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 |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 94 | 94 | 86 | 133 | 0 | 1 | 332 | 117 | 0 |
normalized size | 1 | 1. | 0.91 | 1.41 | 0. | 0.01 | 3.53 | 1.24 | 0. |
time (sec) |
N/A |
0.233 |
0.143 |
0.01 |
0. |
0.271 |
3.848 |
0.264 |
0. |
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Problem 2 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 228 | 228 | 204 | 373 | 0 | 1 | 928 | 355 | 0 |
normalized size | 1 | 1. | 0.89 | 1.64 | 0. | 0. | 4.07 | 1.56 | 0. |
time (sec) |
N/A |
0.739 |
0.536 |
0.009 |
0. |
0.278 |
12.608 |
0.265 |
0. |
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Problem 3 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 441 | 441 | 422 | 822 | 0 | 1 | 1940 | 841 | 0 |
normalized size | 1 | 1. | 0.96 | 1.86 | 0. | 0. | 4.4 | 1.91 | 0. |
time (sec) |
N/A |
1.581 |
1.816 |
0.012 |
0. |
0.282 |
30.066 |
0.267 |
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(-2) |
F(-1) |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 274 | 274 | 212 | 745 | 0 | 0 | 0 | 359 | 0 |
normalized size | 1 | 1. | 0.77 | 2.72 | 0. | 0. | 0. | 1.31 | 0. |
time (sec) |
N/A |
0.651 |
0.765 |
0.012 |
0. |
0. |
0. |
0.267 |
0. |
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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(-2) |
F(-1) |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 596 | 596 | 523 | 10537 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 0.88 | 17.68 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.941 |
4.053 |
0.04 |
0. |
0. |
0. |
0.272 |
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 |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 331 | 331 | 450 | 3358 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.36 | 10.15 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.322 |
3. |
0.075 |
0. |
0. |
0. |
0. |
0. |
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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 |
B |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 370 | 714 | 0 | 8253 | 0 | 0 | 238 |
normalized size | 1 | 1. | 1.49 | 2.87 | 0. | 33.14 | 0. | 0. | 0.96 |
time (sec) |
N/A |
0.492 |
2.255 |
0.029 |
0. |
53.151 |
0. |
0. |
64.376 |
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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 |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 381 | 380 | 517 | 2758 | 0 | 0 | 0 | 0 | 439 |
normalized size | 1 | 1. | 1.36 | 7.24 | 0. | 0. | 0. | 0. | 1.15 |
time (sec) |
N/A |
1.922 |
2.781 |
0.034 |
0. |
0. |
0. |
0. |
167.217 |
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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 |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 797 | 796 | 1847 | 6422 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.32 | 8.06 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.318 |
7.371 |
0.04 |
0. |
0. |
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 |
A |
A |
A |
A |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 47 | 47 | 55 | 46 | 88 | 62 | 0 | 65 | 44 |
normalized size | 1 | 1. | 1.17 | 0.98 | 1.87 | 1.32 | 0. | 1.38 | 0.94 |
time (sec) |
N/A |
0.093 |
0.026 |
0.015 |
0.756 |
0.286 |
0. |
0.27 |
15.265 |
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Problem 11 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
C |
B |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 117 | 117 | 394 | 637 | 0 | 1227 | 0 | 0 | 138 |
normalized size | 1 | 1. | 3.37 | 5.44 | 0. | 10.49 | 0. | 0. | 1.18 |
time (sec) |
N/A |
0.38 |
0.646 |
0.171 |
0. |
0.304 |
0. |
0. |
29.971 |
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Problem 12 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
C |
B |
F |
A |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 484 | 484 | 182 | 6871419 | 0 | 16226 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.38 | 14197.2 | 0. | 33.52 | 0. | 0. | 0. |
time (sec) |
N/A |
25.519 |
0.505 |
0.623 |
0. |
0.649 |
0. |
0. |
0. |
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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 |
B |
F(-2) |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 182 | 175 | 510 | 0 | 1 | 1260 | 258 | 0 |
normalized size | 1 | 0.99 | 0.95 | 2.77 | 0. | 0.01 | 6.85 | 1.4 | 0. |
time (sec) |
N/A |
0.7 |
0.363 |
0.01 |
0. |
0.296 |
29.302 |
0.268 |
0. |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 542 | 542 | 535 | 1672 | 0 | 1 | 0 | 996 | 0 |
