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 |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 147 | 147 | 158 | 173 | 0 | 1 | 0 | 178 | 139 |
normalized size | 1 | 1. | 1.07 | 1.18 | 0. | 0.01 | 0. | 1.21 | 0.95 |
time (sec) |
N/A |
0.129 |
0.217 |
0.007 |
0. |
0.243 |
0. |
0.226 |
16.086 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 121 | 117 | 91 | 176 | 494 | 0 | 0 | 104 |
normalized size | 1 | 1. | 0.97 | 0.75 | 1.45 | 4.08 | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.072 |
0.116 |
0.029 |
0.79 |
0.226 |
0. |
0. |
4.326 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 86 | 71 | 139 | 386 | 0 | 0 | 80 |
normalized size | 1 | 1. | 0.91 | 0.75 | 1.46 | 4.06 | 0. | 0. | 0.84 |
time (sec) |
N/A |
0.053 |
0.096 |
0.01 |
0.783 |
0.235 |
0. |
0. |
3.273 |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 69 | 69 | 83 | 51 | 103 | 278 | 0 | 0 | 56 |
normalized size | 1 | 1. | 1.2 | 0.74 | 1.49 | 4.03 | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.037 |
0.073 |
0.01 |
0.793 |
0.219 |
0. |
0. |
2.431 |
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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 |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 62 | 31 | 66 | 170 | 0 | 0 | 32 |
normalized size | 1 | 1. | 1.44 | 0.72 | 1.53 | 3.95 | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.025 |
0.054 |
0.01 |
0.807 |
0.218 |
0. |
0. |
1.829 |
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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 |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 102 | 82 | 158 | 92 | 0 | 77 | 90 |
normalized size | 1 | 1. | 1.01 | 0.81 | 1.56 | 0.91 | 0. | 0.76 | 0.89 |
time (sec) |
N/A |
0.064 |
0.11 |
0.005 |
0.79 |
0.22 |
0. |
0.215 |
3.579 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 92 | 64 | 122 | 78 | 0 | 63 | 70 |
normalized size | 1 | 1. | 1.16 | 0.81 | 1.54 | 0.99 | 0. | 0.8 | 0.89 |
time (sec) |
N/A |
0.047 |
0.061 |
0.006 |
0.798 |
0.216 |
0. |
0.214 |
2.818 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 57 | 57 | 74 | 46 | 85 | 65 | 0 | 50 | 49 |
normalized size | 1 | 1. | 1.3 | 0.81 | 1.49 | 1.14 | 0. | 0.88 | 0.86 |
time (sec) |
N/A |
0.033 |
0.071 |
0.004 |
0.794 |
0.21 |
0. |
0.216 |
2.184 |
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Problem 9 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 72 | 28 | 49 | 51 | 0 | 36 | 29 |
normalized size | 1 | 1. | 2.06 | 0.8 | 1.4 | 1.46 | 0. | 1.03 | 0.83 |
time (sec) |
N/A |
0.023 |
0.033 |
0.004 |
0.804 |
0.212 |
0. |
0.211 |
1.726 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 45 | 28 | 49 | 47 | 0 | 34 | 26 |
normalized size | 1 | 1. | 1.29 | 0.8 | 1.4 | 1.34 | 0. | 0.97 | 0.74 |
time (sec) |
N/A |
0.024 |
0.043 |
0.005 |
0.799 |
0.213 |
0. |
0.209 |
1.689 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 72 | 28 | 49 | 51 | 0 | 36 | 29 |
normalized size | 1 | 1. | 2.06 | 0.8 | 1.4 | 1.46 | 0. | 1.03 | 0.83 |
time (sec) |
N/A |
0.024 |
0.039 |
0.005 |
0.852 |
0.211 |
0. |
0.211 |
1.729 |
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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 |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 63 | 42 | 74 | 58 | 0 | 47 | 41 |
normalized size | 1 | 1. | 1.24 | 0.82 | 1.45 | 1.14 | 0. | 0.92 | 0.8 |
time (sec) |
N/A |
0.027 |
0.069 |
0.005 |
0.795 |
0.231 |
0. |
0.213 |
1.894 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 40 | 33 | 55 | 144 | 0 | 45 | 31 |
normalized size | 1 | 1. | 1.14 | 0.94 | 1.57 | 4.11 | 0. | 1.29 | 0.89 |
time (sec) |
N/A |
0.02 |
0.043 |
0.005 |
0.75 |
0.232 |
0. |
0.211 |
1.478 |
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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 |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 44 | 33 | 58 | 144 | 0 | 45 | 32 |
normalized size | 1 | 1. | 1.19 | 0.89 | 1.57 | 3.89 | 0. | 1.22 | 0.86 |
time (sec) |
N/A |
0.02 |
0.044 |
0.005 |
0.727 |
0.215 |
0. |
0.211 |
1.488 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 46 | 33 | 58 | 163 | 0 | 50 | 29 |
normalized size | 1 | 1. | 1.18 | 0.85 | 1.49 | 4.18 | 0. | 1.28 | 0.74 |
time (sec) |
N/A |
0.02 |
0.045 |
0.005 |
0.716 |
0.216 |
0. |
0.211 |
1.482 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 70 | 75 | 150 | 127 | 0 | 100 | 82 |
normalized size | 1 | 1. | 0.84 | 0.9 | 1.81 | 1.53 | 0. | 1.2 | 0.99 |
time (sec) |
N/A |
0.052 |
0.066 |
0.006 |
0.739 |
0.217 |
0. |
0.222 |
4.947 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
A |
A |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 50 | 10 | 28 | 26 | 0 | 0 | 8 |
normalized size | 1 | 1. | 3.12 | 0.62 | 1.75 | 1.62 | 0. | 0. | 0.5 |
time (sec) |
N/A |
0.016 |
0.018 |
0.01 |
0.792 |
0.213 |
0. |
0. |
1.361 |
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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 |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 24 | 21 | 38 | 42 | 0 | 0 | 20 |
normalized size | 1 | 1. | 0.92 | 0.81 | 1.46 | 1.62 | 0. | 0. | 0.77 |
time (sec) |
N/A |
0.01 |
0.015 |
0.01 |
0.711 |
0.212 |
0. |
0. |
1.279 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 36 | 42 | 74 | 127 | 0 | 0 | 42 |
normalized size | 1 | 1. | 0.68 | 0.79 | 1.4 | 2.4 | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.022 |
0.024 |
0.01 |
0.694 |
0.223 |
0. |
0. |
1.841 |
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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 |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 79 | 48 | 62 | 111 | 197 | 0 | 0 | 65 |
normalized size | 1 | 1. | 0.61 | 0.78 | 1.41 | 2.49 | 0. | 0. | 0.82 |
time (sec) |
N/A |
0.035 |
0.032 |
0.012 |
0.695 |
0.225 |
0. |
0. |
2.58 |
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 45 | 9 | 11 | 26 | 0 | 11 | 8 |
normalized size | 1 | 1. | 3.75 | 0.75 | 0.92 | 2.17 | 0. | 0.92 | 0.67 |
time (sec) |
N/A |
0.014 |
0.016 |
0.005 |
0.778 |
0.216 |
0. |
0.214 |
1.353 |
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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 |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 21 | 25 | 38 | 24 | 0 | 39 | 19 |
normalized size | 1 | 1. | 0.95 | 1.14 | 1.73 | 1.09 | 0. | 1.77 | 0.86 |
time (sec) |
N/A |
0.01 |
0.014 |
0.005 |
0.698 |
0.221 |
0. |
0.217 |
1.182 |
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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 |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 31 | 35 | 74 | 53 | 0 | 53 | 37 |
normalized size | 1 | 1. | 0.69 | 0.78 | 1.64 | 1.18 | 0. | 1.18 | 0.82 |
