2 detailed summary tables of results
2.1 Detailed conclusion table per each integral for all CAS systems
Detailed conclusion table per each integral is given by table below. The elapsed time is in
seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as
F(-2) if the failure was due to an exception being raised, which could indicate a bug in the
system. If the failure was due to integral not being evaluated within the time limit, then it is
given just an F.
In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)
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Problem 1 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 14 | 18 | 18 | 12 | 18 | 12 |
normalized size | 1 | 1. | 1. | 0.93 | 1.2 | 1.2 | 0.8 | 1.2 | 0.8 |
time (sec) |
N/A |
0.009 |
0.005 |
0.004 |
1.365 |
0.206 |
0.038 |
0.199 |
0.669 |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
C |
C |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 52 | 37 | 34 | 55 | 1 | 42 | 55 | 42 |
normalized size | 1 | 3.47 | 2.47 | 2.27 | 3.67 | 0.07 | 2.8 | 3.67 | 2.8 |
time (sec) |
N/A |
0.097 |
0.02 |
0.005 |
1.375 |
0.21 |
52.66 |
0.212 |
8.535 |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
F |
A |
F |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 119 | 370 | 0 | 363 | 0 | 239 | 0 |
normalized size | 1 | 1. | 1.45 | 4.51 | 0. | 4.43 | 0. | 2.91 | 0. |
time (sec) |
N/A |
0.144 |
0.159 |
0.062 |
0. |
0.22 |
0. |
0.206 |
0. |
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Problem 4 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 43 | 43 | 43 | 172 | 0 | 201 | 0 | 127 | 34 |
normalized size | 1 | 1. | 1. | 4. | 0. | 4.67 | 0. | 2.95 | 0.79 |
time (sec) |
N/A |
0.038 |
0.042 |
0.069 |
0. |
0.216 |
0. |
0.233 |
4.029 |
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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 |
B |
F |
A |
F |
F(-2) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 65 | 115 | 0 | 274 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.88 | 1.55 | 0. | 3.7 | 0. | 0. | 0. |
time (sec) |
N/A |
0.146 |
0.146 |
0.023 |
0. |
0.225 |
0. |
0. |
0. |
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Problem 6 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
B |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 64 | 64 | 165 | 125 | 72 | 230 | 0 | 0 | 53 |
normalized size | 1 | 1. | 2.58 | 1.95 | 1.12 | 3.59 | 0. | 0. | 0.83 |
time (sec) |
N/A |
0.076 |
0.179 |
0.038 |
1.546 |
0.231 |
0. |
0. |
5.039 |
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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 |
F |
A |
F(-2) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 90 | 45 | 0 | 216 | 0 | 136 | 41 |
normalized size | 1 | 1. | 1.88 | 0.94 | 0. | 4.5 | 0. | 2.83 | 0.85 |
time (sec) |
N/A |
0.039 |
0.071 |
0.026 |
0. |
0.222 |
0. |
0.203 |
3.715 |
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Problem 8 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 30 | 30 | 29 | 21 | 0 | 24 | 53 | 27 | 26 |
normalized size | 1 | 1. | 0.97 | 0.7 | 0. | 0.8 | 1.77 | 0.9 | 0.87 |
time (sec) |
N/A |
0.128 |
0.023 |
0.004 |
0. |
0.208 |
1.502 |
0.206 |
4.971 |
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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 |
B |
F |
A |
F |
F |
F |
verified |
N/A |
NO |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 365 | 0 | 902 | 0 | 1185 | 0 | 0 | 0 |
normalized size | 1 | 1.66 | 0. | 4.1 | 0. | 5.39 | 0. | 0. | 0. |
time (sec) |
N/A |
0.997 |
4.931 |
0.177 |
0. |
0.253 |
0. |
0. |
0. |
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Problem 10 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
B |
A |
B |
F |
A |
F(-1) |
F |
F(-1) |
verified |
N/A |
NO |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 541 | 0 | 1542 | 0 | 1185 | 0 | 0 | 0 |
normalized size | 1 | 2.46 | 0. | 7.01 | 0. | 5.39 | 0. | 0. | 0. |
time (sec) |
N/A |
1.561 |
1.66 |
0.033 |
0. |
0.255 |
0. |
0. |
0. |
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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 |
B |
F(-2) |
A |
F(-2) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 138 | 138 | 403 | 278 | 0 | 680 | 0 | 0 | 184 |
normalized size | 1 | 1. | 2.92 | 2.01 | 0. | 4.93 | 0. | 0. | 1.33 |
time (sec) |
N/A |
0.162 |
0.413 |
0.032 |
0. |
0.287 |
0. |
0. |
18.456 |
