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 |
F |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 66 | 0 | 0 | 88 | 0 | 0 | 60 |
normalized size | 1 | 1. | 0.99 | 0. | 0. | 1.31 | 0. | 0. | 0.9 |
time (sec) |
N/A |
0.075 |
0.42 |
0.23 |
0. |
0.257 |
0. |
0. |
6.511 |
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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 | 141 | 141 | 100 | 260 | 417 | 306 | 350 | 1 | 139 |
normalized size | 1 | 1. | 0.71 | 1.84 | 2.96 | 2.17 | 2.48 | 0.01 | 0.99 |
time (sec) |
N/A |
0.203 |
0.074 |
0.017 |
0.716 |
0.257 |
0.605 |
0.355 |
39.746 |
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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 | 110 | 110 | 78 | 165 | 278 | 198 | 231 | 1 | 107 |
normalized size | 1 | 1. | 0.71 | 1.5 | 2.53 | 1.8 | 2.1 | 0.01 | 0.97 |
time (sec) |
N/A |
0.134 |
0.061 |
0.012 |
0.703 |
0.237 |
0.494 |
0.325 |
27.086 |
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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 | 79 | 79 | 56 | 91 | 166 | 113 | 133 | 1 | 75 |
normalized size | 1 | 1. | 0.71 | 1.15 | 2.1 | 1.43 | 1.68 | 0.01 | 0.95 |
time (sec) |
N/A |
0.083 |
0.048 |
0.013 |
0.697 |
0.261 |
0.4 |
0.301 |
15.498 |
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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 | 48 | 48 | 34 | 38 | 81 | 51 | 60 | 1 | 41 |
normalized size | 1 | 1. | 0.71 | 0.79 | 1.69 | 1.06 | 1.25 | 0.02 | 0.85 |
time (sec) |
N/A |
0.037 |
0.026 |
0.004 |
0.692 |
0.234 |
0.294 |
0.261 |
6.634 |
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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 | 20 | 20 | 21 | 21 | 27 | 28 | 20 | 27 | 14 |
normalized size | 1 | 1. | 1.05 | 1.05 | 1.35 | 1.4 | 1. | 1.35 | 0.7 |
time (sec) |
N/A |
0.011 |
0.002 |
0.003 |
0.681 |
0.23 |
0.166 |
0.241 |
2.002 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 56 | 50 | 53 | 0 | 0 | 27 |
normalized size | 1 | 1. | 1. | 1.81 | 1.61 | 1.71 | 0. | 0. | 0.87 |
time (sec) |
N/A |
0.04 |
0.016 |
0.034 |
0.753 |
0.247 |
0. |
0. |
5.153 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 55 | 97 | 59 | 104 | 0 | 0 | 51 |
normalized size | 1 | 1. | 0.96 | 1.7 | 1.04 | 1.82 | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.078 |
0.118 |
0.034 |
0.787 |
0.245 |
0. |
0. |
9.92 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 88 | 151 | 59 | 181 | 0 | 0 | 87 |
normalized size | 1 | 1. | 0.93 | 1.59 | 0.62 | 1.91 | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.126 |
0.112 |
0.043 |
0.789 |
0.239 |
0. |
0. |
17.269 |
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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 |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 99 | 193 | 59 | 282 | 0 | 0 | 119 |
normalized size | 1 | 1. | 0.77 | 1.51 | 0.46 | 2.2 | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.176 |
0.133 |
0.052 |
0.806 |
0.239 |
0. |
0. |
26.501 |
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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 |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 121 | 235 | 59 | 405 | 0 | 0 | 151 |
normalized size | 1 | 1. | 0.75 | 1.46 | 0.37 | 2.52 | 0. | 0. | 0.94 |
time (sec) |
N/A |
0.234 |
0.147 |
0.066 |
0.789 |
0.248 |
0. |
0. |
37.737 |
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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 | 141 | 141 | 100 | 260 | 417 | 306 | 350 | 1 | 139 |
normalized size | 1 | 1. | 0.71 | 1.84 | 2.96 | 2.17 | 2.48 | 0.01 | 0.99 |
time (sec) |
N/A |
0.218 |
0.033 |
0.019 |
0.746 |
0.235 |
0.612 |
0.345 |
57.049 |
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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 |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 110 | 78 | 165 | 278 | 198 | 231 | 1 | 107 |
normalized size | 1 | 1. | 0.71 | 1.5 | 2.53 | 1.8 | 2.1 | 0.01 | 0.97 |
time (sec) |
N/A |
0.154 |
0.017 |
0.011 |
0.734 |
0.231 |
0.494 |
0.309 |
36.464 |
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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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 56 | 91 | 166 | 113 | 133 | 1 | 75 |
normalized size | 1 | 1. | 0.71 | 1.15 | 2.1 | 1.43 | 1.68 | 0.01 | 0.95 |
time (sec) |
N/A |
0.083 |
0.015 |
0.012 |
0.734 |
0.229 |
0.395 |
0.273 |
35.713 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 55 | 97 | 59 | 104 | 0 | 0 | 51 |
normalized size | 1 | 1. | 0.96 | 1.7 | 1.04 | 1.82 | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.075 |
