |
0.341 |
0.217 |
1.172 |
|
|
|
|
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Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 12 | 12 | 12 | 7 | 12 | 10 |
normalized size | 1 | 1. | 1. | 1.2 | 1.2 | 1.2 | 0.7 | 1.2 | 1. |
time (sec) |
N/A |
0.013 |
0.003 |
0.008 |
1.349 |
0.218 |
0.056 |
0.219 |
1.188 |
|
|
|
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Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 7 | 7 | 8 | 8 | 5 | 8 | 7 |
normalized size | 1 | 1. | 0.64 | 0.64 | 0.73 | 0.73 | 0.45 | 0.73 | 0.64 |
time (sec) |
N/A |
0.01 |
0.002 |
0.002 |
1.374 |
0.198 |
0.057 |
0.22 |
0.926 |
|
|
|
|
|
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|
Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 11 | 10 | 12 | 12 | 7 | 12 | 10 |
normalized size | 1 | 1. | 0.69 | 0.62 | 0.75 | 0.75 | 0.44 | 0.75 | 0.62 |
time (sec) |
N/A |
0.013 |
0.002 |
0.003 |
1.418 |
0.193 |
0.07 |
0.238 |
1.039 |
|
|
|
|
|
|
|
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|
|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 12 | 12 | 15 | 15 | 10 | 15 | 17 |
normalized size | 1 | 1. | 0.63 | 0.63 | 0.79 | 0.79 | 0.53 | 0.79 | 0.89 |
time (sec) |
N/A |
0.026 |
0.002 |
0.004 |
1.361 |
0.206 |
0.062 |
0.216 |
1.717 |
|
|
|
|
|
|
|
|
|
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|
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 19 | 19 | 22 | 22 | 17 | 22 | 27 |
normalized size | 1 | 1. | 0.59 | 0.59 | 0.69 | 0.69 | 0.53 | 0.69 | 0.84 |
time (sec) |
N/A |
0.03 |
0.004 |
0.003 |
1.416 |
0.208 |
0.079 |
0.237 |
1.892 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 16 | 17 | 15 | 15 | 20 | 15 | 20 |
normalized size | 1 | 1. | 0.67 | 0.71 | 0.62 | 0.62 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A |
0.014 |
0.004 |
0.004 |
1.469 |
0.21 |
0.211 |
0.234 |
1.024 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 18 | 14 | 18 | 18 | 12 | 18 | 19 |
normalized size | 1 | 1. | 0.69 | 0.54 | 0.69 | 0.69 | 0.46 | 0.69 | 0.73 |
time (sec) |
N/A |
0.034 |
0.004 |
0.004 |
1.407 |
0.212 |
0.08 |
0.237 |
1.914 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 28 | 40 | 36 | 42 | 139 | 49 | 36 |
normalized size | 1 | 1. | 0.68 | 0.98 | 0.88 | 1.02 | 3.39 | 1.2 | 0.88 |
time (sec) |
N/A |
0.028 |
0.029 |
0.015 |
1.347 |
0.22 |
2.095 |
0.236 |
1.907 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
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|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 29 | 41 | 39 | 45 | 136 | 51 | 36 |
normalized size | 1 | 1. | 0.69 | 0.98 | 0.93 | 1.07 | 3.24 | 1.21 | 0.86 |
time (sec) |
N/A |
0.026 |
0.029 |
0.006 |
1.385 |
0.224 |
2.135 |
0.236 |
1.884 |
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
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|
|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 18 | 12 | 20 | 12 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 1.2 | 0.8 | 1.33 | 0.8 |
time (sec) |
N/A |
0.007 |
0.002 |
0.004 |
1.387 |
0.224 |
0.234 |
0.218 |
0.843 |
|
|
|
|
|
|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 64 | 22 | 47 | 45 | 0 | 34 | 15 |
normalized size | 1 | 1. | 3.37 | 1.16 | 2.47 | 2.37 | 0. | 1.79 | 0.79 |
time (sec) |
N/A |
0.028 |
0.112 |
0.004 |
1.373 |
0.242 |
0. |
0.231 |
1.765 |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 64 | 20 | 47 | 47 | 0 | 35 | 15 |
normalized size | 1 | 1. | 3.76 | 1.18 | 2.76 | 2.76 | 0. | 2.06 | 0.88 |
time (sec) |
N/A |
0.028 |
0.071 |
0.004 |
1.496 |
0.23 |
0. |
0.229 |
1.74 |
|
|
|
|
|
|
|
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|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 24 | 31 | 31 | 22 | 31 | 22 |
normalized size | 1 | 1. | 1. | 0.96 | 1.24 | 1.24 | 0.88 | 1.24 | 0.88 |
time (sec) |
N/A |
0.054 |
0.012 |
0.158 |
1.574 |
0.219 |
0.21 |
0.235 |
2.871 |
|
|
|
|
|
|
|
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|
|
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|
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|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 26 | 21 | 45 | 53 | 22 | 51 | 15 |
normalized size | 1 | 1. | 1.18 | 0.95 | 2.05 | 2.41 | 1. | 2.32 | 0.68 |
time (sec) |
N/A |
0.035 |
0.008 |
0.013 |
1.529 |
0.238 |
2.239 |
0.237 |
2.698 |
|
|
|
|
|
|
|
|
|
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 15 | 11 | 31 | 19 | 12 | 12 |
normalized size | 1 | 1. | 1. | 0.94 | 0.69 | 1.94 | 1.19 | 0.75 | 0.75 |
time (sec) |
N/A |
0.007 |
0.005 |
0.005 |
1.572 |
0.2 |
1.632 |
0.239 |
0.883 |
|
|
|
|
|
|
|
|
|
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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 |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 14 | 10 | 15 | 28 | 0 | 12 | 22 |
normalized size | 1 | 1. | 1.4 | 1. | 1.5 | 2.8 | 0. | 1.2 | 2.2 |
time (sec) |
N/A |
0.022 |
0.009 |
0.026 |
1.676 |
0.201 |
0. |
0.223 |
0.689 |
|
|
|
|
|
|
|
|
|
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|
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|
|
|
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|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 11 | 14 | 14 | 20 | 14 | 5 |
normalized size | 1 | 1. | 1. | 1.1 | 1.4 | 1.4 | 2. | 1.4 | 0.5 |
time (sec) |
N/A |
0.007 |
0.003 |
0.013 |
1.572 |
0.194 |
0.112 |
0.22 |
0.731 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
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 | 24 | 24 | 24 | 16 | 0 | 1 | 53 | 20 | 22 |