normalized size | 1 | 1. | 0.99 | 3.08 | 0. | 0. | 0. | 1.84 | 0. |
time (sec) |
N/A |
2.961 |
1.853 |
0.013 |
0. |
0.426 |
0. |
0.278 |
0. |
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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 |
B |
F(-2) |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 406 | 398 | 267 | 1698 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0.98 | 0.66 | 4.18 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.127 |
1.062 |
0.014 |
0. |
0. |
0. |
0. |
0. |
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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 |
B |
F(-2) |
F(-1) |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1075 | 1067 | 1376 | 54204 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 0.99 | 1.28 | 50.42 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
11.087 |
8.889 |
0.054 |
0. |
0. |
0. |
0.388 |
0. |
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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(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 131 | 340 | 0 | 1 | 709 | 296 | 131 |
normalized size | 1 | 1. | 0.94 | 2.43 | 0. | 0.01 | 5.06 | 2.11 | 0.94 |
time (sec) |
N/A |
0.308 |
0.263 |
0.007 |
0. |
0.306 |
4.818 |
0.277 |
49.73 |
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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 |
B |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 131 | 340 | 0 | 1 | 680 | 279 | 126 |
normalized size | 1 | 1. | 0.94 | 2.43 | 0. | 0.01 | 4.86 | 1.99 | 0.9 |
time (sec) |
N/A |
0.241 |
0.049 |
0.006 |
0. |
0.302 |
4.752 |
0.276 |
50.043 |
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Problem 19 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 617 | 615 | 1629 | 16209 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.64 | 26.27 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
18.536 |
6.249 |
0.026 |
0. |
0. |
0. |
0. |
0. |
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Problem 20 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
B |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1092 | 1092 | 3733 | 59465 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 3.42 | 54.46 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
32.056 |
6.52 |
0.04 |
0. |
0. |
0. |
0. |
0. |
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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 |
B |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 696 | 2269 | 0 | 0 | 0 | 0 | 394 |
normalized size | 1 | 1. | 1.67 | 5.45 | 0. | 0. | 0. | 0. | 0.95 |
time (sec) |
N/A |
6.323 |
1.727 |
0.079 |
0. |
0. |
0. |
0. |
141.626 |
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Problem 22 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
C |
A |
F(-2) |
A |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 780 | 780 | 411 | 784 | 0 | 9262 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.53 | 1.01 | 0. | 11.87 | 0. | 0. | 0. |
time (sec) |
N/A |
10.709 |
2.732 |
0.065 |
0. |
45.857 |
0. |
0. |
0. |
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Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 512 | 1771 | 0 | 12119 | 0 | 0 | 308 |
normalized size | 1 | 1. | 1.7 | 5.86 | 0. | 40.13 | 0. | 0. | 1.02 |
time (sec) |
N/A |
2.143 |
1.207 |
0.067 |
0. |
56.029 |
0. |
0. |
64.421 |
|
|
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Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 101 | 101 | 282 | 608 | 0 | 2045 | 0 | 1 | 155 |
normalized size | 1 | 1. | 2.79 | 6.02 | 0. | 20.25 | 0. | 0.01 | 1.53 |
time (sec) |
N/A |
0.318 |
0.774 |
0.044 |
0. |
0.4 |
0. |
1.286 |
28.905 |
|
|
|
|
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Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 161 | 324 | 487 | 466 | 0 | 0 | 144 |
normalized size | 1 | 1. | 1.16 | 2.33 | 3.5 | 3.35 | 0. | 0. | 1.04 |
time (sec) |
N/A |
0.485 |
0.675 |
0.079 |
0.8 |
0.301 |
0. |
0. |
39.843 |
|
|
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Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 263 | 760 | 915 | 586 | 0 | 0 | 168 |
normalized size | 1 | 1. | 1.58 | 4.58 | 5.51 | 3.53 | 0. | 0. | 1.01 |
time (sec) |
N/A |
0.581 |
1.521 |
0.033 |
0.807 |
0.294 |
0. |
0. |
50.533 |
|
|
|
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Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
A |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 304 | 1560 | 1723 | 872 | 0 | 0 | 189 |
normalized size | 1 | 1. | 1.58 | 8.08 | 8.93 | 4.52 | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.709 |