0.02 |
0.052 |
0.783 |
0.241 |
0. |
0. |
25.081 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 88 | 151 | 59 | 181 | 0 | 0 | 87 |
normalized size | 1 | 1. | 0.93 | 1.59 | 0.62 | 1.91 | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.16 |
0.024 |
0.068 |
0.812 |
0.243 |
0. |
0. |
34.87 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 128 | 128 | 99 | 193 | 59 | 282 | 0 | 0 | 119 |
normalized size | 1 | 1. | 0.77 | 1.51 | 0.46 | 2.2 | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.227 |
0.027 |
0.094 |
0.844 |
0.24 |
0. |
0. |
54.404 |
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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 |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 121 | 235 | 59 | 405 | 0 | 0 | 151 |
normalized size | 1 | 1. | 0.75 | 1.46 | 0.37 | 2.52 | 0. | 0. | 0.94 |
time (sec) |
N/A |
0.304 |
0.029 |
0.124 |
0.915 |
0.239 |
0. |
0. |
84.485 |
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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 |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 74 | 0 | 0 | 92 | 0 | 0 | 65 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 1.28 | 0. | 0. | 0.9 |
time (sec) |
N/A |
0.095 |
0.048 |
0.072 |
0. |
0.254 |
0. |
0. |
11.985 |
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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 |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 73 | 0 | 0 | 0 | 0 | 0 | 65 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 0. | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.118 |
0.098 |
0.26 |
0. |
0. |
0. |
0. |
36.493 |
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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 |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 73 | 0 | 0 | 0 | 0 | 0 | 65 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 0. | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.104 |
0.049 |
0.086 |
0. |
0. |
0. |
0. |
25.867 |
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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 |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 73 | 0 | 0 | 0 | 0 | 0 | 65 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 0. | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.098 |
0.047 |
0.138 |
0. |
0. |
0. |
0. |
18.494 |
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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 |
F |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 66 | 0 | 0 | 88 | 0 | 0 | 60 |
normalized size | 1 | 1. | 0.99 | 0. | 0. | 1.31 | 0. | 0. | 0.9 |
time (sec) |
N/A |
0.046 |
0.018 |
0. |
0. |
0.269 |
0. |
0. |
6.744 |
|
|
|
|
|
|
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|
Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 68 | 0 | 0 | 90 | 0 | 0 | 60 |
normalized size | 1 | 1. | 0.99 | 0. | 0. | 1.3 | 0. | 0. | 0.87 |
time (sec) |
N/A |
0.048 |
0.049 |
0.065 |
0. |
0.263 |
0. |
0. |
6.738 |
|
|
|
|
|
|
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|
Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 75 | 0 | 0 | 0 | 0 | 0 | 65 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.098 |
0.046 |
0.119 |
0. |
0. |
0. |
0. |
18.702 |
|
|
|
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Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 75 | 0 | 0 | 0 | 0 | 0 | 65 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.104 |
0.047 |
0.082 |
0. |
0. |
0. |
0. |
26.248 |
|
|
|
|
|
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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 | 15 | 15 | 15 | 14 | 18 | 18 | 15 | 18 | 10 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 1.2 | 1. | 1.2 | 0.67 |
time (sec) |
N/A |
0.007 |
0.002 |
0.007 |
0.79 |
0.28 |
0.152 |
0.249 |
1.225 |
|
|
|
|
|
|
|
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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 | 15 | 15 | 15 | 16 | 20 | 20 | 15 | 20 | 10 |
normalized size | 1 | 1. | 1. | 1.07 | 1.33 | 1.33 | 1. | 1.33 | 0.67 |
time (sec) |
N/A |
0.008 |
0.002 |
0.006 |
0.784 |
0.27 |
0.156 |
0.252 |
1.535 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 14 | 18 | 18 | 10 | 18 | 10 |
normalized size | 1 | 1. | 1. | 0.74 | 0.95 | 0.95 | 0.53 | 0.95 | 0.53 |
time (sec) |
N/A |
0.011 |
0.004 |
0.033 |
0.788 |
0.275 |
0.152 |
0.259 |
1.049 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 30 |
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 | 131 | 131 | 99 | 99 | 120 | 119 | 0 | 130 | 129 |