normalized size | 1 | 1. | 1. | 0.67 | 0. | 0.04 | 2.21 | 0.83 | 0.92 |
time (sec) |
N/A |
0.017 |
0.008 |
0.005 |
0. |
0.195 |
0.135 |
0.224 |
1.071 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 17 | 22 | 22 | 26 | 22 | 22 |
normalized size | 1 | 1. | 1. | 0.89 | 1.16 | 1.16 | 1.37 | 1.16 | 1.16 |
time (sec) |
N/A |
0.026 |
0.009 |
0.004 |
1.532 |
0.194 |
0.094 |
0.225 |
0.663 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 21 | 16 | 20 | 18 | 15 | 20 | 15 |
normalized size | 1 | 1. | 1. | 0.76 | 0.95 | 0.86 | 0.71 | 0.95 | 0.71 |
time (sec) |
N/A |
0.018 |
0.003 |
0.005 |
1.525 |
0.208 |
0.32 |
0.218 |
1.829 |
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Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
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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 | 40 | 40 | 30 | 34 | 45 | 32 | 32 | 45 | 27 |
normalized size | 1 | 1. | 0.75 | 0.85 | 1.12 | 0.8 | 0.8 | 1.12 | 0.68 |
time (sec) |
N/A |
0.048 |
0.014 |
0.019 |
1.523 |
0.22 |
0.495 |
0.212 |
3.055 |
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Problem 94 |
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 | 35 | 35 | 26 | 30 | 46 | 34 | 29 | 42 | 29 |
normalized size | 1 | 1. | 0.74 | 0.86 | 1.31 | 0.97 | 0.83 | 1.2 | 0.83 |
time (sec) |
N/A |
0.083 |
0.007 |
0.01 |
1.562 |
0.216 |
0.467 |
0.223 |
6.056 |
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Problem 95 |
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 | 22 | 22 | 18 | 17 | 22 | 19 | 19 | 22 | 19 |
normalized size | 1 | 1. | 0.82 | 0.77 | 1. | 0.86 | 0.86 | 1. | 0.86 |
time (sec) |
N/A |
0.013 |
0.011 |
0.003 |
1.54 |
0.217 |
1.135 |
0.215 |
1.368 |
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Problem 96 |
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 | 8 | 8 | 8 | 7 | 8 | 8 | 7 | 8 | 0 |
normalized size | 1 | 1. | 1. | 0.88 | 1. | 1. | 0.88 | 1. | 0. |
time (sec) |
N/A |
0.055 |
0.004 |
0.006 |
1.376 |
0.231 |
3.551 |
0.218 |
0. |
|
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Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 20 | 18 | 23 | 109 | 15 | 23 | 15 |
normalized size | 1 | 1. | 0.87 | 0.78 | 1. | 4.74 | 0.65 | 1. | 0.65 |
time (sec) |
N/A |
0.009 |
0.009 |
0.004 |
1.537 |
0.204 |
0.22 |
0.217 |
0.565 |
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Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 20 | 16 | 0 | 20 | 0 | 0 | 19 |
normalized size | 1 | 1. | 0.91 | 0.73 | 0. | 0.91 | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.062 |
0.082 |
0.006 |
0. |
0.222 |
0. |
0. |
3.298 |
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Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 16 | 0 | 20 | 0 | 0 | 17 |
normalized size | 1 | 1. | 1. | 0.8 | 0. | 1. | 0. | 0. | 0.85 |
time (sec) |
N/A |
0.035 |
0.064 |
0.006 |
0. |
0.228 |
0. |
0. |
2.392 |
|
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Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 16 | 20 | 28 | 12 | 20 | 12 |
normalized size | 1 | 1. | 1. | 0.84 | 1.05 | 1.47 | 0.63 | 1.05 | 0.63 |
time (sec) |
N/A |
0.013 |
0.012 |
0.019 |
1.516 |
0.19 |
0.108 |
0.208 |
1.358 |
|
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Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 4 | 4 | 4 | 4 | 4 | 4 | 15 | 4 | 3 |
normalized size | 1 | 1. | 1. | 1. | 1. | 1. | 3.75 | 1. | 0.75 |
time (sec) |
N/A |
0.028 |
0.006 |
0.004 |
1.551 |
0.203 |
0.115 |
0.207 |
2.555 |
|
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Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 24 | 25 | 26 | 38 | 19 | 28 | 26 |
normalized size | 1 | 1. | 0.89 | 0.93 | 0.96 | 1.41 | 0.7 | 1.04 | 0.96 |
time (sec) |
N/A |
0.039 |
0.016 |
0.01 |
1.384 |
0.228 |
22.768 |
0.208 |
2.949 |
|
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Problem 103 |
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 | 42 | 42 | 67 | 62 | 66 | 51 | 0 | 49 | 36 |
normalized size | 1 | 1. | 1.6 | 1.48 | 1.57 | 1.21 | 0. | 1.17 | 0.86 |
time (sec) |
N/A |
0.034 |
0.082 |
0.027 |
1.501 |
0.209 |
0. |
0.218 |
1.858 |
|
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Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 84 | 122 | 0 | 88 | 0 | 82 | 56 |
normalized size | 1 | 1. | 1.18 | 1.72 | 0. | 1.24 | 0. | 1.15 | 0.79 |
time (sec) |
N/A |
0.052 |
0.185 |
0.02 |
0. |
0.223 |
0. |
0.215 |
1.931 |
|
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Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 64 | 28 | 0 | 35 | 0 | 30 | 26 |
normalized size | 1 | 1. | 2. | 0.88 | 0. | 1.09 | 0. | 0.94 | 0.81 |
time (sec) |
N/A |
0.026 |
0.039 |
0.006 |
0. |
0.208 |
0. |
0.242 |
1.191 |
|
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Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 18 | 12 | 20 | 12 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 1.2 | 0.8 | 1.33 | 0.8 |
time (sec) |
N/A |
0.015 |
0.006 |
0.007 |
1.378 |
0.198 |
0.114 |
0.222 |
2.017 |
|
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Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 14 | 18 | 18 | 14 | 20 | 14 |
normalized size | 1 | 1. | 1. | 0.74 | 0.95 | 0.95 | 0.74 | 1.05 | 0.74 |
time (sec) |
N/A |
0.015 |
0.006 |
0.007 |
1.576 |
0.195 |
0.094 |
0.227 |
2.574 |
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Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 20 | 26 | 26 | 19 | 28 | 0 |