time (sec) |
N/A |
0.02 |
0.023 |
0.004 |
0.69 |
0.216 |
0. |
0.219 |
1.616 |
|
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Problem 24 |
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 | 67 | 67 | 51 | 45 | 111 | 76 | 0 | 66 | 56 |
normalized size | 1 | 1. | 0.76 | 0.67 | 1.66 | 1.13 | 0. | 0.99 | 0.84 |
time (sec) |
N/A |
0.033 |
0.032 |
0.005 |
0.704 |
0.226 |
0. |
0.221 |
2.153 |
|
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Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 58 | 35 | 0 | 36 | 0 | 20 | 8 |
normalized size | 1 | 1. | 4.83 | 2.92 | 0. | 3. | 0. | 1.67 | 0.67 |
time (sec) |
N/A |
0.019 |
0.032 |
0.009 |
0. |
0.216 |
0. |
0.221 |
3.317 |
|
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Problem 26 |
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 | 24 | 24 | 45 | 37 | 0 | 36 | 0 | 49 | 20 |
normalized size | 1 | 1. | 1.88 | 1.54 | 0. | 1.5 | 0. | 2.04 | 0.83 |
time (sec) |
N/A |
0.02 |
0.039 |
0.004 |
0. |
0.212 |
0. |
0.222 |
2.541 |
|
|
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Problem 27 |
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 | 10 | 10 | 38 | 7 | 11 | 24 | 0 | 8 | 5 |
normalized size | 1 | 1. | 3.8 | 0.7 | 1.1 | 2.4 | 0. | 0.8 | 0.5 |
time (sec) |
N/A |
0.015 |
0.014 |
0.005 |
0.782 |
0.22 |
0. |
0.213 |
1.342 |
|
|
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Problem 28 |
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 | 16 | 16 | 33 | 14 | 23 | 23 | 0 | 24 | 14 |
normalized size | 1 | 1. | 2.06 | 0.88 | 1.44 | 1.44 | 0. | 1.5 | 0.88 |
time (sec) |
N/A |
0.011 |
0.013 |
0.004 |
0.728 |
0.212 |
0. |
0.212 |
1.191 |
|
|
|
|
|
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|
Problem 29 |
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 | 16 | 16 | 37 | 14 | 23 | 23 | 0 | 24 | 14 |
normalized size | 1 | 1. | 2.31 | 0.88 | 1.44 | 1.44 | 0. | 1.5 | 0.88 |
time (sec) |
N/A |
0.011 |
0.014 |
0.005 |
0.704 |
0.212 |
0. |
0.213 |
1.186 |
|
|
|
|
|
|
|
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|
|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 448 | 448 | 94 | 0 | 0 | 0 | 0 | 0 | 398 |
normalized size | 1 | 1. | 0.21 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
1.338 |
0.084 |
0.057 |
0. |
0. |
0. |
0. |
41.363 |
|
|
|
|
|
|
|
|
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|
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|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 387 | 387 | 70 | 0 | 0 | 0 | 0 | 0 | 332 |
normalized size | 1 | 1. | 0.18 | 0. | 0. | 0. | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.932 |
0.057 |
0.044 |
0. |
0. |
0. |
0. |
32.401 |
|
|
|
|
|
|
|
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|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 322 | 322 | 44 | 0 | 0 | 0 | 0 | 0 | 264 |
normalized size | 1 | 1. | 0.14 | 0. | 0. | 0. | 0. | 0. | 0.82 |
time (sec) |
N/A |
0.788 |
0.023 |
0.055 |
0. |
0. |
0. |
0. |
23.123 |
|
|
|
|
|
|
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|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 384 | 384 | 57 | 0 | 0 | 0 | 0 | 0 | 328 |
normalized size | 1 | 1. | 0.15 | 0. | 0. | 0. | 0. | 0. | 0.85 |
time (sec) |
N/A |
0.922 |
0.049 |
0.084 |
0. |
0. |
0. |
0. |
32.462 |
|
|
|
|
|
|
|
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|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 448 | 448 | 90 | 0 | 0 | 0 | 0 | 0 | 400 |
normalized size | 1 | 1. | 0.2 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
1.063 |
0.097 |
0.142 |
0. |
0. |
0. |
0. |
41.483 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 842 | 842 | 94 | 0 | 0 | 0 | 0 | 0 | 731 |
normalized size | 1 | 1. | 0.11 | 0. | 0. | 0. | 0. | 0. | 0.87 |
time (sec) |
N/A |
2.02 |
0.07 |
0.058 |
0. |
0. |
0. |
0. |
82.292 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 781 | 781 | 70 | 0 | 0 | 0 | 0 | 0 | 663 |
normalized size | 1 | 1. | 0.09 | 0. | 0. | 0. | 0. | 0. | 0.85 |
time (sec) |
N/A |
1.829 |
0.053 |
0.054 |
0. |
0. |
0. |
0. |
68.578 |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
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|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 715 | 715 | 46 | 0 | 0 | 0 | 0 | 0 | 595 |
normalized size | 1 | 1. | 0.06 | 0. | 0. | 0. | 0. | 0. | 0.83 |
time (sec) |
N/A |
1.665 |
0.026 |
0.047 |
0. |
0. |
0. |
0. |
55.449 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 773 | 773 | 57 | 0 | 0 | 0 | 0 | 0 | 660 |
normalized size | 1 | 1. | 0.07 | 0. | 0. | 0. | 0. | 0. | 0.85 |
time (sec) |
N/A |
1.835 |
0.046 |
0.087 |
0. |
0. |
0. |
0. |
68.937 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 838 | 838 | 90 | 0 | 0 | 0 | 0 | 0 | 728 |
normalized size | 1 | 1. | 0.11 | 0. | 0. | 0. | 0. | 0. | 0.87 |
time (sec) |
N/A |
1.994 |
0.099 |
0.144 |
0. |
0. |
0. |
0. |
82.681 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 119 | 119 | 94 | 0 | 0 | 0 | 0 | 0 | 109 |
normalized size | 1 | 1. | 0.79 | 0. | 0. | 0. | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.111 |
0.07 |
0.063 |
0. |
0. |
0. |
0. |
17.234 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
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|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 70 | 0 | 0 | 0 | 0 | 0 | 80 |
normalized size | 1 | 1. | 0.78 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.078 |
0.064 |
0.056 |
0. |
0. |
0. |
0. |
14.028 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 90 | 90 | 70 | 0 | 0 | 0 | 0 | 0 | 78 |
normalized size | 1 | 1. | 0.78 | 0. | 0. | 0. | 0. | 0. | 0.87 |
time (sec) |
N/A |
0.075 |
0.052 |
0.049 |
0. |
0. |
0. |
0. |
13.896 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 46 | 0 | 0 | 0 | 0 | 0 | 51 |
normalized size | 1 | 1. | 0.79 | 0. | 0. | 0. | 0. | 0. | 0.88 |
time (sec) |
N/A |
0.051 |
0.029 |
0.047 |
0. |
0. |
0. |
0. |
11.858 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 44 | 0 | 0 | 0 | 0 | 0 | 53 |
normalized size | 1 | 1. | 0.75 | 0. | 0. | 0. | 0. | 0. | 0.9 |
time (sec) |
N/A |
0.05 |
0.022 |
0.058 |
0. |
0. |
0. |
0. |
11.931 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 83 | 83 | 59 | 0 | 0 | 0 | 0 | 0 | 75 |
normalized size | 1 | 1. | 0.71 | 0. | 0. | 0. | 0. | 0. | 0.9 |
time (sec) |
N/A |
0.073 |
0.053 |
0.09 |
0. |
0. |
0. |
0. |
13.592 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 90 | 0 | 0 | 0 | 0 | 0 | 109 |
normalized size | 1 | 1. | 0.78 | 0. | 0. | 0. | 0. | 0. | 0.95 |
time (sec) |
N/A |
0.101 |