normalized size | 1 | 1. | 0.76 | 0.76 | 0.92 | 0.91 | 0. | 0.99 | 0.98 |
time (sec) |
N/A |
0.243 |
0.097 |
0.158 |
0.82 |
0.275 |
0. |
0.257 |
26.922 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 31 |
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 | 108 | 108 | 87 | 87 | 104 | 103 | 0 | 113 | 105 |
normalized size | 1 | 1. | 0.81 | 0.81 | 0.96 | 0.95 | 0. | 1.05 | 0.97 |
time (sec) |
N/A |
0.147 |
0.053 |
0.017 |
0.84 |
0.276 |
0. |
0.261 |
19.77 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 32 |
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 | 85 | 85 | 75 | 75 | 88 | 86 | 0 | 97 | 82 |
normalized size | 1 | 1. | 0.88 | 0.88 | 1.04 | 1.01 | 0. | 1.14 | 0.96 |
time (sec) |
N/A |
0.11 |
0.042 |
0.016 |
0.847 |
0.28 |
0. |
0.254 |
13.634 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 33 |
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 | 62 | 62 | 62 | 66 | 73 | 74 | 0 | 81 | 56 |
normalized size | 1 | 1. | 1. | 1.06 | 1.18 | 1.19 | 0. | 1.31 | 0.9 |
time (sec) |
N/A |
0.075 |
0.032 |
0.014 |
0.822 |
0.276 |
0. |
0.267 |
8.725 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 34 |
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 | 38 | 38 | 38 | 27 | 35 | 35 | 0 | 41 | 37 |
normalized size | 1 | 1. | 1. | 0.71 | 0.92 | 0.92 | 0. | 1.08 | 0.97 |
time (sec) |
N/A |
0.044 |
0.007 |
0.019 |
0.796 |
0.269 |
0. |
0.257 |
5.112 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 54 | 64 | 32 | 73 | 0 | 0 | 53 |
normalized size | 1 | 1. | 1. | 1.19 | 0.59 | 1.35 | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.077 |
0.032 |
0.017 |
0.851 |
0.268 |
0. |
0. |
8.214 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 77 | 77 | 64 | 72 | 32 | 90 | 0 | 0 | 76 |
normalized size | 1 | 1. | 0.83 | 0.94 | 0.42 | 1.17 | 0. | 0. | 0.99 |
time (sec) |
N/A |
0.106 |
0.065 |
0.019 |
0.836 |
0.277 |
0. |
0. |
11.79 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 100 | 100 | 76 | 84 | 32 | 107 | 0 | 0 | 100 |
normalized size | 1 | 1. | 0.76 | 0.84 | 0.32 | 1.07 | 0. | 0. | 1. |
time (sec) |
N/A |
0.139 |
0.08 |
0.02 |
0.836 |
0.27 |
0. |
0. |
15.763 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 92 | 96 | 32 | 123 | 0 | 0 | 124 |
normalized size | 1 | 1. | 0.75 | 0.78 | 0.26 | 1. | 0. | 0. | 1.01 |
time (sec) |
N/A |
0.175 |
0.053 |
0.02 |
0.838 |
0.269 |
0. |
0. |
20.711 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 208 | 208 | 239 | 0 | 240 | 306 | 0 | 1 | 202 |
normalized size | 1 | 1. | 1.15 | 0. | 1.15 | 1.47 | 0. | 0. | 0.97 |
time (sec) |
N/A |
0.445 |
0.779 |
0.026 |
0.821 |
0.31 |
0. |
0.296 |
61.814 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 173 | 173 | 204 | 0 | 211 | 221 | 0 | 779 | 167 |
normalized size | 1 | 1. | 1.18 | 0. | 1.22 | 1.28 | 0. | 4.5 | 0.97 |
time (sec) |
N/A |
0.262 |
0.439 |
0.027 |
0.835 |
0.269 |
0. |
0.264 |
45.037 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 169 | 0 | 181 | 157 | 0 | 408 | 131 |
normalized size | 1 | 1. | 1.22 | 0. | 1.31 | 1.14 | 0. | 2.96 | 0.95 |
time (sec) |
N/A |
0.198 |
0.333 |
0.026 |
0.816 |
0.27 |
0. |
0.259 |
31.816 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 105 | 105 | 108 | 0 | 153 | 131 | 0 | 170 | 95 |
normalized size | 1 | 1. | 1.03 | 0. | 1.46 | 1.25 | 0. | 1.62 | 0.9 |
time (sec) |
N/A |
0.137 |
0.187 |
0.024 |
0.851 |
0.258 |
0. |
0.251 |
20.582 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 70 | 0 | 70 | 76 | 0 | 78 | 70 |
normalized size | 1 | 1. | 0.97 | 0. | 0.97 | 1.06 | 0. | 1.08 | 0.97 |
time (sec) |
N/A |
0.084 |
0.076 |
0.029 |
0.862 |
0.259 |
0. |
0.257 |
11.968 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
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 | 97 | 97 | 110 | 0 | 81 | 136 | 0 | 0 | 92 |
normalized size | 1 | 1. | 1.13 | 0. | 0.84 | 1.4 | 0. | 0. | 0.95 |
time (sec) |
N/A |
0.146 |
0.15 |
0.026 |
0.887 |
0.259 |
0. |
0. |
19.558 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 140 | 0 | 81 | 203 | 0 | 0 | 126 |
normalized size | 1 | 1. | 1.08 | 0. | 0.62 | 1.56 | 0. | 0. | 0.97 |
time (sec) |
N/A |
0.202 |
0.428 |
0.026 |
0.883 |
0.254 |
0. |
0. |
28.426 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 165 | 165 | 148 | 0 | 81 | 305 | 0 | 0 | 162 |
normalized size | 1 | 1. | 0.9 | 0. | 0.49 | 1.85 | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.266 |
0.403 |
0.026 |
0.859 |
0.282 |
0. |
0. |
39.261 |
|
|
|
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 200 | 200 | 153 | 0 | 81 | 428 | 0 | 0 | 197 |