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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 |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 125 | 125 | 0 | 0 | 0 | 0 | 0 | 0 | 202 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 1.62 |
time (sec) |
N/A |
0.328 |
0.154 |
0.036 |
0. |
0. |
0. |
0. |
21.574 |
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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 |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 0 | 0 | 0 | 0 | 0 | 0 | 155 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 1.91 |
time (sec) |
N/A |
0.278 |
0.119 |
0.037 |
0. |
0. |
0. |
0. |
17.113 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
F |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 145 | 0 | 0 | 81 | 15 | 0 | 29 |
normalized size | 1 | 1. | 4.68 | 0. | 0. | 2.61 | 0.48 | 0. | 0.94 |
time (sec) |
N/A |
0.089 |
2.357 |
0.024 |
0. |
0.39 |
2.212 |
0. |
3.712 |
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Problem 15 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
C |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 33 | 33 | 162 | 22 | 0 | 39 | 15 | 0 | 29 |
normalized size | 1 | 1. | 4.91 | 0.67 | 0. | 1.18 | 0.45 | 0. | 0.88 |
time (sec) |
N/A |
0.091 |
1.435 |
0.055 |
0. |
0.4 |
1.164 |
0. |
3.951 |
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Problem 16 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 16 | 20 | 31 | 56 | 20 | 17 |
normalized size | 1 | 1. | 1. | 0.84 | 1.05 | 1.63 | 2.95 | 1.05 | 0.89 |
time (sec) |
N/A |
0.434 |
0.025 |
0.004 |
1.341 |
0.203 |
12.491 |
0.214 |
11.273 |
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Problem 17 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
F |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 36 | 120 | 0 | 43 | 2147 | 0 | 0 |
normalized size | 1 | 1. | 0.69 | 2.31 | 0. | 0.83 | 41.29 | 0. | 0. |
time (sec) |
N/A |
0.047 |
0.04 |
0.045 |
0. |
0.229 |
4.98 |
0. |
0. |
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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 |
F |
F |
A |
F |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 39 | 0 | 0 | 45 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 0. | 0. | 0.8 | 0. | 0. | 0. |
time (sec) |
N/A |
0.046 |
0.04 |
0.045 |
0. |
0.23 |
0. |
0. |
0. |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
F |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 0 | 20 | 20 | 311 | 0 | 12 |
normalized size | 1 | 1. | 1. | 0. | 1.18 | 1.18 | 18.29 | 0. | 0.71 |
time (sec) |
N/A |
0.087 |
0.027 |
0.029 |
1.396 |
0.23 |
5.359 |
0. |
4.054 |
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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 |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 0 | 24 | 24 | 36 | 0 | 14 |
normalized size | 1 | 1. | 1. | 0. | 1.2 | 1.2 | 1.8 | 0. | 0.7 |
time (sec) |
N/A |
0.092 |
0.028 |
0.045 |
1.397 |
0.232 |
3.559 |
0. |
4.364 |
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Problem 21 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 37 | 48 | 54 | 70 | 36 | 55 | 39 |
normalized size | 1 | 1. | 0.88 | 1.14 | 1.29 | 1.67 | 0.86 | 1.31 | 0.93 |
time (sec) |
N/A |
0.063 |
0.063 |
0.017 |
1.352 |
0.224 |
0.176 |
0.198 |
5.391 |
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Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 22 | 21 | 27 | 26 | 22 | 26 | 15 |
normalized size | 1 | 1. | 1. | 0.95 | 1.23 | 1.18 | 1. | 1.18 | 0.68 |
time (sec) |
N/A |
0.041 |
0.021 |
0.004 |
1.342 |
0.216 |
0.116 |
0.201 |
4.678 |
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Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 62 | 62 | 49 | 51 | 69 | 78 | 49 | 100 | 54 |
normalized size | 1 | 1. | 0.79 | 0.82 | 1.11 | 1.26 | 0.79 | 1.61 | 0.87 |
time (sec) |
N/A |
0.154 |
0.052 |
0.019 |
1.368 |
0.231 |
0.216 |
0.199 |
10.102 |
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Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 961 | 455 | 0 | 720 | 0 | 0 | 87 |
normalized size | 1 | 1. | 11.17 | 5.29 | 0. | 8.37 | 0. | 0. | 1.01 |
time (sec) |
N/A |
0.226 |
5.47 |
0.057 |
0. |
0.252 |
0. |
0. |
18.81 |
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Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
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|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 0 | 0 | 20 | 15 | 0 | 15 |