0.105 |
0.153 |
0. |
0. |
0. |
0. |
16.242 |
|
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 146 | 146 | 114 | 0 | 0 | 0 | 0 | 0 | 139 |
normalized size | 1 | 1. | 0.78 | 0. | 0. | 0. | 0. | 0. | 0.95 |
time (sec) |
N/A |
0.13 |
0.144 |
0.1 |
0. |
0. |
0. |
0. |
19.614 |
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 45 | 0 | 0 | 0 | 0 | 0 | 42 |
normalized size | 1 | 1. | 0.82 | 0. | 0. | 0. | 0. | 0. | 0.76 |
time (sec) |
N/A |
0.032 |
0.041 |
0.044 |
0. |
0. |
0. |
0. |
2.753 |
|
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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 |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 51 | 51 | 51 | 44 | 58 | 1 | 49 | 58 | 0 |
normalized size | 1 | 1. | 1. | 0.86 | 1.14 | 0.02 | 0.96 | 1.14 | 0. |
time (sec) |
N/A |
0.044 |
0.003 |
0.001 |
0.701 |
0.185 |
0.107 |
0.209 |
0. |
|
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Problem 50 |
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 | 35 | 35 | 35 | 32 | 42 | 1 | 32 | 42 | 0 |
normalized size | 1 | 1. | 1. | 0.91 | 1.2 | 0.03 | 0.91 | 1.2 | 0. |
time (sec) |
N/A |
0.029 |
0.002 |
0.002 |
0.694 |
0.187 |
0.098 |
0.208 |
0. |
|
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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 |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 22 | 28 | 1 | 22 | 28 | 0 |
normalized size | 1 | 1. | 1. | 0.88 | 1.12 | 0.04 | 0.88 | 1.12 | 0. |
time (sec) |
N/A |
0.019 |
0.002 |
0.002 |
0.704 |
0.191 |
0.088 |
0.21 |
0. |
|
|
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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 |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 11 | 14 | 1 | 8 | 14 | 0 |
normalized size | 1 | 1. | 1. | 0.92 | 1.17 | 0.08 | 0.67 | 1.17 | 0. |
time (sec) |
N/A |
0.008 |
0. |
0.001 |
0.698 |
0.19 |
0.067 |
0.209 |
0. |
|
|
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Problem 53 |
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 |
0.019 |
0.008 |
0.005 |
0. |
0.221 |
0.29 |
0.209 |
2.447 |
|
|
|
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Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 45 | 45 | 45 | 36 | 0 | 1 | 78 | 47 | 36 |
normalized size | 1 | 1. | 1. | 0.8 | 0. | 0.02 | 1.73 | 1.04 | 0.8 |
time (sec) |
N/A |
0.029 |
0.045 |
0.002 |
0. |
0.229 |
1.41 |
0.21 |
3.773 |
|
|
|
|
|
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|
Problem 55 |
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 | 62 | 62 | 55 | 51 | 0 | 1 | 105 | 61 | 54 |
normalized size | 1 | 1. | 0.89 | 0.82 | 0. | 0.02 | 1.69 | 0.98 | 0.87 |
time (sec) |
N/A |
0.041 |
0.088 |
0.002 |
0. |
0.23 |
1.834 |
0.209 |
5.708 |
|
|
|
|
|
|
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|
|
Problem 56 |
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 | 84 | 84 | 71 | 66 | 0 | 1 | 97 | 85 | 78 |
normalized size | 1 | 1. | 0.85 | 0.79 | 0. | 0.01 | 1.15 | 1.01 | 0.93 |
time (sec) |
N/A |
0.054 |
0.081 |
0.006 |
0. |
0.249 |
14.343 |
0.215 |
5.836 |
|
|
|
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|
Problem 57 |
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 | 65 | 65 | 62 | 51 | 0 | 1 | 70 | 66 | 60 |
normalized size | 1 | 1. | 0.95 | 0.78 | 0. | 0.02 | 1.08 | 1.02 | 0.92 |
time (sec) |
N/A |
0.037 |
0.058 |
0.004 |
0. |
0.24 |
9.943 |
0.215 |
4.418 |
|
|
|
|
|
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|
Problem 58 |
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 | 46 | 46 | 49 | 36 | 0 | 1 | 41 | 50 | 39 |
normalized size | 1 | 1. | 1.07 | 0.78 | 0. | 0.02 | 0.89 | 1.09 | 0.85 |
time (sec) |
N/A |
0.024 |
0.024 |
0.003 |
0. |
0.236 |
6.226 |
0.211 |
3.174 |
|
|
|
|
|
|
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|
Problem 59 |
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 | 25 | 25 | 25 | 21 | 0 | 1 | 17 | 31 | 22 |
normalized size | 1 | 1. | 1. | 0.84 | 0. | 0.04 | 0.68 | 1.24 | 0.88 |
time (sec) |
N/A |
0.015 |
0.01 |
0.003 |
0. |
0.227 |
3.573 |
0.215 |
2.432 |
|
|
|
|
|
|
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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 | 16 | 16 | 16 | 15 | 19 | 31 | 17 | 19 | 12 |
normalized size | 1 | 1. | 1. | 0.94 | 1.19 | 1.94 | 1.06 | 1.19 | 0.75 |
time (sec) |
N/A |
0.008 |
0.012 |
0.004 |
0.706 |
0.215 |
1.803 |
0.215 |
1.274 |
|
|
|
|
|
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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 | 39 | 39 | 29 | 26 | 42 | 63 | 95 | 36 | 32 |
normalized size | 1 | 1. | 0.74 | 0.67 | 1.08 | 1.62 | 2.44 | 0.92 | 0.82 |
time (sec) |
N/A |
0.021 |
0.021 |
0.004 |
0.702 |
0.225 |
2.666 |
0.215 |
2.014 |
|
|
|
|
|
|
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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 | 58 | 58 | 40 | 37 | 62 | 93 | 413 | 55 | 51 |
normalized size | 1 | 1. | 0.69 | 0.64 | 1.07 | 1.6 | 7.12 | 0.95 | 0.88 |
time (sec) |
N/A |
0.03 |
0.027 |
0.004 |
0.708 |
0.235 |
5.259 |
0.217 |
3.327 |
|
|
|
|
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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 | 77 | 77 | 51 | 48 | 82 | 123 | 1265 | 74 | 70 |
normalized size | 1 | 1. | 0.66 | 0.62 | 1.06 | 1.6 | 16.43 | 0.96 | 0.91 |
time (sec) |
N/A |
0.043 |
0.032 |
0.006 |
0.699 |
0.252 |
9.963 |
0.217 |
5.014 |
|
|
|
|
|
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|
Problem 64 |
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 | 23 | 23 | 20 | 35 | 41 | 26 | 0 | 69 | 19 |
normalized size | 1 | 1. | 0.87 | 1.52 | 1.78 | 1.13 | 0. | 3. | 0.83 |
time (sec) |
N/A |
0.01 |
0.016 |
0.004 |
0.804 |
0.209 |
0. |
0.209 |
1.22 |
|
|
|
|
|
|
|
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|
|
Problem 65 |
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 | 23 | 23 | 25 | 25 | 41 | 12 | 0 | 35 | 19 |
normalized size | 1 | 1. | 1.09 | 1.09 | 1.78 | 0.52 | 0. | 1.52 | 0.83 |
time (sec) |
N/A |
0.01 |
0.009 |
0.004 |
0.769 |
0.219 |
0. |
0.21 |
1.246 |
|
|
|
|
|
|
|
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|
|
Problem 66 |
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 | 29 | 29 | 26 | 23 | 8 | 11 | 0 | 34 | 26 |
normalized size | 1 | 1. | 0.9 | 0.79 | 0.28 | 0.38 | 0. | 1.17 | 0.9 |
time (sec) |
N/A |
0.014 |
0.01 |
0.007 |
0.791 |
0.212 |
0. |
0.212 |
1.546 |
|
|
|
|
|
|
|
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|
|
Problem 67 |
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 | 25 | 25 | 20 | 17 | 12 | 19 | 0 | 4 | 20 |