normalized size | 1 | 1. | 1. | 0.87 | 1.13 | 1.13 | 0.83 | 1.22 | 0. |
time (sec) |
N/A |
0.04 |
0.008 |
0.01 |
1.422 |
0.196 |
0.096 |
0.221 |
0. |
|
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Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
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 | 18 | 23 | 23 | 17 | 27 | 17 |
normalized size | 1 | 1. | 1. | 0.78 | 1. | 1. | 0.74 | 1.17 | 0.74 |
time (sec) |
N/A |
0.049 |
0.009 |
0.012 |
1.448 |
0.201 |
0.142 |
0.219 |
5.961 |
|
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Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 22 | 19 | 24 | 35 | 19 | 32 | 19 |
normalized size | 1 | 1. | 0.92 | 0.79 | 1. | 1.46 | 0.79 | 1.33 | 0.79 |
time (sec) |
N/A |
0.043 |
0.016 |
0.012 |
1.384 |
0.196 |
0.121 |
0.211 |
2.945 |
|
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Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 28 | 29 | 38 | 51 | 3 | 39 | 29 |
normalized size | 1 | 1. | 1. | 1.04 | 1.36 | 1.82 | 0.11 | 1.39 | 1.04 |
time (sec) |
N/A |
0.049 |
0.017 |
0.01 |
1.503 |
0.199 |
0.141 |
0.211 |
4.142 |
|
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Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 61 | 37 | 49 | 84 | 14 | 50 | 0 |
normalized size | 1 | 1. | 1.24 | 0.76 | 1. | 1.71 | 0.29 | 1.02 | 0. |
time (sec) |
N/A |
0.136 |
0.051 |
0.014 |
1.577 |
0.204 |
0.196 |
0.21 |
0. |
|
|
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Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 24 | 19 | 54 | 51 | 0 | 50 | 22 |
normalized size | 1 | 1. | 1.14 | 0.9 | 2.57 | 2.43 | 0. | 2.38 | 1.05 |
time (sec) |
N/A |
0.019 |
0.024 |
0.033 |
1.616 |
0.216 |
14.501 |
0.238 |
0.541 |
|
|
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Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 266 | 19 | 74 | 17 | 19 | 12 |
normalized size | 1 | 1. | 1. | 16.62 | 1.19 | 4.62 | 1.06 | 1.19 | 0.75 |
time (sec) |
N/A |
0.081 |
0.013 |
0.089 |
1.348 |
0.212 |
2.161 |
0.209 |
3.026 |
|
|
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|
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Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
|
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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 | 11 | 11 | 9 | 9 | 12 | 12 | 8 | 15 | 8 |
normalized size | 1 | 1. | 0.82 | 0.82 | 1.09 | 1.09 | 0.73 | 1.36 | 0.73 |
time (sec) |
N/A |
0.018 |
0.006 |
0.002 |
1.343 |
0.19 |
0.084 |
0.225 |
1.477 |
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Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
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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 |
0.037 |
0.009 |
0.01 |
1.366 |
0.202 |
0.131 |
0.23 |
2.214 |
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Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
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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 | 30 | 30 | 28 | 21 | 27 | 36 | 22 | 30 | 22 |
normalized size | 1 | 1. | 0.93 | 0.7 | 0.9 | 1.2 | 0.73 | 1. | 0.73 |
time (sec) |
N/A |
0.036 |
0.014 |
0.011 |
1.396 |
0.195 |
0.094 |
0.225 |
4.234 |
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Problem 118 |
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 | 27 | 27 | 27 | 24 | 31 | 31 | 20 | 35 | 0 |
normalized size | 1 | 1. | 1. | 0.89 | 1.15 | 1.15 | 0.74 | 1.3 | 0. |
time (sec) |
N/A |
0.047 |
0.009 |
0.012 |
1.431 |
0.201 |
0.13 |
0.232 |
0. |
|
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Problem 119 |
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 | 23 | 23 | 24 | 24 | 27 | 43 | 17 | 22 | 0 |
normalized size | 1 | 1. | 1.04 | 1.04 | 1.17 | 1.87 | 0.74 | 0.96 | 0. |
time (sec) |
N/A |
0.039 |
0.017 |
0.011 |
1.553 |
0.194 |
0.117 |
0.224 |
0. |
|
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Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 16 | 15 | 19 | 19 | 14 | 20 | 14 |
normalized size | 1 | 1. | 1. | 0.94 | 1.19 | 1.19 | 0.88 | 1.25 | 0.88 |
time (sec) |
N/A |
0.028 |
0.007 |
0.008 |
1.622 |
0.192 |
0.085 |
0.217 |
3.872 |
|
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Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 18 | 13 | 16 | 16 | 14 | 16 | 14 |
normalized size | 1 | 1. | 1. | 0.72 | 0.89 | 0.89 | 0.78 | 0.89 | 0.78 |
time (sec) |
N/A |
0.033 |
0.011 |
0.011 |
1.519 |
0.195 |
0.192 |
0.215 |
5.02 |
|
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Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 12 | 15 | 15 | 8 | 18 | 8 |
normalized size | 1 | 1. | 1. | 1.09 | 1.36 | 1.36 | 0.73 | 1.64 | 0.73 |
time (sec) |
N/A |
0.02 |
0.003 |
0.009 |
1.337 |
0.232 |
0.089 |
0.211 |
1.571 |
|
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Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 24 | 21 | 32 | 43 | 19 | 39 | 22 |
normalized size | 1 | 1. | 1. | 0.88 | 1.33 | 1.79 | 0.79 | 1.62 | 0.92 |
time (sec) |
N/A |
0.026 |
0.013 |
0.016 |
1.348 |
0.23 |
0.11 |
0.218 |
1.954 |
|
|
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Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 44 | 39 | 62 | 112 | 46 | 70 | 41 |
normalized size | 1 | 1. | 0.96 | 0.85 | 1.35 | 2.43 | 1. | 1.52 | 0.89 |
time (sec) |
N/A |
0.052 |
0.025 |
0.016 |
1.355 |
0.206 |
0.231 |
0.213 |
3.032 |
|
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Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 11 | 14 | 22 | 8 | 15 | 8 |