normalized size | 1 | 1. | 1. | 0. | 0. | 1.05 | 0.79 | 0. | 0.79 |
time (sec) |
N/A |
0.106 |
0.026 |
0.039 |
0. |
0.218 |
0.282 |
0. |
3.644 |
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Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
|
|
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|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 26 | 0 | 0 | 30 | 27 | 0 | 20 |
normalized size | 1 | 1. | 1. | 0. | 0. | 1.15 | 1.04 | 0. | 0.77 |
time (sec) |
N/A |
0.161 |
0.041 |
0.05 |
0. |
0.223 |
1.344 |
0. |
4.681 |
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Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 85 | 0 | 0 | 1 | 46 | 0 | 58 |
normalized size | 1 | 1. | 1.35 | 0. | 0. | 0.02 | 0.73 | 0. | 0.92 |
time (sec) |
N/A |
0.365 |
0.251 |
0.028 |
0. |
0.243 |
2.87 |
0. |
9.559 |
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Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 82 | 82 | 161 | 25 | 0 | 1 | 51 | 0 | 73 |
normalized size | 1 | 1. | 1.96 | 0.3 | 0. | 0.01 | 0.62 | 0. | 0.89 |
time (sec) |
N/A |
0.14 |
0.081 |
0.008 |
0. |
0.241 |
2.482 |
0. |
8.607 |
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Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
F |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 679 | 679 | 412 | 0 | 699 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.61 | 0. | 1.03 | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
7.496 |
0.267 |
0.063 |
1.399 |
0. |
0. |
0. |
0. |
|
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Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 0 | 20 | 20 | 311 | 0 | 12 |
normalized size | 1 | 1. | 1. | 0. | 1.18 | 1.18 | 18.29 | 0. | 0.71 |
time (sec) |
N/A |
0.088 |
0.04 |
0.037 |
1.402 |
0.241 |
7.301 |
0. |
3.919 |
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Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
A |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 52 | 52 | 36 | 120 | 0 | 43 | 2147 | 0 | 0 |
normalized size | 1 | 1. | 0.69 | 2.31 | 0. | 0.83 | 41.29 | 0. | 0. |
time (sec) |
N/A |
0.046 |
0.023 |
0.033 |
0. |
0.244 |
6.697 |
0. |
0. |
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Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 34 | 33 | 44 | 65 | 65 | 0 | 0 | 27 |
normalized size | 1 | 1. | 0.97 | 1.29 | 1.91 | 1.91 | 0. | 0. | 0.79 |
time (sec) |
N/A |
0.06 |
0.056 |
0.066 |
1.766 |
0.224 |
0. |
0. |
9.298 |
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Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 41 | 65 | 84 | 84 | 36 | 86 | 49 |
normalized size | 1 | 1. | 0.71 | 1.12 | 1.45 | 1.45 | 0.62 | 1.48 | 0.84 |
time (sec) |
N/A |
0.078 |
0.021 |
0.056 |
1.497 |
0.214 |
1.607 |
0.207 |
2.456 |
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Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 58 | 58 | 41 | 48 | 84 | 84 | 37 | 86 | 49 |
normalized size | 1 | 1. | 0.71 | 0.83 | 1.45 | 1.45 | 0.64 | 1.48 | 0.84 |
time (sec) |
N/A |
0.069 |
0.02 |
0.063 |
1.5 |
0.216 |
1.72 |
0.204 |
2.453 |
|
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Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 86 | 12 | 105 | 122 | 29 | 0 | 71 |
normalized size | 1 | 1. | 1.76 | 0.24 | 2.14 | 2.49 | 0.59 | 0. | 1.45 |
time (sec) |
N/A |
0.016 |
0.071 |
0.034 |
1.502 |
0.216 |
1.61 |
0. |
3.587 |
|
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Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 55 | 55 | 39 | 65 | 84 | 96 | 32 | 85 | 48 |
normalized size | 1 | 1. | 0.71 | 1.18 | 1.53 | 1.75 | 0.58 | 1.55 | 0.87 |
time (sec) |
N/A |
0.07 |
0.019 |
0.057 |
1.474 |
0.215 |
1.605 |
0.209 |
2.299 |
|
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Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 121 | 97 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0.8 | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.083 |
0.073 |
0.049 |
0. |
0. |
0. |
0. |
0. |
|
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Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 145 | 145 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.194 |
0.089 |
0.059 |
0. |
0. |
0. |
0. |
0. |
|
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Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 110 | 176 | 109 | 0 | 0 | 0 | 0 | 0 | 155 |