normalized size | 1 | 1. | 0.8 | 0.68 | 0.48 | 0.76 | 0. | 0.16 | 0.8 |
time (sec) |
N/A |
0.01 |
0.01 |
0.005 |
0.787 |
0.221 |
0. |
0.562 |
1.224 |
|
|
|
|
|
|
|
|
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|
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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 | 23 | 23 | 25 | 25 | 41 | 12 | 8 | 35 | 20 |
normalized size | 1 | 1. | 1.09 | 1.09 | 1.78 | 0.52 | 0.35 | 1.52 | 0.87 |
time (sec) |
N/A |
0.01 |
0.02 |
0.005 |
0.799 |
0.216 |
0.105 |
0.211 |
1.401 |
|
|
|
|
|
|
|
|
|
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|
|
|
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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 | 29 | 29 | 26 | 23 | 8 | 11 | 7 | 20 | 27 |
normalized size | 1 | 1. | 0.9 | 0.79 | 0.28 | 0.38 | 0.24 | 0.69 | 0.93 |
time (sec) |
N/A |
0.014 |
0.018 |
0.007 |
0.805 |
0.233 |
0.116 |
0.21 |
1.754 |
|
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 27 | 27 | 41 | 12 | 0 | 39 | 20 |
normalized size | 1 | 1. | 1.17 | 1.17 | 1.78 | 0.52 | 0. | 1.7 | 0.87 |
time (sec) |
N/A |
0.009 |
0.013 |
0.003 |
0.776 |
0.209 |
0. |
0.21 |
1.458 |
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 28 | 25 | 8 | 8 | 0 | 35 | 27 |
normalized size | 1 | 1. | 0.97 | 0.86 | 0.28 | 0.28 | 0. | 1.21 | 0.93 |
time (sec) |
N/A |
0.014 |
0.012 |
0.005 |
0.806 |
0.221 |
0. |
0.211 |
1.798 |
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 27 | 27 | 41 | 12 | 0 | 39 | 20 |
normalized size | 1 | 1. | 1.17 | 1.17 | 1.78 | 0.52 | 0. | 1.7 | 0.87 |
time (sec) |
N/A |
0.01 |
0.011 |
0.003 |
0.792 |
0.215 |
0. |
0.209 |
1.395 |
|
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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 |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 28 | 25 | 8 | 8 | 0 | 35 | 27 |
normalized size | 1 | 1. | 0.97 | 0.86 | 0.28 | 0.28 | 0. | 1.21 | 0.93 |
time (sec) |
N/A |
0.017 |
0.007 |
0.003 |
0.796 |
0.216 |
0. |
0.212 |
1.89 |
|
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Problem 74 |
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 | 109 | 109 | 207 | 636 | 316 | 315 | 253 | 489 | 95 |
normalized size | 1 | 1. | 1.9 | 5.83 | 2.9 | 2.89 | 2.32 | 4.49 | 0.87 |
time (sec) |
N/A |
0.302 |
0.055 |
0.007 |
0.721 |
0.22 |
0.433 |
0.209 |
48.389 |
|
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Problem 75 |
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 | 109 | 109 | 207 | 636 | 316 | 317 | 250 | 489 | 95 |
normalized size | 1 | 1. | 1.9 | 5.83 | 2.9 | 2.91 | 2.29 | 4.49 | 0.87 |
time (sec) |
N/A |
0.295 |
0.076 |
0.006 |
0.718 |
0.213 |
0.419 |
0.209 |
47.351 |
|
|
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Problem 76 |
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 | 109 | 109 | 199 | 636 | 316 | 306 | 253 | 489 | 99 |
normalized size | 1 | 1. | 1.83 | 5.83 | 2.9 | 2.81 | 2.32 | 4.49 | 0.91 |
time (sec) |
N/A |
0.289 |
0.052 |
0.006 |
0.732 |
0.212 |
0.431 |
0.209 |
47.709 |
|
|
|
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Problem 77 |
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 | 109 | 109 | 207 | 636 | 316 | 317 | 248 | 489 | 97 |
normalized size | 1 | 1. | 1.9 | 5.83 | 2.9 | 2.91 | 2.28 | 4.49 | 0.89 |
time (sec) |
N/A |
0.292 |
0.078 |
0.006 |
0.726 |
0.217 |
0.411 |
0.209 |
44.205 |
|
|
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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 | 18 | 18 | 18 | 17 | 22 | 22 | 22 | 22 | 19 |
normalized size | 1 | 1. | 1. | 0.94 | 1.22 | 1.22 | 1.22 | 1.22 | 1.06 |
time (sec) |
N/A |
0.027 |
0.008 |
0.005 |
0.795 |
0.224 |
0.225 |
0.206 |
1.416 |
|
|
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|
|
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|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 12 | 12 | 12 | 9 | 11 | 0 | 7 | 11 | 7 |
normalized size | 1 | 1. | 1. | 0.75 | 0.92 | 0. | 0.58 | 0.92 | 0.58 |
time (sec) |
N/A |
0.017 |
0.023 |
0.018 |
0.792 |
0. |
0.393 |
0.21 |
1.358 |
|
|
|
|
|
|
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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 | 19 | 19 | 34 | 17 | 36 | 51 | 39 | 42 | 22 |
normalized size | 1 | 1. | 1.79 | 0.89 | 1.89 | 2.68 | 2.05 | 2.21 | 1.16 |
time (sec) |
N/A |
0.036 |
0.035 |
0.002 |
0.82 |
0.22 |
0.22 |
0.211 |
1.437 |
|
|
|
|
|
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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 | 13 | 13 | 13 | 14 | 18 | 18 | 10 | 20 | 10 |
normalized size | 1 | 1. | 1. | 1.08 | 1.38 | 1.38 | 0.77 | 1.54 | 0.77 |
time (sec) |
N/A |
0.012 |
0.005 |
0.007 |
0.739 |
0.214 |
0.19 |
0.208 |
1.513 |
|
|
|
|
|
|
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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 | 21 | 21 | 21 | 16 | 20 | 20 | 14 | 23 | 14 |
normalized size | 1 | 1. | 1. | 0.76 | 0.95 | 0.95 | 0.67 | 1.1 | 0.67 |
time (sec) |
N/A |
0.014 |
0.005 |
0.008 |
0.728 |
0.213 |
0.212 |
0.21 |
1.655 |
|
|
|
|
|
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|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
B |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 6 | 17 | 17 | 14 | 18 | 18 | 12 | 20 | 12 |
normalized size | 1 | 2.83 | 2.83 | 2.33 | 3. | 3. | 2. | 3.33 | 2. |
time (sec) |
N/A |
0.012 |
0.005 |
0.008 |
0.727 |
0.226 |
0.179 |
0.209 |
1.421 |
|
|
|
|
|
|
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|
Problem 84 |
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 | 24 | 51 | 82 | 76 | 54 | 26 |
normalized size | 1 | 1. | 1. | 0.89 | 1.89 | 3.04 | 2.81 | 2. | 0.96 |
time (sec) |
N/A |
0.04 |
0.014 |
0.005 |
0.742 |
0.244 |
0.526 |
0.21 |
3.156 |
|
|
|
|
|
|
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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 | 27 | 27 | 29 | 26 | 53 | 81 | 76 | 61 | 26 |
normalized size | 1 | 1. | 1.07 | 0.96 | 1.96 | 3. | 2.81 | 2.26 | 0.96 |
time (sec) |
N/A |
0.041 |
0.014 |
0.004 |
0.734 |
0.219 |
0.566 |
0.211 |
3.085 |
|
|
|
|
|
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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 | 31 | 31 | 31 | 28 | 36 | 46 | 87 | 36 | 24 |
normalized size | 1 | 1. | 1. | 0.9 | 1.16 | 1.48 | 2.81 | 1.16 | 0.77 |
time (sec) |
N/A |
0.046 |
0.014 |
0.004 |
0.728 |
0.23 |
0.442 |
0.208 |
2.863 |
|
|
|
|
|
|
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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 | 27 | 27 | 29 | 26 | 53 | 81 | 76 | 61 | 26 |
normalized size | 1 | 1. | 1.07 | 0.96 | 1.96 | 3. | 2.81 | 2.26 | 0.96 |