0.936 |
0.027 |
0.853 |
0.299 |
0. |
0. |
84.182 |
|
|
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Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 220 | 186 | 490 | 431 | 0 | 0 | 150 |
normalized size | 1 | 1. | 1.46 | 1.23 | 3.25 | 2.85 | 0. | 0. | 0.99 |
time (sec) |
N/A |
0.601 |
1.253 |
0.06 |
0.8 |
0.285 |
0. |
0. |
40.304 |
|
|
|
|
|
|
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|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 174 | 174 | 252 | 466 | 902 | 763 | 0 | 0 | 170 |
normalized size | 1 | 1. | 1.45 | 2.68 | 5.18 | 4.39 | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.725 |
1.792 |
0.026 |
0.805 |
0.288 |
0. |
0. |
53.005 |
|
|
|
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|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 197 | 197 | 283 | 878 | 1723 | 1088 | 0 | 0 | 194 |
normalized size | 1 | 1. | 1.44 | 4.46 | 8.75 | 5.52 | 0. | 0. | 0.98 |
time (sec) |
N/A |
0.816 |
3.365 |
0.023 |
0.837 |
0.29 |
0. |
0. |
79.285 |
|
|
|
|
|
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|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 41 | 14 | 0 | 66 | 36 | 78 | 14 |
normalized size | 1 | 1. | 2.73 | 0.93 | 0. | 4.4 | 2.4 | 5.2 | 0.93 |
time (sec) |
N/A |
0.052 |
0.018 |
0.011 |
0. |
0.273 |
2.397 |
0.277 |
13.311 |
|
|
|
|
|
|
|
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|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 44 | 44 | 109 | 40 | 0 | 134 | 0 | 146 | 42 |
normalized size | 1 | 1. | 2.48 | 0.91 | 0. | 3.05 | 0. | 3.32 | 0.95 |
time (sec) |
N/A |
0.145 |
0.153 |
0.013 |
0. |
0.276 |
0. |
0.277 |
54.53 |
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 24 | 20 | 0 | 180 | 68 | 0 | 24 |
normalized size | 1 | 1. | 1. | 0.83 | 0. | 7.5 | 2.83 | 0. | 1. |
time (sec) |
N/A |
0.057 |
0.019 |
0.018 |
0. |
0.272 |
2.308 |
0. |
14.814 |
|
|
|
|
|
|
|
|
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|
|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
A |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 56 | 56 | 126 | 45 | 0 | 433 | 0 | 0 | 56 |
normalized size | 1 | 1. | 2.25 | 0.8 | 0. | 7.73 | 0. | 0. | 1. |
time (sec) |
N/A |
0.136 |
0.212 |
0.014 |
0. |
0.293 |
0. |
0. |
34.288 |
|
|
|
|
|
|
|
|
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|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 249 | 249 | 767 | 3606 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 3.08 | 14.48 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.944 |
1.85 |
0.028 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 48 | 48 | 46 | 48 | 0 | 115 | 0 | 109 | 46 |
normalized size | 1 | 1. | 0.96 | 1. | 0. | 2.4 | 0. | 2.27 | 0.96 |
time (sec) |
N/A |
0.148 |
0.068 |
0.007 |
0. |
0.456 |
0. |
0.275 |
33.254 |
|
|
|
|
|
|
|
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|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 1057 | 94 | 0 | 76 | 0 | 132 | 15 |
normalized size | 1 | 1. | 62.18 | 5.53 | 0. | 4.47 | 0. | 7.76 | 0.88 |
time (sec) |
N/A |
0.067 |
6.283 |
0.015 |
0. |
0.288 |
0. |
0.274 |
18.129 |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 38 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 86 | 86 | 1079 | 123 | 0 | 167 | 0 | 220 | 83 |
normalized size | 1 | 1. | 12.55 | 1.43 | 0. | 1.94 | 0. | 2.56 | 0.97 |
time (sec) |
N/A |
0.438 |
6.27 |
0.011 |
0. |
0.293 |
0. |
0.273 |
61.225 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 136 | 136 | 108 | 121 | 0 | 0 | 0 | 0 | 129 |
normalized size | 1 | 1. | 0.79 | 0.89 | 0. | 0. | 0. | 0. | 0.95 |
time (sec) |
N/A |
0.299 |
0.182 |
0.025 |
0. |
0. |
0. |
0. |
42.465 |
|
|
|
|
|
|
|
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|
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|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 212 | 212 | 108 | 105 | 0 | 1 | 0 | 158 | 196 |
normalized size | 1 | 1. | 0.51 | 0.5 | 0. | 0. | 0. | 0.75 | 0.92 |
time (sec) |
N/A |
0.393 |
0.129 |
0.043 |
0. |
0.324 |
0. |
0.27 |
40.439 |
|
|
|
|
|
|
|
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|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 96 | 84 | 0 | 1 | 0 | 132 | 146 |
normalized size | 1 | 1. | 0.6 | 0.52 | 0. | 0.01 | 0. | 0.82 | 0.91 |
time (sec) |
N/A |
0.226 |
0.095 |
0.013 |
0. |
0.325 |
0. |
0.272 |
28.43 |
|
|
|
|
|
|
|
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|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 148 | 148 | 85 | 65 | 0 | 1 | 0 | 107 | 136 |