normalized size | 1 | 1.6 | 0.99 | 0. | 0. | 0. | 0. | 0. | 1.41 |
time (sec) |
N/A |
0.099 |
0.19 |
0.098 |
0. |
0. |
0. |
0. |
4.678 |
|
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Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 131 | 85 | 0 | 0 | 0 | 0 | 0 | 204 |
normalized size | 1 | 1.62 | 1.05 | 0. | 0. | 0. | 0. | 0. | 2.52 |
time (sec) |
N/A |
0.139 |
0.022 |
0.019 |
0. |
0. |
0. |
0. |
7.393 |
|
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Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
A |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 117 | 49 | 0 | 104 | 0 | 0 | 0 | 155 |
normalized size | 1 | 1.77 | 0.74 | 0. | 1.58 | 0. | 0. | 0. | 2.35 |
time (sec) |
N/A |
0.113 |
0.035 |
0.064 |
1.524 |
0. |
0. |
0. |
5.457 |
|
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Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 79 | 145 | 61 | 0 | 0 | 0 | 0 | 0 | 216 |
normalized size | 1 | 1.84 | 0.77 | 0. | 0. | 0. | 0. | 0. | 2.73 |
time (sec) |
N/A |
0.188 |
0.058 |
0.02 |
0. |
0. |
0. |
0. |
9.593 |
|
|
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|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
C |
F |
F |
F(-1) |
F(-1) |
F |
F |
verified |
N/A |
N/A |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 118 | 0 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0.61 | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
27.68 |
0.228 |
0.028 |
0. |
0. |
0. |
0. |
0. |
|
|
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|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.338 |
1.235 |
0.062 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
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Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.82 |
0.415 |
0.073 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
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Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
A |
F |
F |
F(-2) |
F |
F |
F(-1) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 326 | 576 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1.77 | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.525 |
0.165 |
0.183 |
0. |
0. |
0. |
0. |
0. |
|
|
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 407 | 407 | 206 | 584 | 0 | 1827 | 0 | 0 | 478 |
normalized size | 1 | 1. | 0.51 | 1.43 | 0. | 4.49 | 0. | 0. | 1.17 |
time (sec) |
N/A |
1.477 |
2.259 |
0.132 |
0. |
0.281 |
0. |
0. |
48.171 |
|
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F(-1) |
F |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 648 | 648 | 662 | 719 | 0 | 2839 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.02 | 1.11 | 0. | 4.38 | 0. | 0. | 0. |
time (sec) |
N/A |
2.686 |
6.077 |
0.072 |
0. |
0.34 |
0. |
0. |
0. |
|
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
F(-1) |
F(-1) |
A |
F |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1058 | 1058 | 1242 | 989 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.17 | 0.93 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
5.375 |
6.165 |
0.138 |
0. |
0. |
0. |
0.227 |
0. |
|
|
|
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Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 378 | 378 | 1236 | 21028 | 0 | 6251 | 0 | 0 | 379 |
normalized size | 1 | 1. | 3.27 | 55.63 | 0. | 16.54 | 0. | 0. | 1. |
time (sec) |
N/A |
1.586 |
6.467 |
0.765 |
0. |
0.363 |
0. |
0. |
79.056 |
|
|
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Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 638 | 638 | 1431 | 86793 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 2.24 | 136.04 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.835 |
6.717 |
4.895 |
0. |
0. |
0. |
0.351 |
0. |
|
|
|
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Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 66 | 204 | 213 | 1275 | 0 | 1 | 0 | 0 | 0 |
normalized size | 1 | 3.09 | 3.23 | 19.32 | 0. | 0.02 | 0. | 0. | 0. |
time (sec) |
N/A |
2.372 |
0.563 |
0.168 |
0. |
0.617 |
0. |
0. |
0. |
|
|
|
|
|
|
|
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|
Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-2) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 205 | 0 | 0 | 0 | 0 | 0 | 231 |
normalized size | 1 | 1. | 1.04 | 0. | 0. | 0. | 0. | 0. | 1.17 |
time (sec) |
N/A |
0.241 |
0.468 |
0.052 |
0. |
0. |
0. |
0. |
13.653 |
|
|
|
|
|
|