time (sec) |
N/A |
0.039 |
0.014 |
0.006 |
0.716 |
0.224 |
0.584 |
0.209 |
2.923 |
|
|
|
|
|
|
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|
Problem 88 |
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 | 38 | 38 | 38 | 35 | 0 | 1 | 124 | 46 | 34 |
normalized size | 1 | 1. | 1. | 0.92 | 0. | 0.03 | 3.26 | 1.21 | 0.89 |
time (sec) |
N/A |
0.065 |
0.019 |
0.008 |
0. |
0.217 |
0.553 |
0.209 |
4.595 |
|
|
|
|
|
|
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|
|
Problem 89 |
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 | 35 | 35 | 34 | 35 | 0 | 1 | 100 | 41 | 27 |
normalized size | 1 | 1. | 0.97 | 1. | 0. | 0.03 | 2.86 | 1.17 | 0.77 |
time (sec) |
N/A |
0.065 |
0.016 |
0.008 |
0. |
0.218 |
0.578 |
0.208 |
7.517 |
|
|
|
|
|
|
|
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|
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|
|
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 | 32 | 32 | 41 | 31 | 0 | 115 | 102 | 74 | 27 |
normalized size | 1 | 1. | 1.28 | 0.97 | 0. | 3.59 | 3.19 | 2.31 | 0.84 |
time (sec) |
N/A |
0.051 |
0.018 |
0.005 |
0. |
0.216 |
0.654 |
0.213 |
7.222 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
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 | 43 | 43 | 43 | 37 | 49 | 68 | 39 | 49 | 36 |
normalized size | 1 | 1. | 1. | 0.86 | 1.14 | 1.58 | 0.91 | 1.14 | 0.84 |
time (sec) |
N/A |
0.037 |
0.04 |
0.005 |
0.791 |
0.212 |
0.335 |
0.207 |
1.864 |
|
|
|
|
|
|
|
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|
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|
|
|
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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 | 43 | 43 | 62 | 37 | 63 | 99 | 58 | 69 | 39 |
normalized size | 1 | 1. | 1.44 | 0.86 | 1.47 | 2.3 | 1.35 | 1.6 | 0.91 |
time (sec) |
N/A |
0.04 |
0.054 |
0.003 |
0.785 |
0.215 |
0.325 |
0.208 |
1.865 |
|
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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 | 33 | 32 | 46 | 72 | 29 | 49 | 29 |
normalized size | 1 | 1. | 0.97 | 0.94 | 1.35 | 2.12 | 0.85 | 1.44 | 0.85 |
time (sec) |
N/A |
0.022 |
0.019 |
0.014 |
0.722 |
0.217 |
0.312 |
0.21 |
1.951 |
|
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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 | 42 | 42 | 42 | 32 | 46 | 72 | 32 | 49 | 32 |
normalized size | 1 | 1. | 1. | 0.76 | 1.1 | 1.71 | 0.76 | 1.17 | 0.76 |
time (sec) |
N/A |
0.026 |
0.023 |
0.013 |
0.716 |
0.22 |
0.324 |
0.21 |
2.156 |
|
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Problem 95 |
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 | 71 | 71 | 70 | 68 | 0 | 1 | 265 | 90 | 60 |
normalized size | 1 | 1. | 0.99 | 0.96 | 0. | 0.01 | 3.73 | 1.27 | 0.85 |
time (sec) |
N/A |
0.082 |
0.105 |
0.005 |
0. |
0.232 |
2.781 |
0.208 |
7.53 |
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Problem 96 |
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 | 72 | 72 | 72 | 86 | 0 | 1 | 228 | 101 | 58 |
normalized size | 1 | 1. | 1. | 1.19 | 0. | 0.01 | 3.17 | 1.4 | 0.81 |
time (sec) |
N/A |
0.096 |
0.072 |
0.004 |
0. |
0.225 |
2.589 |
0.209 |
11.565 |
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Problem 97 |
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 | 69 | 69 | 78 | 84 | 0 | 216 | 218 | 122 | 60 |
normalized size | 1 | 1. | 1.13 | 1.22 | 0. | 3.13 | 3.16 | 1.77 | 0.87 |
time (sec) |
N/A |
0.07 |
0.11 |
0.004 |
0. |
0.237 |
2.674 |
0.214 |
9.552 |
|
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Problem 98 |
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 | 65 | 111 | 215 | 120 | 212 | 135 | 94 |
normalized size | 1 | 1. | 1.05 | 1.79 | 3.47 | 1.94 | 3.42 | 2.18 | 1.52 |
time (sec) |
N/A |
0.268 |
0.154 |
0.044 |
0.828 |
0.244 |
2.99 |
0.222 |
80.535 |
|
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Problem 99 |
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 | 58 | 34 | 31 | 88 | 85 | 56 | 76 | 49 |
normalized size | 1 | 1.76 | 1.03 | 0.94 | 2.67 | 2.58 | 1.7 | 2.3 | 1.48 |
time (sec) |
N/A |
0.074 |
0.056 |
0.013 |
0.703 |
0.235 |
0.806 |
0.218 |
4.474 |
|
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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 | 31 | 58 | 32 | 31 | 82 | 80 | 56 | 73 | 49 |
normalized size | 1 | 1.87 | 1.03 | 1. | 2.65 | 2.58 | 1.81 | 2.35 | 1.58 |
time (sec) |
N/A |
0.064 |
0.051 |
0.009 |
0.756 |
0.23 |
0.795 |
0.22 |
4.648 |
|
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Problem 101 |
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 | 17 | 17 | 19 | 33 | 36 | 20 | 165 | 36 | 17 |
normalized size | 1 | 1. | 1.12 | 1.94 | 2.12 | 1.18 | 9.71 | 2.12 | 1. |
time (sec) |
N/A |
0.039 |
0.034 |
0.02 |
0.795 |
0.226 |
0.45 |
0.207 |
3.907 |
|
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Problem 102 |
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 |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 56 | 39 | 45 | 28 | 70 | 45 | 17 |
normalized size | 1 | 1. | 2.43 | 1.7 | 1.96 | 1.22 | 3.04 | 1.96 | 0.74 |
time (sec) |
N/A |
0.054 |
0.061 |
0.044 |
0.788 |
0.231 |
2.255 |
0.208 |
4.857 |
|
|
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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 | 38 | 38 | 39 | 29 | 51 | 177 | 0 | 54 | 44 |
normalized size | 1 | 1. | 1.03 | 0.76 | 1.34 | 4.66 | 0. | 1.42 | 1.16 |
time (sec) |
N/A |
0.027 |
0.028 |
0.005 |
0.791 |
0.215 |
0. |
0.21 |
2.024 |
|
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Problem 104 |
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 | 30 | 30 | 30 | 25 | 51 | 53 | 0 | 32 | 44 |
normalized size | 1 | 1. | 1. | 0.83 | 1.7 | 1.77 | 0. | 1.07 | 1.47 |
time (sec) |
N/A |
0.024 |
0.025 |
0.004 |
0.829 |
0.221 |
0. |
0.209 |
1.936 |
|
|
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Problem 105 |
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 | 49 | 49 | 49 | 50 | 70 | 177 | 0 | 55 | 44 |
normalized size | 1 | 1. | 1. | 1.02 | 1.43 | 3.61 | 0. | 1.12 | 0.9 |
time (sec) |
N/A |
0.028 |
0.027 |
0.006 |
0.804 |
0.216 |
0. |
0.209 |
1.983 |
|
|
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Problem 106 |
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 | 45 | 45 | 46 | 35 | 62 | 85 | 0 | 72 | 53 |
normalized size | 1 | 1. | 1.02 | 0.78 | 1.38 | 1.89 | 0. | 1.6 | 1.18 |
time (sec) |
N/A |
0.036 |
0.03 |
0.003 |
0.816 |
0.23 |
0. |
0.212 |
2.054 |
|
|
|
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|
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Problem 107 |