normalized size | 1 | 1. | 0.76 | 0. | 0.4 | 2.14 | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.337 |
0.616 |
0.025 |
0.929 |
0.279 |
0. |
0. |
52.311 |
|
|
|
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Problem 48 |
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 | 151 | 151 | 91 | 145 | 107 | 105 | 0 | 108 | 138 |
normalized size | 1 | 1. | 0.6 | 0.96 | 0.71 | 0.7 | 0. | 0.72 | 0.91 |
time (sec) |
N/A |
0.241 |
0.066 |
0.011 |
0.803 |
0.26 |
0. |
0.253 |
30.593 |
|
|
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 63 | 0 | 81 | 151 | 0 | 0 | 71 |
normalized size | 1 | 1. | 0.89 | 0. | 1.14 | 2.13 | 0. | 0. | 1. |
time (sec) |
N/A |
0.057 |
0.203 |
0.026 |
0.904 |
0.284 |
0. |
0. |
6.848 |
|
|
|
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|
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Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 78 | 0 | 0 | 167 | 0 | 0 | 102 |
normalized size | 1 | 1. | 0.8 | 0. | 0. | 1.7 | 0. | 0. | 1.04 |
time (sec) |
N/A |
0.17 |
0.302 |
0.093 |
0. |
0.271 |
0. |
0. |
14.81 |
|
|
|
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Problem 51 |
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 | 48 | 48 | 34 | 38 | 81 | 51 | 60 | 1 | 41 |
normalized size | 1 | 1. | 0.71 | 0.79 | 1.69 | 1.06 | 1.25 | 0.02 | 0.85 |
time (sec) |
N/A |
0.038 |
0.023 |
0. |
0.828 |
0.291 |
0.297 |
0.263 |
6.742 |
|
|
|
|
|
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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 | 135 | 135 | 56 | 80 | 158 | 100 | 116 | 1 | 126 |
normalized size | 1 | 1. | 0.41 | 0.59 | 1.17 | 0.74 | 0.86 | 0.01 | 0.93 |
time (sec) |
N/A |
0.193 |
0.049 |
0.004 |
0.858 |
0.307 |
0.384 |
0.253 |
23.661 |
|
|
|
|
|
|
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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 | 229 | 229 | 84 | 138 | 262 | 165 | 190 | 1 | 223 |
normalized size | 1 | 1. | 0.37 | 0.6 | 1.14 | 0.72 | 0.83 | 0. | 0.97 |
time (sec) |
N/A |
0.35 |
0.078 |
0.006 |
0.822 |
0.268 |
0.487 |
0.289 |
38.517 |
|
|
|
|
|
|
|
|
|
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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 | 348 | 348 | 117 | 212 | 393 | 246 | 284 | 1 | 347 |
normalized size | 1 | 1. | 0.34 | 0.61 | 1.13 | 0.71 | 0.82 | 0. | 1. |
time (sec) |
N/A |
0.57 |
0.097 |
0.009 |
0.835 |
0.272 |
0.606 |
0.329 |
57.089 |
|
|
|
|
|
|
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|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 116 | 116 | 61 | 334 | 166 | 170 | 0 | 0 | 94 |
normalized size | 1 | 1. | 0.53 | 2.88 | 1.43 | 1.47 | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.29 |
0.1 |
0.13 |
1.181 |
0.271 |
0. |
0. |
25.023 |
|
|
|
|
|
|
|
|
|
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|
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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 | 397 | 397 | 121 | 182 | 265 | 163 | 236 | 273 | 371 |
normalized size | 1 | 1. | 0.3 | 0.46 | 0.67 | 0.41 | 0.59 | 0.69 | 0.93 |
time (sec) |
N/A |
0.841 |
0.08 |
0.007 |
0.818 |
0.257 |
0.521 |
0.258 |
56.65 |
|
|
|
|
|
|
|
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|
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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 | 318 | 318 | 130 | 143 | 221 | 138 | 196 | 220 | 294 |
normalized size | 1 | 1. | 0.41 | 0.45 | 0.69 | 0.43 | 0.62 | 0.69 | 0.92 |
time (sec) |
N/A |
0.656 |
0.037 |
0.009 |
0.796 |
0.263 |
0.464 |
0.275 |
47.551 |
|
|
|
|
|
|
|
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|
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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 |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 96 | 102 | 178 | 105 | 148 | 166 | 168 |
normalized size | 1 | 1. | 0.52 | 0.55 | 0.97 | 0.57 | 0.8 | 0.9 | 0.91 |
time (sec) |
N/A |
0.397 |
0.031 |
0.007 |
0.8 |
0.248 |
0.398 |
0.241 |
31.567 |
|
|
|
|
|
|
|
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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 |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 41 | 68 | 139 | 77 | 104 | 117 | 65 |
normalized size | 1 | 1. | 0.51 | 0.85 | 1.74 | 0.96 | 1.3 | 1.46 | 0.81 |
time (sec) |
N/A |
0.111 |
0.016 |
0.006 |
0.837 |
0.242 |
0.355 |
0.25 |
11.973 |
|
|
|
|
|
|
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|
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|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 102 | 102 | 52 | 113 | 93 | 68 | 0 | 128 | 92 |