|
|
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|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-2) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 220 | 0 | 0 | 0 | 0 | 0 | 282 |
normalized size | 1 | 1. | 1.11 | 0. | 0. | 0. | 0. | 0. | 1.42 |
time (sec) |
N/A |
0.212 |
0.442 |
0.073 |
0. |
0. |
0. |
0. |
13.12 |
|
|
|
|
|
|
|
|
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|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 97 | 273 | 0 | 0 | 0 | 0 | 0 | 94 |
normalized size | 1 | 1.1 | 3.1 | 0. | 0. | 0. | 0. | 0. | 1.07 |
time (sec) |
N/A |
0.047 |
0.81 |
0.199 |
0. |
0. |
0. |
0. |
2.42 |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
A |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 107 | 107 | 34 | 69 | 142 | 143 | 32 | 0 | 85 |
normalized size | 1 | 1. | 0.32 | 0.64 | 1.33 | 1.34 | 0.3 | 0. | 0.79 |
time (sec) |
N/A |
0.102 |
0.018 |
0.069 |
1.666 |
0.21 |
1.783 |
0. |
4.775 |
|
|
|
|
|
|
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|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 67 | 67 | 48 | 49 | 96 | 115 | 37 | 97 | 56 |
normalized size | 1 | 1. | 0.72 | 0.73 | 1.43 | 1.72 | 0.55 | 1.45 | 0.84 |
time (sec) |
N/A |
0.084 |
0.025 |
0.073 |
1.534 |
0.208 |
1.678 |
0.24 |
2.768 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.099 |
0.372 |
0.072 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
F |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 280 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.385 |
0.042 |
0.112 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 24 | 31 | 31 | 22 | 31 | 22 |
normalized size | 1 | 1. | 1. | 0.96 | 1.24 | 1.24 | 0.88 | 1.24 | 0.88 |
time (sec) |
N/A |
0.012 |
0.012 |
0.001 |
1.39 |
0.194 |
0.107 |
0.245 |
3.601 |
|
|
|
|
|
|
|
|
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|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 59 | 59 | 86 | 52 | 0 | 51 | 73 | 0 | 56 |
normalized size | 1 | 1. | 1.46 | 0.88 | 0. | 0.86 | 1.24 | 0. | 0.95 |
time (sec) |
N/A |
0.06 |
0.027 |
0.043 |
0. |
0.195 |
0.213 |
0. |
7.633 |
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 99 | 75 | 0 | 89 | 100 | 0 | 80 |
normalized size | 1 | 1. | 1.27 | 0.96 | 0. | 1.14 | 1.28 | 0. | 1.03 |
time (sec) |
N/A |
0.124 |
0.029 |
0.033 |
0. |
0.198 |
0.218 |
0. |
14.771 |
|
|
|
|
|
|
|
|
|
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|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 49 | 49 | 110 | 100 | 0 | 105 | 0 | 0 | 36 |
normalized size | 1 | 1. | 2.24 | 2.04 | 0. | 2.14 | 0. | 0. | 0.73 |
time (sec) |
N/A |
0.026 |
0.144 |
0.022 |
0. |
0.257 |
0. |
0. |
2.408 |
|
|
|
|
|
|
|
|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 108 | 365 | 0 | 81 | 0 | 0 | 46 |
normalized size | 1 | 1. | 2.04 | 6.89 | 0. | 1.53 | 0. | 0. | 0.87 |
time (sec) |
N/A |
0.037 |
0.134 |
0.04 |
0. |
0.254 |
0. |
0. |
2.585 |
|
|
|
|
|
|
|
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|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 75 | 75 | 0 | 1421 | 0 | 1 | 0 | 0 | 63 |
normalized size | 1 | 1. | 0. | 18.95 | 0. | 0.01 | 0. | 0. | 0.84 |
time (sec) |
N/A |
0.161 |
0.329 |
0.098 |
0. |
0.27 |
0. |
0. |
9.109 |
|
|
|
|
|
|
|
|
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|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 171 | 171 | 322 | 456 | 0 | 2419 | 0 | 0 | 144 |
normalized size | 1 | 1. | 1.88 | 2.67 | 0. | 14.15 | 0. | 0. | 0.84 |
time (sec) |
N/A |
0.142 |
0.427 |
0.101 |
0. |
0.339 |
0. |
0. |
6.94 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 80 | 80 | 203 | 0 | 0 | 0 | 0 | 0 | 178 |
normalized size | 1 | 1. | 2.54 | 0. | 0. | 0. | 0. | 0. | 2.22 |
time (sec) |
N/A |
0.118 |
0.56 |
0.088 |
0. |
0. |
0. |
0. |
28.634 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 88 | 88 | 221 | 0 | 0 | 0 | 0 | 0 | 199 |
normalized size | 1 | 1. | 2.51 | 0. | 0. | 0. | 0. | 0. | 2.26 |
time (sec) |
N/A |
0.131 |
0.555 |
0.043 |
0. |
0. |
0. |
0. |
29.508 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 69 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 205 | 0 | 0 | 0 | 0 | 0 | 170 |
normalized size | 1 | 1. | 1.38 | 0. | 0. | 0. | 0. | 0. | 1.14 |
time (sec) |
N/A |
0.136 |
0.446 |
0.07 |
0. |
0. |
0. |
0. |
39.319 |
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Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 219 | 0 | 0 | 0 | 0 | 0 | 173 |