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 | 45 | 45 | 46 | 35 | 62 | 70 | 0 | 49 | 56 |
normalized size | 1 | 1. | 1.02 | 0.78 | 1.38 | 1.56 | 0. | 1.09 | 1.24 |
time (sec) |
N/A |
0.043 |
0.035 |
0.005 |
0.832 |
0.221 |
0. |
0.21 |
2.027 |
|
|
|
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Problem 108 |
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 | 55 | 50 | 78 | 85 | 0 | 73 | 53 |
normalized size | 1 | 1. | 0.89 | 0.81 | 1.26 | 1.37 | 0. | 1.18 | 0.85 |
time (sec) |
N/A |
0.034 |
0.046 |
0.004 |
0.847 |
0.223 |
0. |
0.213 |
2.013 |
|
|
|
|
|
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Problem 109 |
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 | 43 | 43 | 44 | 32 | 55 | 72 | 0 | 42 | 56 |
normalized size | 1 | 1. | 1.02 | 0.74 | 1.28 | 1.67 | 0. | 0.98 | 1.3 |
time (sec) |
N/A |
0.029 |
0.034 |
0.004 |
0.821 |
0.224 |
0. |
0.21 |
2.079 |
|
|
|
|
|
|
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|
Problem 110 |
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 | 59 | 59 | 53 | 50 | 78 | 86 | 0 | 73 | 54 |
normalized size | 1 | 1. | 0.9 | 0.85 | 1.32 | 1.46 | 0. | 1.24 | 0.92 |
time (sec) |
N/A |
0.032 |
0.038 |
0.005 |
0.826 |
0.227 |
0. |
0.212 |
2.004 |
|
|
|
|
|
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|
Problem 111 |
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 | 59 | 59 | 54 | 46 | 62 | 115 | 0 | 51 | 53 |
normalized size | 1 | 1. | 0.92 | 0.78 | 1.05 | 1.95 | 0. | 0.86 | 0.9 |
time (sec) |
N/A |
0.033 |
0.049 |
0.007 |
0.917 |
0.22 |
0. |
0.211 |
2.008 |
|
|
|
|
|
|
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|
Problem 112 |
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 | 55 | 50 | 78 | 88 | 0 | 73 | 54 |
normalized size | 1 | 1. | 0.89 | 0.81 | 1.26 | 1.42 | 0. | 1.18 | 0.87 |
time (sec) |
N/A |
0.033 |
0.047 |
0.005 |
0.833 |
0.224 |
0. |
0.212 |
2.102 |
|
|
|
|
|
|
|
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|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 40 | 32 | 55 | 69 | 0 | 42 | 54 |
normalized size | 1 | 1. | 1.03 | 0.82 | 1.41 | 1.77 | 0. | 1.08 | 1.38 |
time (sec) |
N/A |
0.022 |
0.033 |
0.005 |
0.865 |
0.223 |
0. |
0.21 |
2.061 |
|
|
|
|
|
|
|
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|
|
Problem 114 |
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 | 14 | 14 | 14 | 9 | 11 | 27 | 0 | 27 | 22 |
normalized size | 1 | 1. | 1. | 0.64 | 0.79 | 1.93 | 0. | 1.93 | 1.57 |
time (sec) |
N/A |
0.017 |
0.009 |
0.004 |
0.871 |
0.218 |
0. |
0.212 |
1.508 |
|
|
|
|
|
|
|
|
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|
|
Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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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 | 7 | 11 | 28 | 0 | 8 | 26 |
normalized size | 1 | 1. | 1.4 | 0.7 | 1.1 | 2.8 | 0. | 0.8 | 2.6 |
time (sec) |
N/A |
0.015 |
0.01 |
0.003 |
0.805 |
0.229 |
0. |
0.212 |
1.528 |
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Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 30 | 30 | 27 | 0 | 28 | 22 |
normalized size | 1 | 1. | 0.96 | 1.2 | 1.2 | 1.08 | 0. | 1.12 | 0.88 |
time (sec) |
N/A |
0.016 |
0.01 |
0.005 |
0.872 |
0.233 |
0. |
0.212 |
1.486 |
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Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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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 | 15 | 22 | 55 | 0 | 45 | 32 |
normalized size | 1 | 1. | 1. | 0.83 | 1.22 | 3.06 | 0. | 2.5 | 1.78 |
time (sec) |
N/A |
0.022 |
0.011 |
0.004 |
0.829 |
0.232 |
0. |
0.214 |
1.481 |
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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 |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 15 | 22 | 38 | 0 | 22 | 34 |
normalized size | 1 | 1. | 1. | 0.79 | 1.16 | 2. | 0. | 1.16 | 1.79 |
time (sec) |
N/A |
0.026 |
0.016 |
0.004 |
0.884 |
0.233 |
0. |
0.215 |
1.532 |
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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 |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 28 | 30 | 38 | 54 | 0 | 46 | 32 |
normalized size | 1 | 1. | 0.8 | 0.86 | 1.09 | 1.54 | 0. | 1.31 | 0.91 |
time (sec) |
N/A |
0.02 |
0.017 |
0.004 |
0.848 |
0.231 |
0. |
0.216 |
1.49 |
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Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 12 | 15 | 38 | 0 | 15 | 34 |
normalized size | 1 | 1. | 1. | 0.71 | 0.88 | 2.24 | 0. | 0.88 | 2. |
time (sec) |
N/A |
0.017 |
0.01 |
0.005 |
0.848 |
0.22 |
0. |
0.216 |
1.498 |
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Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 26 | 30 | 38 | 54 | 0 | 46 | 32 |
normalized size | 1 | 1. | 0.81 | 0.94 | 1.19 | 1.69 | 0. | 1.44 | 1. |
time (sec) |
N/A |
0.02 |
0.01 |
0.004 |
0.834 |
0.223 |
0. |
0.214 |
1.481 |
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Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 28 | 26 | 22 | 86 | 0 | 24 | 34 |
normalized size | 1 | 1. | 0.85 | 0.79 | 0.67 | 2.61 | 0. | 0.73 | 1.03 |
time (sec) |
N/A |
0.02 |
0.022 |
0.003 |
0.797 |
0.223 |
0. |
0.215 |
1.486 |
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Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 28 | 30 | 38 | 54 | 0 | 46 | 32 |
normalized size | 1 | 1. | 0.8 | 0.86 | 1.09 | 1.54 | 0. | 1.31 | 0.91 |
time (sec) |
N/A |
0.02 |
0.016 |
0.003 |
0.813 |
0.223 |
0. |
0.216 |
1.495 |
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Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
|
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 | 12 | 15 | 38 | 0 | 15 | 34 |
normalized size | 1 | 1. | 1. | 0.92 | 1.15 | 2.92 | 0. | 1.15 | 2.62 |
time (sec) |
N/A |
0.011 |
0.01 |
0.004 |
0.789 |
0.223 |
0. |
0.215 |
1.525 |
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Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 51 | 0 | 1 | 0 | 66 | 42 |
normalized size | 1 | 1. | 1. | 2.32 | 0. | 0.05 | 0. | 3. | 1.91 |
time (sec) |
N/A |
0.029 |
0.045 |
0.015 |
0. |
0.237 |
0. |
0.233 |
6.632 |
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Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 44 | 0 | 1 | 0 | 72 | 44 |
normalized size | 1 | 1. | 1. | 1.91 | 0. | 0.04 | 0. | 3.13 | 1.91 |
time (sec) |
N/A |
0.028 |
0.045 |
0.018 |
0. |
0.236 |
0. |
0.229 |
6.409 |
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Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 44 | 0 | 1 | 0 | 72 | 44 |