normalized size | 1 | 1. | 0.57 | 0.44 | 0. | 0.01 | 0. | 0.72 | 0.92 |
time (sec) |
N/A |
0.149 |
0.075 |
0.013 |
0. |
0.34 |
0. |
0.272 |
26.19 |
|
|
|
|
|
|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 160 | 160 | 139 | 94 | 0 | 1 | 0 | 138 | 150 |
normalized size | 1 | 1. | 0.87 | 0.59 | 0. | 0.01 | 0. | 0.86 | 0.94 |
time (sec) |
N/A |
0.377 |
0.106 |
0.014 |
0. |
0.342 |
0. |
0.275 |
42.121 |
|
|
|
|
|
|
|
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|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 156 | 156 | 120 | 108 | 0 | 1 | 0 | 170 | 146 |
normalized size | 1 | 1. | 0.77 | 0.69 | 0. | 0.01 | 0. | 1.09 | 0.94 |
time (sec) |
N/A |
0.371 |
0.079 |
0.017 |
0. |
0.336 |
0. |
0.277 |
38.292 |
|
|
|
|
|
|
|
|
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|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 161 | 161 | 125 | 141 | 0 | 1 | 0 | 269 | 151 |
normalized size | 1 | 1. | 0.78 | 0.88 | 0. | 0.01 | 0. | 1.67 | 0.94 |
time (sec) |
N/A |
0.38 |
0.179 |
0.018 |
0. |
0.335 |
0. |
0.282 |
41.578 |
|
|
|
|
|
|
|
|
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|
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Problem 46 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 317 | 317 | 236 | 532 | 0 | 1 | 0 | 497 | 313 |
normalized size | 1 | 1. | 0.74 | 1.68 | 0. | 0. | 0. | 1.57 | 0.99 |
time (sec) |
N/A |
0.833 |
0.431 |
0.022 |
0. |
0.354 |
0. |
0.289 |
71.228 |
|
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 227 | 227 | 176 | 383 | 0 | 1 | 0 | 362 | 221 |
normalized size | 1 | 1. | 0.78 | 1.69 | 0. | 0. | 0. | 1.59 | 0.97 |
time (sec) |
N/A |
0.376 |
0.36 |
0.016 |
0. |
0.336 |
0. |
0.288 |
47.435 |
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 198 | 198 | 132 | 259 | 0 | 1 | 0 | 250 | 180 |
normalized size | 1 | 1. | 0.67 | 1.31 | 0. | 0.01 | 0. | 1.26 | 0.91 |
time (sec) |
N/A |
0.258 |
0.247 |
0.014 |
0. |
0.329 |
0. |
0.282 |
44.775 |
|
|
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 211 | 211 | 246 | 214 | 0 | 1 | 0 | 0 | 197 |
normalized size | 1 | 1. | 1.17 | 1.01 | 0. | 0. | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.537 |
0.274 |
0.015 |
0. |
0.995 |
0. |
0. |
68.453 |
|
|
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Problem 50 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 202 | 202 | 168 | 259 | 0 | 1 | 0 | 0 | 189 |
normalized size | 1 | 1. | 0.83 | 1.28 | 0. | 0. | 0. | 0. | 0.94 |
time (sec) |
N/A |
0.501 |
0.39 |
0.018 |
0. |
0.461 |
0. |
0. |
63.063 |
|
|
|
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Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
F(-2) |
A |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 215 | 215 | 177 | 345 | 0 | 1 | 0 | 0 | 201 |
normalized size | 1 | 1. | 0.82 | 1.6 | 0. | 0. | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.537 |
0.447 |
0.019 |
0. |
0.6 |
0. |
0. |
66.684 |
|
|
|
|
|
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|
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Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 452 | 452 | 882 | 7739 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.95 | 17.12 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.096 |
3.326 |
0.077 |
0. |
0. |
0. |
0.667 |
0. |
|
|
|
|
|
|
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Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 395 | 395 | 785 | 5581 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.99 | 14.13 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.701 |
1.684 |
0.02 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 298 | 298 | 472 | 3249 | 0 | 0 | 0 | 0 | 296 |
normalized size | 1 | 1. | 1.58 | 10.9 | 0. | 0. | 0. | 0. | 0.99 |
time (sec) |
N/A |
0.894 |
2.38 |
0.019 |
0. |
0. |
0. |
0. |
77.585 |
|
|
|
|
|
|
|
|
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|
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|
|
Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 358 | 358 | 667 | 3544 | 0 | 1 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.86 | 9.9 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.709 |
1.207 |
0.022 |
0. |
39.914 |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 382 | 382 | 600 | 3703 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.57 | 9.69 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.126 |
1.159 |
0.051 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 507 | 507 | 767 | 3993 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.51 | 7.88 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.11 |