normalized size | 1 | 1. | 0.51 | 1.11 | 0.91 | 0.67 | 0. | 1.25 | 0.9 |
time (sec) |
N/A |
0.274 |
0.026 |
0.01 |
0.847 |
0.261 |
0. |
0.235 |
23.897 |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-2) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 54 | 92 | 82 | 76 | 0 | 124 | 82 |
normalized size | 1 | 1. | 0.57 | 0.98 | 0.87 | 0.81 | 0. | 1.32 | 0.87 |
time (sec) |
N/A |
0.253 |
0.036 |
0.013 |
0.88 |
0.272 |
0. |
0.263 |
21.576 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 62 |
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 | 130 | 130 | 68 | 112 | 86 | 95 | 133 | 169 | 116 |
normalized size | 1 | 1. | 0.52 | 0.86 | 0.66 | 0.73 | 1.02 | 1.3 | 0.89 |
time (sec) |
N/A |
0.33 |
0.047 |
0.013 |
0.875 |
0.244 |
22.611 |
0.266 |
23.954 |
|
|
|
|
|
|
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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 | 198 | 198 | 81 | 167 | 85 | 112 | 194 | 247 | 180 |
normalized size | 1 | 1. | 0.41 | 0.84 | 0.43 | 0.57 | 0.98 | 1.25 | 0.91 |
time (sec) |
N/A |
0.46 |
0.08 |
0.012 |
0.855 |
0.253 |
28.621 |
0.265 |
30.665 |
|
|
|
|
|
|
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|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 86 | 433 | 166 | 217 | 0 | 0 | 148 |
normalized size | 1 | 1. | 0.62 | 3.12 | 1.19 | 1.56 | 0. | 0. | 1.06 |
time (sec) |
N/A |
0.489 |
0.142 |
0.13 |
1.042 |
0.29 |
0. |
0. |
29.486 |
|
|
|
|
|
|
|
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|
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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 | 414 | 414 | 159 | 250 | 443 | 308 | 323 | 1 | 449 |
normalized size | 1 | 1. | 0.38 | 0.6 | 1.07 | 0.74 | 0.78 | 0. | 1.08 |
time (sec) |
N/A |
1.109 |
0.097 |
0.014 |
0.791 |
0.261 |
0.602 |
0.37 |
87.805 |
|
|
|
|
|
|
|
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|
|
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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 | 328 | 328 | 121 | 197 | 354 | 240 | 260 | 1 | 352 |
normalized size | 1 | 1. | 0.37 | 0.6 | 1.08 | 0.73 | 0.79 | 0. | 1.07 |
time (sec) |
N/A |
0.864 |
0.089 |
0.014 |
0.822 |
0.263 |
0.546 |
0.341 |
68.991 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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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 | 242 | 242 | 91 | 144 | 265 | 178 | 199 | 1 | 253 |
normalized size | 1 | 1. | 0.38 | 0.6 | 1.1 | 0.74 | 0.82 | 0. | 1.05 |
time (sec) |
N/A |
0.584 |
0.078 |
0.012 |
0.828 |
0.273 |
0.47 |
0.346 |
47.535 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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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 | 85 | 85 | 58 | 93 | 181 | 115 | 134 | 1 | 85 |
normalized size | 1 | 1. | 0.68 | 1.09 | 2.13 | 1.35 | 1.58 | 0.01 | 1. |
time (sec) |
N/A |
0.192 |
0.057 |
0.01 |
0.783 |
0.254 |
0.408 |
0.292 |
18.363 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 96 | 96 | 54 | 119 | 117 | 101 | 0 | 0 | 94 |
normalized size | 1 | 1. | 0.56 | 1.24 | 1.22 | 1.05 | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.407 |
0.098 |
0.033 |
0.81 |
0.264 |
0. |
0. |
24.085 |
|
|
|
|
|
|
|
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|
|
Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 85 | 85 | 58 | 129 | 92 | 112 | 0 | 0 | 87 |
normalized size | 1 | 1. | 0.68 | 1.52 | 1.08 | 1.32 | 0. | 0. | 1.02 |
time (sec) |
N/A |
0.43 |
0.109 |
0.047 |
0.824 |
0.271 |
0. |
0. |
20.379 |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 76 | 195 | 100 | 120 | 0 | 0 | 146 |
normalized size | 1 | 1. | 0.56 | 1.43 | 0.74 | 0.88 | 0. | 0. | 1.07 |
time (sec) |
N/A |
0.562 |
0.076 |
0.055 |
0.852 |
0.284 |
0. |
0. |
25.395 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 217 | 217 | 116 | 275 | 115 | 185 | 0 | 0 | 230 |
normalized size | 1 | 1. | 0.53 | 1.27 | 0.53 | 0.85 | 0. | 0. | 1.06 |
time (sec) |
N/A |
0.721 |
0.134 |
0.061 |
0.889 |
0.258 |
0. |
0. |
36.972 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 321 | 321 | 156 | 361 | 126 | 251 | 0 | 0 | 337 |
normalized size | 1 | 1. | 0.49 | 1.12 | 0.39 | 0.78 | 0. | 0. | 1.05 |
time (sec) |
N/A |
0.908 |
0.199 |
0.069 |
0.84 |
0.263 |
0. |
0. |
50.17 |
|
|
|
|
|
|
|
|
|
|
|
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|
|
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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 | 754 | 754 | 458 | 1062 | 1207 | 734 | 1445 | 1 | 694 |
normalized size | 1 | 1. | 0.61 | 1.41 | 1.6 | 0.97 | 1.92 | 0. | 0.92 |