normalized size | 1 | 1. | 1. | 1.1 | 1.4 | 2.2 | 0.8 | 1.5 | 0.8 |
time (sec) |
N/A |
0.011 |
0.004 |
0.007 |
1.342 |
0.191 |
0.064 |
0.21 |
1.019 |
|
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Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
F(-2) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 18 | 23 | 18 | 10 | 22 | 0 |
normalized size | 1 | 1. | 1. | 1.06 | 1.35 | 1.06 | 0.59 | 1.29 | 0. |
time (sec) |
N/A |
0.019 |
0.004 |
0.01 |
1.339 |
0.194 |
0.081 |
0.21 |
0. |
|
|
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Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 15 | 19 | 19 | 17 | 22 | 17 |
normalized size | 1 | 1. | 1. | 0.75 | 0.95 | 0.95 | 0.85 | 1.1 | 0.85 |
time (sec) |
N/A |
0.022 |
0.005 |
0.007 |
1.35 |
0.194 |
0.096 |
0.215 |
2.591 |
|
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Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 12 | 13 | 16 | 22 | 8 | 18 | 8 |
normalized size | 1 | 1. | 0.75 | 0.81 | 1. | 1.38 | 0.5 | 1.12 | 0.5 |
time (sec) |
N/A |
0.016 |
0.005 |
0.01 |
1.363 |
0.194 |
0.071 |
0.212 |
2.189 |
|
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Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 15 | 19 | 23 | 10 | 19 | 10 |
normalized size | 1 | 1. | 1. | 1.07 | 1.36 | 1.64 | 0.71 | 1.36 | 0.71 |
time (sec) |
N/A |
0.024 |
0.012 |
0.009 |
1.487 |
0.197 |
0.141 |
0.221 |
3.553 |
|
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Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 21 | 18 | 23 | 23 | 20 | 27 | 20 |
normalized size | 1 | 1. | 1. | 0.86 | 1.1 | 1.1 | 0.95 | 1.29 | 0.95 |
time (sec) |
N/A |
0.041 |
0.009 |
0.01 |
1.342 |
0.201 |
0.133 |
0.218 |
4.992 |
|
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Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 27 | 28 | 31 | 46 | 20 | 34 | 12 |
normalized size | 1 | 1. | 1.29 | 1.33 | 1.48 | 2.19 | 0.95 | 1.62 | 0.57 |
time (sec) |
N/A |
0.008 |
0.012 |
0.014 |
1.345 |
0.193 |
0.101 |
0.212 |
0.566 |
|
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Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 17 | 22 | 22 | 17 | 23 | 17 |
normalized size | 1 | 1. | 1. | 0.77 | 1. | 1. | 0.77 | 1.05 | 0.77 |
time (sec) |
N/A |
0.018 |
0.005 |
0.009 |
1.516 |
0.188 |
0.078 |
0.213 |
2.68 |
|
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Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 11 | 19 | 24 | 8 | 19 | 12 |
normalized size | 1 | 1. | 1. | 1.1 | 1.9 | 2.4 | 0.8 | 1.9 | 1.2 |
time (sec) |
N/A |
0.046 |
0.008 |
0.009 |
1.343 |
0.196 |
0.102 |
0.223 |
3.272 |
|
|
|
|
|
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|
Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 22 | 26 | 34 | 19 | 28 | 22 |
normalized size | 1 | 1. | 1. | 0.71 | 0.84 | 1.1 | 0.61 | 0.9 | 0.71 |
time (sec) |
N/A |
0.022 |
0.003 |
0.01 |
1.342 |
0.196 |
0.105 |
0.23 |
1.66 |
|
|
|
|
|
|
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|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 18 | 17 | 22 | 22 | 15 | 23 | 15 |
normalized size | 1 | 1. | 1. | 0.94 | 1.22 | 1.22 | 0.83 | 1.28 | 0.83 |
time (sec) |
N/A |
0.043 |
0.008 |
0.007 |
1.503 |
0.202 |
0.129 |
0.227 |
4.772 |
|
|
|
|
|
|
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|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 25 | 10 | 23 | 23 | 17 | 26 | 10 |
normalized size | 1 | 1. | 1.92 | 0.77 | 1.77 | 1.77 | 1.31 | 2. | 0.77 |
time (sec) |
N/A |
0.008 |
0.005 |
0.001 |
1.506 |
0.2 |
0.163 |
0.228 |
0.585 |
|
|
|
|
|
|
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|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 64 | 58 | 97 | 131 | 73 | 97 | 73 |
normalized size | 1 | 1. | 0.75 | 0.68 | 1.14 | 1.54 | 0.86 | 1.14 | 0.86 |
time (sec) |
N/A |
0.081 |
0.03 |
0.023 |
1.523 |
0.202 |
0.19 |
0.215 |
5.485 |
|
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Problem 138 |
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 | 15 | 16 | 20 | 35 | 14 | 20 | 20 |
normalized size | 1 | 1. | 0.65 | 0.7 | 0.87 | 1.52 | 0.61 | 0.87 | 0.87 |
time (sec) |
N/A |
0.02 |
0.014 |
0.007 |
1.532 |
0.195 |
0.127 |
0.214 |
1.805 |
|
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Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 41 | 15 | 15 | 8 | 15 | 8 |
normalized size | 1 | 1. | 1. | 3.73 | 1.36 | 1.36 | 0.73 | 1.36 | 0.73 |
time (sec) |
N/A |
0.006 |
0.01 |
0.013 |
1.386 |
0.187 |
0.161 |
0.214 |
2.756 |
|
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Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 23 | 20 | 31 | 49 | 39 | 63 | 24 |
normalized size | 1 | 1. | 0.51 | 0.44 | 0.69 | 1.09 | 0.87 | 1.4 | 0.53 |
time (sec) |
N/A |
0.084 |
0.035 |
0.053 |
1.607 |
0.221 |
0.835 |
0.216 |
0.802 |
|
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Problem 141 |
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 | 37 | 37 | 31 | 30 | 0 | 1 | 110 | 72 | 34 |
normalized size | 1 | 1. | 0.84 | 0.81 | 0. | 0.03 | 2.97 | 1.95 | 0.92 |
time (sec) |
N/A |
0.064 |
0.03 |
0.02 |
0. |
0.227 |
11.177 |
0.215 |
2.368 |
|
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Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 20 | 16 | 50 | 70 | 36 | 47 | 20 |
normalized size | 1 | 1. | 0.36 | 0.29 | 0.89 | 1.25 | 0.64 | 0.84 | 0.36 |
time (sec) |
N/A |
0.038 |
0.013 |
0.013 |
1.484 |
0.222 |
0.537 |
0.249 |
0.58 |
|