normalized size | 1 | 1. | 1.62 | 0. | 0. | 0. | 0. | 0. | 1.28 |
time (sec) |
N/A |
0.109 |
0.425 |
0.045 |
0. |
0. |
0. |
0. |
36.093 |
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 127 | 127 | 120 | 164 | 0 | 1451 | 0 | 0 | 155 |
normalized size | 1 | 1. | 0.94 | 1.29 | 0. | 11.43 | 0. | 0. | 1.22 |
time (sec) |
N/A |
0.068 |
0.161 |
0.289 |
0. |
0.358 |
0. |
0. |
3.059 |
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Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 157 | 157 | 135 | 240 | 0 | 2641 | 0 | 0 | 223 |
normalized size | 1 | 1. | 0.86 | 1.53 | 0. | 16.82 | 0. | 0. | 1.42 |
time (sec) |
N/A |
0.101 |
0.249 |
0.153 |
0. |
0.461 |
0. |
0. |
4.538 |
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Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 74 | 74 | 118 | 286 | 0 | 950 | 0 | 0 | 37 |
normalized size | 1 | 1. | 1.59 | 3.86 | 0. | 12.84 | 0. | 0. | 0.5 |
time (sec) |
N/A |
0.288 |
0.191 |
0.169 |
0. |
0.342 |
0. |
0. |
4.325 |
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Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 139 | 383 | 0 | 914 | 0 | 0 | 22 |
normalized size | 1 | 1. | 1.35 | 3.72 | 0. | 8.87 | 0. | 0. | 0.21 |
time (sec) |
N/A |
0.545 |
0.181 |
0.197 |
0. |
0.328 |
0. |
0. |
3.314 |
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Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 126 | 0 | 0 | 0 | 0 | 0 | 17 |
normalized size | 1 | 1. | 1.56 | 0. | 0. | 0. | 0. | 0. | 0.21 |
time (sec) |
N/A |
0.04 |
0.152 |
0.07 |
0. |
0. |
0. |
0. |
2.603 |
|
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Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 81 | 81 | 126 | 0 | 0 | 0 | 0 | 0 | 20 |
normalized size | 1 | 1. | 1.56 | 0. | 0. | 0. | 0. | 0. | 0.25 |
time (sec) |
N/A |
0.037 |
0.14 |
0.04 |
0. |
0. |
0. |
0. |
3.072 |
|
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Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 113 | 113 | 118 | 0 | 0 | 0 | 0 | 0 | 144 |
normalized size | 1 | 1. | 1.04 | 0. | 0. | 0. | 0. | 0. | 1.27 |
time (sec) |
N/A |
0.046 |
0.131 |
0.05 |
0. |
0. |
0. |
0. |
5.869 |
|
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Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
F |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 109 | 109 | 124 | 0 | 0 | 0 | 0 | 0 | 192 |
normalized size | 1 | 1. | 1.14 | 0. | 0. | 0. | 0. | 0. | 1.76 |
time (sec) |
N/A |
0.044 |
0.102 |
0.056 |
0. |
0. |
0. |
0. |
5.238 |
|
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Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 87 | 87 | 159 | 206 | 0 | 72 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.83 | 2.37 | 0. | 0.83 | 0. | 0. | 0. |
time (sec) |
N/A |
1.479 |
0.553 |
0.053 |
0. |
0.266 |
0. |
0. |
0. |
|
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Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F |
F |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1 | 579 | 100 | 317 | 0 | 95 | 0 | 0 | 0 |
normalized size | 1 | 579. | 100. | 317. | 0. | 95. | 0. | 0. | 0. |
time (sec) |
N/A |
3.072 |
0.464 |
0.063 |
0. |
0.264 |
0. |
0. |
0. |
|
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Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
C |
C |
C |
F |
A |
F(-2) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 180 | 133 | 536 | 0 | 85 | 0 | 0 | 0 |
normalized size | 1 | 3.91 | 2.89 | 11.65 | 0. | 1.85 | 0. | 0. | 0. |
time (sec) |
N/A |
2.933 |
0.59 |
0.079 |
0. |
0.259 |
0. |
0. |
0. |
|
|
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Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-2) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 32 | 32 | 323 | 258 | 0 | 0 | 0 | 0 | 469 |
normalized size | 1 | 1. | 10.09 | 8.06 | 0. | 0. | 0. | 0. | 14.66 |
time (sec) |
N/A |
0.145 |
0.516 |
0.093 |
0. |
0. |
0. |
0. |
63.878 |
|
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Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 262 | 240 | 0 | 59 | 0 | 0 | 371 |
normalized size | 1 | 1. | 11.39 | 10.43 | 0. | 2.57 | 0. | 0. | 16.13 |
time (sec) |
N/A |
0.091 |
0.283 |
0.031 |
0. |
0.258 |
0. |
0. |
41.593 |
|
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Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 218 | 218 | 206 | 353 | 0 | 0 | 0 | 0 | 34 |