time (sec) |
N/A |
1.522 |
0.265 |
0.014 |
0.901 |
0.271 |
1.792 |
0.257 |
126.016 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 495 | 495 | 320 | 640 | 809 | 478 | 899 | 910 | 454 |
normalized size | 1 | 1. | 0.65 | 1.29 | 1.63 | 0.97 | 1.82 | 1.84 | 0.92 |
time (sec) |
N/A |
1.047 |
0.172 |
0.008 |
0.793 |
0.251 |
1.215 |
0.255 |
83.493 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 271 | 271 | 191 | 297 | 464 | 266 | 447 | 447 | 246 |
normalized size | 1 | 1. | 0.7 | 1.1 | 1.71 | 0.98 | 1.65 | 1.65 | 0.91 |
time (sec) |
N/A |
0.559 |
0.088 |
0.009 |
0.895 |
0.249 |
0.746 |
0.26 |
46.035 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 102 | 102 | 50 | 108 | 201 | 112 | 158 | 178 | 83 |
normalized size | 1 | 1. | 0.49 | 1.06 | 1.97 | 1.1 | 1.55 | 1.75 | 0.81 |
time (sec) |
N/A |
0.154 |
0.024 |
0.007 |
0.855 |
0.237 |
0.429 |
0.259 |
16.162 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 277 | 277 | 175 | 489 | 0 | 317 | 0 | 240 | 238 |
normalized size | 1 | 1. | 0.63 | 1.77 | 0. | 1.14 | 0. | 0.87 | 0.86 |
time (sec) |
N/A |
0.561 |
0.179 |
0.019 |
0. |
0.25 |
0. |
0.258 |
49.252 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 79 |
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 | 258 | 258 | 163 | 406 | 0 | 477 | 0 | 0 | 230 |
normalized size | 1 | 1. | 0.63 | 1.57 | 0. | 1.85 | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.622 |
0.321 |
0.02 |
0. |
0.267 |
0. |
0. |
63.1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 267 | 418 | 0 | 743 | 0 | 1 | 258 |
normalized size | 1 | 1. | 0.91 | 1.42 | 0. | 2.53 | 0. | 0. | 0.88 |
time (sec) |
N/A |
0.683 |
0.72 |
0.02 |
0. |
0.245 |
0. |
0.245 |
69.932 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 389 | 511 | 0 | 1071 | 0 | 1 | 347 |
normalized size | 1 | 1. | 0.98 | 1.29 | 0. | 2.7 | 0. | 0. | 0.88 |
time (sec) |
N/A |
0.859 |
0.872 |
0.019 |
0. |
0.272 |
0. |
0.255 |
87.598 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 82 |
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 | 557 | 557 | 669 | 596 | 0 | 1463 | 0 | 0 | 493 |
normalized size | 1 | 1. | 1.2 | 1.07 | 0. | 2.63 | 0. | 0. | 0.89 |
time (sec) |
N/A |
1.152 |
0.707 |
0.019 |
0. |
0.269 |
0. |
0. |
112.574 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 24 | 0 | 57 | 43 | 0 | 0 | 22 |
normalized size | 1 | 1. | 1. | 0. | 2.38 | 1.79 | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.221 |
0.117 |
0.098 |
0.966 |
0.26 |
0. |
0. |
11.118 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 198 | 57 | 0 | 0 | 0 | 20 |
normalized size | 1 | 1. | 1.05 | 9. | 2.59 | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
0.193 |
0.05 |
0.158 |
0.933 |
0. |
0. |
0. |
11.126 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 198 | 57 | 0 | 0 | 0 | 20 |
normalized size | 1 | 1. | 1.05 | 9. | 2.59 | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
0.132 |
0.046 |
0.116 |
0.957 |
0. |
0. |
0. |
8.157 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 21 | 186 | 51 | 0 | 0 | 0 | 19 |
normalized size | 1 | 1. | 1.05 | 9.3 | 2.55 | 0. | 0. | 0. | 0.95 |
time (sec) |
N/A |
0.07 |
0.043 |
0.139 |
0.95 |
0. |
0. |
0. |
7.743 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 20 | 180 | 49 | 0 | 0 | 0 | 17 |
normalized size | 1 | 1. | 1.05 | 9.47 | 2.58 | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.19 |
0.039 |
0.105 |
0.965 |
0. |
0. |
0. |
15.164 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 136 | 53 | 0 | 0 | 0 | 19 |
normalized size | 1 | 1. | 1.05 | 6.18 | 2.41 | 0. | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.198 |
0.064 |
0.128 |
0.968 |
0. |
0. |
0. |
11.161 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
F(-2) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 23 | 136 | 53 | 0 | 0 | 0 | 20 |
normalized size | 1 | 1. | 1.05 | 6.18 | 2.41 | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
0.196 |
0.063 |
0.128 |
0.971 |
0. |
0. |
0. |
11.181 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 90 |
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 | 91 | 91 | 45 | 43 | 81 | 58 | 51 | 58 | 85 |
normalized size | 1 | 1. | 0.49 | 0.47 | 0.89 | 0.64 | 0.56 | 0.64 | 0.93 |
time (sec) |
N/A |
0.213 |
0.014 |
0.006 |
0.751 |
0.247 |
0.23 |
0.236 |
12.855 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 | 72 | 72 | 37 | 35 | 65 | 47 | 42 | 47 | 66 |
normalized size | 1 | 1. | 0.51 | 0.49 | 0.9 | 0.65 | 0.58 | 0.65 | 0.92 |
time (sec) |
N/A |
0.152 |
0.011 |
0.006 |
0.835 |
0.26 |
0.218 |
0.25 |
9.152 |