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Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 20 | 16 | 26 | 31 | 32 | 54 | 20 |
normalized size | 1 | 1. | 0.65 | 0.52 | 0.84 | 1. | 1.03 | 1.74 | 0.65 |
time (sec) |
N/A |
0.05 |
0.011 |
0.023 |
1.556 |
0.211 |
0.406 |
0.226 |
0.589 |
|
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Problem 144 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 18 | 15 | 19 | 51 | 416 | 65 | 24 |
normalized size | 1 | 1. | 0.5 | 0.42 | 0.53 | 1.42 | 11.56 | 1.81 | 0.67 |
time (sec) |
N/A |
0.067 |
0.021 |
0.029 |
1.522 |
0.243 |
155.717 |
0.228 |
4.666 |
|
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Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 16 | 20 | 58 | 0 | 35 | 10 |
normalized size | 1 | 1. | 1. | 1.07 | 1.33 | 3.87 | 0. | 2.33 | 0.67 |
time (sec) |
N/A |
0.042 |
0.053 |
0.083 |
1.502 |
0.239 |
0. |
0.234 |
25.182 |
|
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Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 14 | 19 | 53 | 0 | 18 | 14 |
normalized size | 1 | 1. | 1. | 0.82 | 1.12 | 3.12 | 0. | 1.06 | 0.82 |
time (sec) |
N/A |
0.022 |
0.038 |
0.234 |
1.344 |
0.218 |
0. |
0.216 |
0.675 |
|
|
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Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 22 | 25 | 55 | 15 | 22 | 34 | 24 |
normalized size | 1 | 1. | 0.73 | 0.83 | 1.83 | 0.5 | 0.73 | 1.13 | 0.8 |
time (sec) |
N/A |
0.045 |
0.011 |
0.066 |
1.489 |
0.231 |
0.419 |
0.225 |
2.118 |
|
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Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 29 | 23 | 30 | 39 | 24 | 30 | 24 |
normalized size | 1 | 1. | 1. | 0.79 | 1.03 | 1.34 | 0.83 | 1.03 | 0.83 |
time (sec) |
N/A |
0.011 |
0.014 |
0.005 |
1.516 |
0.212 |
0.227 |
0.217 |
0.597 |
|
|
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|
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Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 12 | 15 | 15 | 8 | 15 | 8 |
normalized size | 1 | 1. | 1. | 0.92 | 1.15 | 1.15 | 0.62 | 1.15 | 0.62 |
time (sec) |
N/A |
0.006 |
0.003 |
0.004 |
1.338 |
0.208 |
0.151 |
0.215 |
0.876 |
|
|
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Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 41 | 30 | 55 | 54 | 88 | 63 | 29 |
normalized size | 1 | 1. | 1.11 | 0.81 | 1.49 | 1.46 | 2.38 | 1.7 | 0.78 |
time (sec) |
N/A |
0.047 |
0.021 |
0.006 |
1.514 |
0.217 |
2.227 |
0.226 |
2.372 |
|
|
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Problem 151 |
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 | 22 | 22 | 31 | 22 | 34 | 99 | 0 | 35 | 19 |
normalized size | 1 | 1. | 1.41 | 1. | 1.55 | 4.5 | 0. | 1.59 | 0.86 |
time (sec) |
N/A |
0.02 |
0.025 |
0.006 |
1.337 |
0.21 |
0. |
0.228 |
1.326 |
|
|
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Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 27 | 21 | 27 | 109 | 24 | 34 | 24 |
normalized size | 1 | 1. | 1. | 0.78 | 1. | 4.04 | 0.89 | 1.26 | 0.89 |
time (sec) |
N/A |
0.01 |
0.013 |
0.004 |
1.504 |
0.21 |
0.271 |
0.225 |
0.557 |
|
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Problem 153 |
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 | 27 | 27 | 27 | 21 | 30 | 104 | 0 | 36 | 29 |
normalized size | 1 | 1. | 1. | 0.78 | 1.11 | 3.85 | 0. | 1.33 | 1.07 |
time (sec) |
N/A |
0.028 |
0.013 |
0.008 |
1.496 |
0.217 |
0. |
0.222 |
1.503 |
|
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Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 29 | 12 | 20 | 23 | 0 | 24 | 12 |
normalized size | 1 | 1. | 2.07 | 0.86 | 1.43 | 1.64 | 0. | 1.71 | 0.86 |
time (sec) |
N/A |
0.008 |
0.011 |
0.004 |
1.345 |
0.198 |
0. |
0.216 |
0.554 |
|
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Problem 155 |
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 | 68 | 68 | 77 | 88 | 80 | 126 | 0 | 227 | 61 |
normalized size | 1 | 1. | 1.13 | 1.29 | 1.18 | 1.85 | 0. | 3.34 | 0.9 |
time (sec) |
N/A |
0.1 |
0.065 |
0.007 |
1.597 |
0.209 |
0. |
0.233 |
5.768 |
|
|
|
|
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|
Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 13 | 13 | 16 | 0 | 58 | 0 | 12 |
normalized size | 1 | 1. | 1. | 1. | 1.23 | 0. | 4.46 | 0. | 0.92 |
time (sec) |
N/A |
0.025 |
0.005 |
0.016 |
1.345 |
0. |
2.177 |
0. |
1.88 |
|
|
|
|
|
|
|
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|
Problem 157 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 15 | 3 | 3 | 2 | 3 | 15 |
normalized size | 1 | 1. | 1. | 1. | 0.2 | 0.2 | 0.13 | 0.2 | 1. |
time (sec) |
N/A |
0.018 |
0.016 |
0.016 |
1.349 |
0.212 |
0.22 |
0.211 |
1.066 |
|
|
|
|
|
|
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|
Problem 158 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 8 | 3 | 3 | 2 | 3 | 2 |
normalized size | 1 | 1. | 1. | 4. | 1.5 | 1.5 | 1. | 1.5 | 1. |
time (sec) |
N/A |
0.017 |
0.002 |
0.004 |
1.414 |
0.2 |
1.241 |
0.228 |
1.278 |
|
|
|
|
|
|
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|
|
Problem 159 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 4 | 4 | 4 | 9 | 5 | 5 | 3 | 5 | 3 |
normalized size | 1 | 1. | 1. | 2.25 | 1.25 | 1.25 | 0.75 | 1.25 | 0.75 |
time (sec) |
N/A |
0.021 |
0.002 |
0.004 |
1.416 |
0.198 |
1.343 |
0.21 |
1.366 |
|
|
|
|
|
|
|
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|
|
Problem 160 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 11 | 16 | 7 | 18 | 7 | 18 | 7 |