normalized size | 1 | 1. | 1. | 2.2 | 0. | 0.05 | 0. | 3.6 | 2.2 |
time (sec) |
N/A |
0.025 |
0.042 |
0.016 |
0. |
0.247 |
0. |
0.23 |
6.575 |
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Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 24 | 35 | 42 | 0 | 23 | 17 |
normalized size | 1 | 1. | 1. | 1.26 | 1.84 | 2.21 | 0. | 1.21 | 0.89 |
time (sec) |
N/A |
0.011 |
0.012 |
0.005 |
0.746 |
0.221 |
0. |
0.213 |
1.191 |
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Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 28 | 41 | 42 | 0 | 23 | 19 |
normalized size | 1 | 1. | 1. | 1.22 | 1.78 | 1.83 | 0. | 1. | 0.83 |
time (sec) |
N/A |
0.01 |
0.015 |
0.004 |
0.763 |
0.21 |
0. |
0.212 |
1.286 |
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Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 26 | 41 | 39 | 0 | 39 | 17 |
normalized size | 1 | 1. | 1. | 1.13 | 1.78 | 1.7 | 0. | 1.7 | 0.74 |
time (sec) |
N/A |
0.019 |
0.022 |
0.005 |
0.78 |
0.22 |
0. |
0.214 |
3.757 |
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Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 31 | 36 | 80 | 66 | 0 | 49 | 36 |
normalized size | 1 | 1. | 0.72 | 0.84 | 1.86 | 1.53 | 0. | 1.14 | 0.84 |
time (sec) |
N/A |
0.02 |
0.027 |
0.004 |
0.75 |
0.218 |
0. |
0.216 |
1.683 |
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Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 122 | 122 | 126 | 0 | 0 | 0 | 0 | 0 | 105 |
normalized size | 1 | 1. | 1.03 | 0. | 0. | 0. | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.087 |
0.155 |
0.157 |
0. |
0. |
0. |
0. |
4.819 |
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Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 93 | 0 | 0 | 0 | 0 | 0 | 27 |
normalized size | 1 | 1. | 2.51 | 0. | 0. | 0. | 0. | 0. | 0.73 |
time (sec) |
N/A |
0.037 |
0.11 |
0.26 |
0. |
0. |
0. |
0. |
2.114 |
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Problem 134 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 94 | 0 | 0 | 0 | 0 | 0 | 26 |
normalized size | 1 | 1. | 2.94 | 0. | 0. | 0. | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.033 |
0.146 |
0.231 |
0. |
0. |
0. |
0. |
1.917 |
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Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 37 | 37 | 93 | 0 | 0 | 0 | 0 | 0 | 27 |
normalized size | 1 | 1. | 2.51 | 0. | 0. | 0. | 0. | 0. | 0.73 |
time (sec) |
N/A |
0.036 |
0.109 |
0.184 |
0. |
0. |
0. |
0. |
1.984 |
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Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
C |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 92 | 0 | 0 | 0 | 0 | 0 | 17 |
normalized size | 1 | 1. | 4.38 | 0. | 0. | 0. | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.023 |
0.101 |
0.228 |
0. |
0. |
0. |
0. |
1.73 |
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Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 54 | 54 | 48 | 0 | 0 | 0 | 0 | 0 | 44 |
normalized size | 1 | 1. | 0.89 | 0. | 0. | 0. | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.028 |
0.029 |
0.068 |
0. |
0. |
0. |
0. |
1.935 |
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Problem 138 |
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 | 18 | 18 | 17 | 17 | 0 | 26 | 20 | 22 | 12 |
normalized size | 1 | 1. | 0.94 | 0.94 | 0. | 1.44 | 1.11 | 1.22 | 0.67 |
time (sec) |
N/A |
0.008 |
0.008 |
0.003 |
0. |
0.236 |
0.074 |
0.206 |
1.484 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 83 | 0 | 0 | 0 | 0 | 0 | 26 |
normalized size | 1 | 1. | 2.68 | 0. | 0. | 0. | 0. | 0. | 0.84 |
time (sec) |
N/A |
0.028 |
0.08 |
0.151 |
0. |
0. |
0. |
0. |
1.956 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 86 | 0 | 0 | 0 | 0 | 0 | 26 |
normalized size | 1 | 1. | 2.77 | 0. | 0. | 0. | 0. | 0. | 0.84 |
time (sec) |
N/A |
0.026 |
0.173 |
0.154 |
0. |
0. |
0. |
0. |
2.04 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 81 | 0 | 0 | 0 | 0 | 0 | 27 |
normalized size | 1 | 1. | 2.13 | 0. | 0. | 0. | 0. | 0. | 0.71 |
time (sec) |
N/A |
0.032 |
0.112 |
0.157 |
0. |
0. |
0. |
0. |
2.068 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 35 | 35 | 58 | 0 | 0 | 0 | 0 | 0 | 26 |
normalized size | 1 | 1. | 1.66 | 0. | 0. | 0. | 0. | 0. | 0.74 |
time (sec) |
N/A |
0.033 |
0.036 |
0.096 |
0. |
0. |
0. |
0. |
1.955 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 38 | 38 | 81 | 0 | 0 | 0 | 0 | 0 | 27 |
normalized size | 1 | 1. | 2.13 | 0. | 0. | 0. | 0. | 0. | 0.71 |
time (sec) |
N/A |
0.03 |
0.114 |
0.158 |
0. |
0. |
0. |
0. |
2.102 |
|
|
|
|
|
|
|
|
|
|
|
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 [35] had the largest ratio of [ 0.5385
]
|
|
|
|
|
|
|
|
|
| Table 1: Rubi specific breakdown of results for each integral
|
|
|
|
|
|
|
# |
grade |
|
|
normalized | antiderivative |
leaf size |
|
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
6 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
2 |
A |
6 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
3 |
A |
5 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
4 |
A |
4 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
5 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
6 |
A |
6 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
7 |
A |
5 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
8 |
A |
4 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
9 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
10 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
11 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
12 |
A |
4 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
13 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
14 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
15 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
16 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
17 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
18 |
A |
1 |
1 |
1. |
15 |
0.067 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
20 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
|
21 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
22 |
A |
1 |
1 |
1. |
13 |
0.077 |
|
|
|
|
|
|
|
23 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
24 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
25 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
26 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
27 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
28 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
29 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