|
|
|
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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 | 53 | 53 | 29 | 27 | 49 | 36 | 34 | 36 | 48 |
normalized size | 1 | 1. | 0.55 | 0.51 | 0.92 | 0.68 | 0.64 | 0.68 | 0.91 |
time (sec) |
N/A |
0.097 |
0.009 |
0.006 |
0.778 |
0.249 |
0.2 |
0.239 |
5.879 |
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Problem 93 |
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 | 21 | 19 | 32 | 26 | 26 | 26 | 29 |
normalized size | 1 | 1. | 0.62 | 0.56 | 0.94 | 0.76 | 0.76 | 0.76 | 0.85 |
time (sec) |
N/A |
0.043 |
0.006 |
0.003 |
0.772 |
0.245 |
0.176 |
0.252 |
3.054 |
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Problem 94 |
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 | 14 | 19 | 19 | 14 | 19 | 12 |
normalized size | 1 | 1. | 1. | 0.88 | 1.19 | 1.19 | 0.88 | 1.19 | 0.75 |
time (sec) |
N/A |
0.013 |
0.003 |
0.003 |
0.787 |
0.248 |
0.137 |
0.238 |
1.193 |
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Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 27 | 57 | 14 | 14 | 0 | 14 | 32 |
normalized size | 1 | 1. | 1. | 2.11 | 0.52 | 0.52 | 0. | 0.52 | 1.19 |
time (sec) |
N/A |
0.088 |
0.007 |
0.088 |
0.848 |
0.262 |
0. |
0.231 |
5.481 |
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Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 47 | 116 | 18 | 39 | 0 | 39 | 48 |
normalized size | 1 | 1. | 0.98 | 2.42 | 0.38 | 0.81 | 0. | 0.81 | 1. |
time (sec) |
N/A |
0.134 |
0.019 |
0.033 |
0.848 |
0.25 |
0. |
0.243 |
7.81 |
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Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 71 | 71 | 56 | 155 | 20 | 51 | 0 | 62 | 68 |
normalized size | 1 | 1. | 0.79 | 2.18 | 0.28 | 0.72 | 0. | 0.87 | 0.96 |
time (sec) |
N/A |
0.18 |
0.031 |
0.043 |
0.832 |
0.244 |
0. |
0.238 |
10.422 |
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Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 92 | 92 | 64 | 189 | 20 | 62 | 0 | 85 | 87 |
normalized size | 1 | 1. | 0.7 | 2.05 | 0.22 | 0.67 | 0. | 0.92 | 0.95 |
time (sec) |
N/A |
0.234 |
0.039 |
0.046 |
0.831 |
0.235 |
0. |
0.264 |
13.476 |
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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 [48] had the largest ratio of [ 0.25
]
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| Table 1: Rubi specific breakdown of results for each integral
|
|
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|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size |
|
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
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|
|
1 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
2 |
A |
5 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
3 |
A |
4 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
4 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
5 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
6 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
7 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
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8 |
A |
2 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
9 |
A |
3 |
2 |
1. |
17 |
0.118 |
|
|
|
|
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|
|
10 |
A |
4 |
2 |
1. |
17 |
0.118 |
|
|
|
|
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|
|
11 |
A |
5 |
2 |
1. |
17 |
0.118 |
|
|
|
|
|
|
|
12 |
A |
6 |
3 |
1. |
48 |
0.062 |
|
|
|
|
|
|
|
13 |
A |
5 |
3 |
1. |
37 |
0.081 |
|
|
|
|
|
|
|
14 |
A |
4 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
15 |
A |
3 |
3 |
1. |
28 |
0.107 |
|
|
|
|
|
|
|
16 |
A |
4 |
3 |
1. |
39 |
0.077 |
|
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|
|
|
|
|
17 |
A |
5 |
3 |
1. |
50 |
0.06 |
|
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|
|
|
|
|
18 |
A |
6 |
3 |
1. |
61 |
0.049 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
20 |
A |
2 |
2 |
1. |
50 |
0.04 |
|
|
|
|
|
|
|
|
21 |
A |
2 |
2 |
1. |
39 |
0.051 |
|
|
|
|
|
|
|
22 |
A |
2 |
2 |
1. |
28 |
0.071 |
|
|
|
|
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23 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
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|
|
24 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
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|
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|
25 |
A |
2 |
2 |
1. |
30 |
0.067 |
|
|
|
|
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|
|
26 |
A |
2 |
2 |
1. |
41 |
0.049 |
|