normalized size | 1 | 1. | 1. | 1.45 | 0.64 | 1.64 | 0.64 | 1.64 | 0.64 |
time (sec) |
N/A |
0.033 |
0.005 |
0.004 |
1.43 |
0.198 |
1.604 |
0.226 |
1.896 |
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Problem 161 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 14 | 14 | 14 | 15 | 18 | 18 | 10 | 0 | 10 |
normalized size | 1 | 1. | 1. | 1.07 | 1.29 | 1.29 | 0.71 | 0. | 0.71 |
time (sec) |
N/A |
0.023 |
0.003 |
0.004 |
1.406 |
0.202 |
1.703 |
0. |
1.363 |
|
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Problem 162 |
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 | 15 | 15 | 15 | 17 | 22 | 19 | 0 | 19 | 12 |
normalized size | 1 | 1. | 1. | 1.13 | 1.47 | 1.27 | 0. | 1.27 | 0.8 |
time (sec) |
N/A |
0.034 |
0.007 |
0.023 |
1.442 |
0.199 |
0. |
0.232 |
2.028 |
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Problem 163 |
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 | 13 | 13 | 13 | 14 | 18 | 14 | 0 | 14 | 8 |
normalized size | 1 | 1. | 1. | 1.08 | 1.38 | 1.08 | 0. | 1.08 | 0.62 |
time (sec) |
N/A |
0.135 |
0.006 |
0.007 |
1.403 |
0.198 |
0. |
0.225 |
5.998 |
|
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Problem 164 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 22 | 22 | 31 | 0 | 0 | 12 |
normalized size | 1 | 1. | 1. | 1.16 | 1.16 | 1.63 | 0. | 0. | 0.63 |
time (sec) |
N/A |
0.04 |
0.011 |
0.008 |
1.439 |
0.201 |
0. |
0. |
2.506 |
|
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Problem 165 |
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 | 18 | 18 | 18 | 19 | 24 | 26 | 0 | 22 | 14 |
normalized size | 1 | 1. | 1. | 1.06 | 1.33 | 1.44 | 0. | 1.22 | 0.78 |
time (sec) |
N/A |
0.038 |
0.009 |
0.175 |
1.413 |
0.211 |
0. |
0.211 |
2.456 |
|
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Problem 166 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 11 | 10 | 12 | 12 | 7 | 12 | 10 |
normalized size | 1 | 1. | 0.69 | 0.62 | 0.75 | 0.75 | 0.44 | 0.75 | 0.62 |
time (sec) |
N/A |
0.016 |
0.002 |
0.001 |
1.351 |
0.209 |
0.09 |
0.211 |
1.102 |
|
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|
Problem 167 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 16 | 15 | 19 | 19 | 12 | 19 | 19 |
normalized size | 1 | 1. | 0.62 | 0.58 | 0.73 | 0.73 | 0.46 | 0.73 | 0.73 |
time (sec) |
N/A |
0.035 |
0.003 |
0.004 |
1.347 |
0.212 |
0.089 |
0.216 |
1.755 |
|
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|
Problem 168 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 21 | 20 | 26 | 26 | 17 | 26 | 27 |
normalized size | 1 | 1. | 0.58 | 0.56 | 0.72 | 0.72 | 0.47 | 0.72 | 0.75 |
time (sec) |
N/A |
0.054 |
0.004 |
0.004 |
1.357 |
0.198 |
0.125 |
0.228 |
2.577 |
|
|
|
|
|
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|
Problem 169 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 39 | 111 | 244 | 81 | 360 | 104 | 39 |
normalized size | 1 | 1. | 0.81 | 2.31 | 5.08 | 1.69 | 7.5 | 2.17 | 0.81 |
time (sec) |
N/A |
0.069 |
0.111 |
0.119 |
1.529 |
0.233 |
4.261 |
0.246 |
4.609 |
|
|
|
|
|
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|
Problem 170 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
F |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 2 | 2 | 2 | 9 | 4 | 0 | 0 | 4 | 2 |
normalized size | 1 | 1. | 1. | 4.5 | 2. | 0. | 0. | 2. | 1. |
time (sec) |
N/A |
0.004 |
0.003 |
0.007 |
1.422 |
0. |
0. |
0.229 |
0.025 |
|
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|
Problem 171 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 10 | 17 | 8 | 0 | 0 | 15 | 7 |
normalized size | 1 | 1. | 1. | 1.7 | 0.8 | 0. | 0. | 1.5 | 0.7 |
time (sec) |
N/A |
0.007 |
0.002 |
0.003 |
1.412 |
0. |
0. |
0.227 |
0.471 |
|
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|
Problem 172 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 0 | 30 | 20 | 0 | 0 | 24 |
normalized size | 1 | 1. | 1. | 0. | 1.36 | 0.91 | 0. | 0. | 1.09 |
time (sec) |
N/A |
0.029 |
0.033 |
0.135 |
1.501 |
0.226 |
0. |
0. |
0.584 |
|
|
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|
Problem 173 |
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 | 12 | 12 | 10 | 12 | 15 | 12 | 0 | 12 | 8 |
normalized size | 1 | 1. | 0.83 | 1. | 1.25 | 1. | 0. | 1. | 0.67 |
time (sec) |
N/A |
0.027 |
0.004 |
0.006 |
1.43 |
0.199 |
0. |
0.224 |
1.598 |
|
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Problem 174 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 23 | 0 | 27 | 0 | 27 | 19 |
normalized size | 1 | 1. | 1. | 1.05 | 0. | 1.23 | 0. | 1.23 | 0.86 |
time (sec) |
N/A |
0.095 |
0.007 |
0.014 |
0. |
0.201 |
0. |
0.226 |
6.847 |
|
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Problem 175 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 88 | 116 | 0 | 0 | 27 | 0 | 95 |
normalized size | 1 | 1. | 0.85 | 1.13 | 0. | 0. | 0.26 | 0. | 0.92 |
time (sec) |
N/A |
0.04 |
0.069 |
0.096 |
0. |
0. |
0.853 |
0. |
0.809 |
|
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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 [83] had the largest ratio of [ 2.
]
|
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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 |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
2 |
A |
2 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
3 |
A |
2 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
5 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
6 |
A |
2 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