30 |
A |
6 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
31 |
A |
5 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
32 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
34 |
A |
6 |
5 |
1. |
13 |
0.385 |
|
|
|
|
|
|
|
35 |
A |
8 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
36 |
A |
7 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
37 |
A |
6 |
6 |
1. |
13 |
0.462 |
|
|
|
|
|
|
|
38 |
A |
7 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
39 |
A |
8 |
7 |
1. |
13 |
0.538 |
|
|
|
|
|
|
|
40 |
A |
5 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
|
41 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
42 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
43 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
44 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
45 |
A |
4 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
46 |
A |
5 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
47 |
A |
6 |
4 |
1. |
13 |
0.308 |
|
|
|
|
|
|
|
48 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
49 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
50 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
51 |
A |
2 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
52 |
A |
1 |
0 |
1. |
7 |
0. |
|
|
|
|
|
|
|
53 |
A |
1 |
1 |
1. |
9 |
0.111 |
|
|
|
|
|
|
|
54 |
A |
2 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
55 |
A |
3 |
2 |
1. |
9 |
0.222 |
|
|
|
|
|
|
|
56 |
A |
5 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
57 |
A |
4 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
58 |
A |
3 |
3 |
1. |
11 |
0.273 |
|
|
|
|
|
|
|
59 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
60 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
|
61 |
A |
2 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
62 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
63 |
A |
4 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
64 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
65 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
66 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
67 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
68 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
69 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
70 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
71 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
72 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
73 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
74 |
A |
3 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
75 |
A |
3 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
76 |
A |
3 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
77 |
A |
3 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
78 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
79 |
A |
2 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
80 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
|
81 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
82 |
A |
3 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
83 |
B |
3 |
2 |
2.83 |
10 |
0.2 |
|
|
|
|
|
|
|
84 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
85 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
86 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
87 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
88 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
89 |
A |
2 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
90 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
91 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
92 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
93 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
94 |
A |
4 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
95 |
A |
3 |
3 |
1. |
12 |
0.25 |
|
|
|
|
|
|
|
96 |
A |
3 |
3 |
1. |
13 |
0.231 |
|
|
|
|
|
|
|
97 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
98 |
A |
2 |
2 |
1. |
40 |
0.05 |
|
|
|
|
|
|
|
99 |
A |
3 |
2 |
1.76 |
30 |
0.067 |
|
|
|
|
|
|
|
100 |
A |
3 |
2 |
1.87 |
31 |
0.065 |
|
|
|
|
|
|
|
|
101 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
102 |
A |
2 |
2 |
1. |
16 |
0.125 |
|
|
|
|
|
|
|
103 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
104 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
105 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
106 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
107 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
108 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
109 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
110 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
111 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
112 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
113 |
A |
3 |
3 |
1. |
14 |
0.214 |
|
|
|
|
|
|
|
114 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
115 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
116 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
117 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
118 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
119 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
120 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
|
121 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
122 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
123 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
124 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
125 |
A |
2 |
2 |
1. |
27 |
0.074 |
|
|
|
|
|
|
|
126 |
A |
2 |
2 |
1. |
30 |
0.067 |
|
|
|
|
|
|
|
127 |
A |
2 |
2 |
1. |
28 |
0.071 |
|
|
|
|
|
|
|
128 |
A |
1 |
1 |
1. |
12 |
0.083 |
|
|
|
|
|
|
|
129 |
A |
1 |
1 |
1. |
14 |
0.071 |
|
|
|
|
|
|
|
130 |
A |
1 |
1 |
1. |
16 |
0.062 |
|
|
|
|
|
|
|
131 |
A |
2 |
2 |
1. |
14 |
0.143 |
|
|
|
|
|
|
|
132 |
A |
1 |
1 |
1. |
12 |
0.083 |
|
|
|
|
|
|
|
133 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
134 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
135 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
136 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
137 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
138 |
A |
1 |
1 |
1. |
7 |
0.143 |
|
|
|
|
|
|
|
139 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
140 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
|
141 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
142 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
143 |
A |
2 |
2 |
1. |
12 |
0.167 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|