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|
|
27 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
28 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
29 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
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|
|
30 |
A |
6 |
3 |
1. |
13 |
0.231 |
|
|
|
|
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|
|
31 |
A |
5 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
32 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
33 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
34 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
35 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
36 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
37 |
A |
5 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
38 |
A |
6 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
39 |
A |
6 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
40 |
A |
5 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
|
41 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
42 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
43 |
A |
2 |
2 |
1. |
19 |
0.105 |
|
|
|
|
|
|
|
44 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
45 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
46 |
A |
5 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
47 |
A |
6 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
48 |
A |
9 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
49 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
50 |
A |
2 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
51 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
52 |
A |
8 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
53 |
A |
12 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
54 |
A |
17 |
3 |
1. |
30 |
0.1 |
|
|
|
|
|
|
|
55 |
A |
6 |
2 |
1. |
21 |
0.095 |
|
|
|
|
|
|
|
56 |
A |
24 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
57 |
A |
20 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
58 |
A |
11 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
59 |
A |
4 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
60 |
A |
9 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
|
61 |
A |
8 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
62 |
A |
9 |
4 |
1. |
21 |
0.19 |
|
|
|
|
|
|
|
63 |
A |
12 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
64 |
A |
5 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
65 |
A |
17 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
66 |
A |
14 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
67 |
A |
11 |
3 |
1. |
20 |
0.15 |
|
|
|
|
|
|
|
68 |
A |
4 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
69 |
A |
6 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
70 |
A |
6 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
71 |
A |
8 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
72 |
A |
11 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
73 |
A |
14 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
74 |
A |
28 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
75 |
A |
20 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
76 |
A |
13 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
77 |
A |
5 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
78 |
A |
13 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
79 |
A |
11 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
80 |
A |
11 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
|
81 |
A |
13 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
82 |
A |
17 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
83 |
A |
1 |
1 |
1. |
39 |
0.026 |
|
|
|
|
|
|
|
84 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
85 |
A |
1 |
1 |
1. |
36 |
0.028 |
|
|
|
|
|
|
|
86 |
A |
1 |
1 |
1. |
35 |
0.029 |
|
|
|
|
|
|
|
87 |
A |
1 |
1 |
1. |
35 |
0.029 |
|
|
|
|
|
|
|
88 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
89 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
90 |
A |
5 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
91 |
A |
4 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
92 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
93 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
94 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
95 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
96 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
97 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
98 |
A |
5 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|