normalized size | 1 | 1. | 0.94 | 1.62 | 0. | 0. | 0. | 0. | 0.16 |
time (sec) |
N/A |
0.116 |
0.43 |
0.283 |
0. |
0. |
0. |
0. |
3.449 |
|
|
|
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|
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Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 210 | 210 | 207 | 350 | 0 | 0 | 0 | 0 | 34 |
normalized size | 1 | 1. | 0.99 | 1.67 | 0. | 0. | 0. | 0. | 0.16 |
time (sec) |
N/A |
0.105 |
0.656 |
0.266 |
0. |
0. |
0. |
0. |
7.693 |
|
|
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Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 222 | 222 | 196 | 349 | 0 | 0 | 0 | 0 | 53 |
normalized size | 1 | 1. | 0.88 | 1.57 | 0. | 0. | 0. | 0. | 0.24 |
time (sec) |
N/A |
0.1 |
0.623 |
0.257 |
0. |
0. |
0. |
0. |
11.817 |
|
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Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 214 | 214 | 198 | 350 | 0 | 0 | 0 | 0 | 51 |
normalized size | 1 | 1. | 0.93 | 1.64 | 0. | 0. | 0. | 0. | 0.24 |
time (sec) |
N/A |
0.096 |
0.539 |
0.256 |
0. |
0. |
0. |
0. |
6.47 |
|
|
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Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
F |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 65 | 65 | 685 | 327 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 10.54 | 5.03 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.211 |
4.031 |
0.24 |
0. |
0. |
0. |
0. |
0. |
|
|
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|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F |
F |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 63 | 63 | 1137 | 311 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 18.05 | 4.94 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.213 |
10.714 |
0.235 |
0. |
0. |
0. |
0. |
0. |
|
|
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Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-2) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.096 |
0.144 |
0.045 |
0. |
0. |
0. |
0. |
0. |
|
|
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Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F |
F |
F |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 108 | 108 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.16 |
0.047 |
0.039 |
0. |
0. |
0. |
0. |
0. |
|
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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 [29] had the largest ratio of [ 2.143
]
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| Table 1: Rubi specific breakdown of results for each integral
|
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|
# |
grade |
|
|
normalized | antiderivative |
leaf size |
|
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
A |
1 |
1 |
1. |
10 |
0.1 |
|
|
|
|
|
|
|
2 |
C |
5 |
2 |
3.47 |
37 |
0.054 |
|
|
|
|
|
|
|
3 |
A |
9 |
6 |
1. |
15 |
0.4 |
|
|
|
|
|
|
|
4 |
A |
3 |
3 |
1. |
19 |
0.158 |
|
|
|
|
|
|
|
5 |
A |
8 |
7 |
1. |
17 |
0.412 |
|
|
|
|
|
|
|
6 |
A |
6 |
6 |
1. |
17 |
0.353 |
|
|
|
|
|
|
|
7 |
A |
3 |
3 |
1. |
17 |
0.176 |
|
|
|
|
|
|
|
8 |
A |
4 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
9 |
A |
18 |
12 |
1.66 |
27 |
0.444 |
|
|
|
|
|
|
|
10 |
B |
25 |
13 |
2.46 |
39 |
0.333 |
|
|
|
|
|
|
|
11 |
A |
7 |
3 |
1. |
45 |
0.067 |
|
|
|
|
|
|
|
12 |
A |
7 |
4 |
1. |
32 |
0.125 |
|
|
|
|
|
|
|
13 |
A |
5 |
3 |
1. |
32 |
0.094 |
|
|
|
|
|
|
|
14 |
A |
2 |
2 |
1. |
27 |
0.074 |
|
|
|
|
|
|
|
15 |
A |
2 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
16 |
A |
2 |
1 |
1. |
30 |
0.033 |
|
|
|
|
|
|
|
17 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
18 |
A |
3 |
2 |
1. |
15 |
0.133 |
|
|
|
|
|
|
|
19 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
20 |
A |
2 |
2 |
1. |
25 |
0.08 |
|
|
|
|
|
|
|
|
21 |
A |
3 |
2 |
1. |
11 |
0.182 |
|
|
|
|
|
|
|
22 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
23 |
A |
6 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
24 |
A |
6 |
5 |
1. |
31 |
0.161 |
|
|
|
|
|
|
|
25 |
A |
2 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
26 |
A |
2 |
2 |
1. |
35 |
0.057 |
|
|
|
|
|
|
|
27 |
A |
5 |
5 |
1. |
32 |
0.156 |
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|
|
|
|
|
|
28 |
A |
6 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
29 |
A |
359 |
30 |
1. |
14 |
2.143 |
|
|
|
|
|
|
|
30 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