7 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
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|
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|
|
|
8 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
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|
|
|
9 |
A |
2 |
2 |
1. |
17 |
0.118 |
|
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|
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|
|
10 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
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|
|
11 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
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|
|
12 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
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|
|
13 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
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|
|
14 |
A |
1 |
1 |
1. |
15 |
0.067 |
|
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|
|
|
|
15 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
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|
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|
|
16 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
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|
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|
|
17 |
A |
1 |
1 |
1. |
15 |
0.067 |
|
|
|
|
|
|
|
18 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
19 |
A |
3 |
2 |
1. |
20 |
0.1 |
|
|
|
|
|
|
|
20 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
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|
21 |
A |
2 |
2 |
1. |
20 |
0.1 |
|
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|
|
22 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
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|
|
23 |
A |
3 |
2 |
1. |
6 |
0.333 |
|
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|
|
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|
|
24 |
A |
4 |
2 |
1. |
6 |
0.333 |
|
|
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|
25 |
A |
4 |
2 |
1. |
6 |
0.333 |
|
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|
|
26 |
A |
2 |
2 |
1. |
5 |
0.4 |
|
|
|
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|
|
27 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
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|
|
28 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
29 |
A |
2 |
1 |
1. |
4 |
0.25 |
|
|
|
|
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|
|
30 |
A |
3 |
2 |
1. |
4 |
0.5 |
|
|
|
|
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|
|
31 |
A |
2 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
32 |
A |
4 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
33 |
A |
2 |
2 |
1. |
6 |
0.333 |
|
|
|
|
|
|
|
34 |
A |
3 |
3 |
1. |
6 |
0.5 |
|
|
|
|
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|
|
35 |
A |
4 |
4 |
1. |
8 |
0.5 |
|
|
|
|
|
|
|
36 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
37 |
A |
2 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
38 |
A |
3 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
39 |
A |
5 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
40 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
|
41 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
42 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
43 |
A |
3 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
44 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
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|
45 |
A |
3 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
46 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
47 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
48 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
49 |
A |
1 |
1 |
1. |
13 |
0.077 |
|
|
|
|
|
|
|
50 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
51 |
A |
2 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
52 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
53 |
A |
5 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
54 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
55 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
56 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
57 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
58 |
A |
1 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
59 |
A |
2 |
2 |
1. |
6 |
0.333 |
|
|
|
|
|
|
|
60 |
A |
1 |
1 |
1. |
5 |
0.2 |
|
|
|
|
|
|
|
|
61 | A | 1 | 1 | 1. | 2 | 0.5 |
|
|
|
|
|
|
|
62 |
A |
1 |
1 |
1. |
8 |
0.125 |
|
|
|
|
|
|
|
63 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
64 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
65 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
66 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
67 |
A |
3 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
68 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
69 |
A |
1 |
1 |
1. |
13 |
0.077 |
|
|
|
|
|
|
|
70 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
71 |
A |
1 |
1 |
1. |
6 |
0.167 |
|
|
|
|
|
|
|
72 |
A |
1 |
1 |
1. |
6 |
0.167 |
|
|
|
|
|
|
|
73 |
A |
4 |
4 |
1. |
7 |
0.571 |
|
|
|
|
|
|
|
74 |
A |
2 |
2 |
1. |
5 |
0.4 |
|
|
|
|
|
|
|
75 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
76 |
A |
3 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
77 |
A |
3 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
78 |
A |
3 |
3 |
1. |
7 |
0.429 |
|
|
|
|
|
|