31 |
A |
3 |
2 |
1. |
13 |
0.154 |
|
|
|
|
|
|
|
32 |
A |
2 |
2 |
1. |
33 |
0.061 |
|
|
|
|
|
|
|
33 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1. |
15 |
0.333 |
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|
|
|
|
|
|
35 |
A |
1 |
1 |
1. |
11 |
0.091 |
|
|
|
|
|
|
|
36 |
A |
5 |
5 |
1. |
15 |
0.333 |
|
|
|
|
|
|
|
37 |
A |
1 |
1 |
0.8 |
17 |
0.059 |
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|
|
|
|
|
|
38 |
A |
3 |
3 |
1. |
18 |
0.167 |
|
|
|
|
|
|
|
39 |
A |
2 |
2 |
1.6 |
16 |
0.125 |
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|
|
|
|
|
|
40 |
A |
5 |
5 |
1.62 |
17 |
0.294 |
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|
|
|
|
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|
|
41 |
A |
5 |
5 |
1.77 |
13 |
0.385 |
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|
|
|
|
|
|
42 |
A |
5 |
5 |
1.84 |
16 |
0.312 |
|
|
|
|
|
|
|
43 |
F |
0 |
0 |
N/A |
0 |
N/A |
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|
|
|
|
|
|
44 |
F |
0 |
0 |
N/A |
0 |
N/A |
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|
|
|
|
|
|
45 |
F |
0 |
0 |
N/A |
0 |
N/A |
|
|
|
|
|
|
|
46 |
C |
7 |
3 |
1.77 |
32 |
0.094 |
|
|
|
|
|
|
|
47 |
A |
19 |
9 |
1. |
20 |
0.45 |
|
|
|
|
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|
|
48 |
A |
29 |
9 |
1. |
20 |
0.45 |
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|
|
|
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|
|
49 |
A |
49 |
9 |
1. |
20 |
0.45 |
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|
|
|
|
|
|
50 |
A |
14 |
6 |
1. |
23 |
0.261 |
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|
|
|
|
|
|
51 |
A |
24 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
52 |
C |
9 |
8 |
3.09 |
48 |
0.167 |
|
|
|
|
|
|
|
53 |
A |
7 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
54 |
A |
7 |
7 |
1. |
24 |
0.292 |
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|
|
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|
|
55 |
A |
1 |
1 |
1.1 |
18 |
0.056 |
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|
|
|
|
|
|
56 |
A |
8 |
8 |
1. |
13 |
0.615 |
|
|
|
|
|
|
|
57 |
A |
6 |
6 |
1. |
15 |
0.4 |
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|
|
|
|
|
|
58 |
F |
0 |
0 |
N/A |
0 |
N/A |
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|
|
|
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|
|
59 |
F |
0 |
0 |
N/A |
0 |
N/A |
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|
|
|
|
|
|
60 |
A |
1 |
1 |
1. |
38 |
0.026 |
|
|
|
|
|
|
|
|
61 |
A |
1 |
1 |
1. |
33 |
0.03 |
|
|
|
|
|
|
|
62 |
A |
2 |
2 |
1. |
39 |
0.051 |
|
|
|
|
|
|
|
63 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
64 |
A |
4 |
4 |
1. |
19 |
0.21 |
|
|
|
|
|
|
|
65 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
66 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
67 |
A |
7 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
68 |
A |
7 |
7 |
1. |
24 |
0.292 |
|
|
|
|
|
|
|
69 |
A |
3 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
70 |
A |
3 |
3 |
1. |
22 |
0.136 |
|
|
|
|
|
|
|
71 |
A |
1 |
1 |
1. |
22 |
0.045 |
|
|
|
|
|
|
|
72 |
A |
1 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
73 |
A |
8 |
8 |
1. |
18 |
0.444 |
|
|
|
|
|
|
|
74 |
A |
8 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
75 |
A |
1 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
76 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
77 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
78 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
79 |
A |
4 |
4 |
1. |
34 |
0.118 |
|
|
|
|
|
|
|
80 |
C |
5 |
5 |
579. |
40 |
0.125 |
|
|
|
|
|
|
|
|
81 |
C |
7 |
7 |
3.91 |
51 |
0.137 |
|
|
|
|
|
|
|
82 |
A |
2 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
83 |
A |
2 |
2 |
1. |
18 |
0.111 |
|
|
|
|
|
|
|
84 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
85 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
86 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
87 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
88 |
A |
2 |
2 |
1. |
40 |
0.05 |
|
|
|
|
|
|
|
89 |
A |
2 |
2 |
1. |
40 |
0.05 |
|
|
|
|
|
|
|
90 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
91 |
A |
3 |
3 |
1. |
15 |
0.2 |
|
|
|
|
|
|
|
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|
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