|
79 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
80 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
|
81 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
82 |
A |
2 |
2 |
1. |
2 |
1. |
|
|
|
|
|
|
|
83 |
A |
4 |
4 |
1. |
2 |
2. |
|
|
|
|
|
|
|
84 |
A |
4 |
4 |
1. |
2 |
2. |
|
|
|
|
|
|
|
85 |
A |
3 |
3 |
1. |
4 |
0.75 |
|
|
|
|
|
|
|
86 |
A |
4 |
4 |
1. |
6 |
0.667 |
|
|
|
|
|
|
|
87 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
88 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
90 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
91 |
A |
2 |
2 |
1. |
10 |
0.2 |
|
|
|
|
|
|
|
92 |
A |
3 |
3 |
1. |
4 |
0.75 |
|
|
|
|
|
|
|
93 |
A |
4 |
3 |
1. |
6 |
0.5 |
|
|
|
|
|
|
|
94 |
A |
5 |
5 |
1. |
6 |
0.833 |
|
|
|
|
|
|
|
95 |
A |
4 |
4 |
1. |
6 |
0.667 |
|
|
|
|
|
|
|
96 |
A |
1 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
97 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
98 |
A |
1 |
1 |
1. |
15 |
0.067 |
|
|
|
|
|
|
|
99 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
100 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
|
101 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
102 |
A |
6 |
6 |
1. |
10 |
0.6 |
|
|
|
|
|
|
|
103 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
104 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
105 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
106 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
107 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
108 |
A |
6 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
109 |
A |
3 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
110 |
A |
2 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
111 |
A |
6 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
112 |
A |
6 |
5 |
1. |
31 |
0.161 |
|
|
|
|
|
|
|
113 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
114 |
A |
3 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
115 |
A |
2 |
1 |
1. |
16 |
0.062 |
|
|
|
|
|
|
|
116 |
A |
2 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
117 |
A |
2 |
1 |
1. |
12 |
0.083 |
|
|
|
|
|
|
|
118 |
A |
3 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
119 |
A |
2 |
1 |
1. |
20 |
0.05 |
|
|
|
|
|
|
|
120 |
A |
3 |
3 |
1. |
16 |
0.188 |
|
|
|
|
|
|
|
|
121 | A | 4 | 3 | 1. | 16 | 0.188 |
|
|
|
|
|
|
|
122 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
123 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
124 |
A |
2 |
1 |
1. |
16 |
0.062 |
|
|
|
|
|
|
|
125 |
A |
2 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
126 |
A |
5 |
5 |
1. |
9 |
0.556 |
|
|
|
|
|
|
|
127 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
128 |
A |
3 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
129 |
A |
4 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
130 |
A |
3 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
131 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
132 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
133 |
A |
3 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
134 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
135 |
A |
5 |
4 |
1. |
18 |
0.222 |
|
|
|
|
|
|
|
136 |
A |
3 |
3 |
1. |
7 |
0.429 |
|
|
|
|
|
|
|
137 |
A |
9 |
6 |
1. |
7 |
0.857 |
|
|
|
|
|
|
|
138 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
139 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
|
|
|
|
|
|
140 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
|
141 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
142 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
143 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
144 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
145 |
A |
2 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
146 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
147 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
148 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
149 |
A |
1 |
1 |
1. |
13 |
0.077 |
|
|
|
|
|
|
|
150 |
A |
4 |
4 |
1. |
15 |
0.267 |
|
|
|
|
|
|
|
151 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
152 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
153 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
154 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
155 |
A |
6 |
6 |
1. |
18 |
0.333 |
|
|
|
|
|
|
|
156 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
157 |
A |
3 |
3 |
1. |
5 |
0.6 |
|
|
|
|
|
|
|
158 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
159 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
160 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
|
161 |
A |
2 |
2 |
1. |
5 |
0.4 |
|
|
|
|
|
|
|
162 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
163 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
164 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
165 |
A |
2 |
3 |
1. |
8 |
0.375 |
|
|
|
|
|
|
|
166 |
A |
2 |
2 |
1. |
7 |
0.286 |
|
|
|
|
|
|
|
167 |
A |
3 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
168 |
A |
4 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
169 |
A |
1 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
170 |
A |
1 |
1 |
1. |
4 |
0.25 |
|
|
|
|
|
|
|
171 |
A |
2 |
2 |
1. |
4 |
0.5 |
|
|
|
|
|
|
|
172 |
A |
2 |
2 |
1. |
8 |
0.25 |
|
|
|
|
|
|
|
173 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
174 |
A |
4 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
175 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|