2.691 |
0.026 |
0. |
0. |
0. |
1.345 |
0. |
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
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|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 795 | 795 | 1565 | 19148 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.97 | 24.09 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
9.888 |
6.225 |
0.043 |
0. |
0. |
0. |
0.918 |
0. |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 591 | 591 | 1176 | 14709 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.99 | 24.89 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
7.026 |
4.085 |
0.024 |
0. |
0. |
0. |
0.826 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 484 | 482 | 932 | 8954 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.93 | 18.5 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
8.827 |
2.716 |
0.022 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 496 | 496 | 956 | 9728 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.93 | 19.61 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
5.342 |
2.071 |
0.027 |
0. |
0. |
0. |
1.315 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 604 | 604 | 880 | 9912 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.46 | 16.41 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
5.933 |
1.498 |
0.029 |
0. |
0. |
0. |
0.664 |
0. |
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 668 | 668 | 949 | 10298 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.42 | 15.42 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
6.973 |
4.534 |
0.03 |
0. |
0. |
0. |
1.619 |
0. |
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 380 | 380 | 696 | 2397 | 0 | 0 | 0 | 0 | 371 |
normalized size | 1 | 1. | 1.83 | 6.31 | 0. | 0. | 0. | 0. | 0.98 |
time (sec) |
N/A |
2.429 |
1.235 |
0.037 |
0. |
0. |
0. |
0. |
145.077 |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 344 | 344 | 602 | 1796 | 0 | 0 | 0 | 0 | 337 |
normalized size | 1 | 1. | 1.75 | 5.22 | 0. | 0. | 0. | 0. | 0.98 |
time (sec) |
N/A |
1.311 |
0.842 |
0.022 |
0. |
0. |
0. |
0. |
96.086 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 294 | 294 | 484 | 1172 | 0 | 6865 | 0 | 0 | 294 |
normalized size | 1 | 1. | 1.65 | 3.99 | 0. | 23.35 | 0. | 0. | 1. |
time (sec) |
N/A |
0.682 |
4.295 |
0.018 |
0. |
0.875 |
0. |
0. |
53.238 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 425 | 589 | 0 | 6849 | 0 | 0 | 267 |
normalized size | 1 | 1. | 1.6 | 2.21 | 0. | 25.75 | 0. | 0. | 1. |
time (sec) |
N/A |
0.453 |
2.574 |
0.017 |
0. |
0.865 |
0. |
0. |
45.554 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 330 | 330 | 513 | 681 | 0 | 0 | 0 | 0 | 325 |
normalized size | 1 | 1. | 1.55 | 2.06 | 0. | 0. | 0. | 0. | 0.98 |
time (sec) |
N/A |
1.856 |
3.422 |
0.021 |
0. |
0. |
0. |
0. |
131.601 |
|
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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 |
B |
F |
F(-1) |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 367 | 367 | 567 | 736 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.54 | 2.01 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.678 |
1.141 |
0.023 |
0. |
0. |
0. |
0. |
0. |
|
|
|
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Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 457 | 457 | 678 | 911 | 0 | 0 | 0 | 0 | 439 |
normalized size | 1 | 1. | 1.48 | 1.99 | 0. | 0. | 0. | 0. | 0.96 |
time (sec) |
N/A |
4.068 |
1.895 |
0.025 |
0. |
0. |
0. |
0. |
177.497 |
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 499 | 499 | 727 | 6124 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.46 | 12.27 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.639 |
1.826 |
0.039 |
0. |
0. |
0. |
0. |
0. |
|
|
|
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Problem 72 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 410 | 410 | 596 | 4752 | 0 | 0 | 0 | 0 | 398 |
normalized size | 1 | 1. | 1.45 | 11.59 | 0. | 0. | 0. | 0. | 0.97 |
time (sec) |
N/A |
1.707 |
1.427 |
0.023 |
0. |
0. |
0. |
0. |
154.803 |
|
|
|
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Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 617 | 3000 | 0 | 0 | 0 | 0 | 400 |
normalized size | 1 | 1. | 1.5 | 7.3 | 0. | 0. | 0. | 0. | 0.97 |
time (sec) |
N/A |
1.96 |
1.752 |
0.02 |
0. |
0. |
0. |
0. |
158.234 |
|
|
|
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Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 598 | 1713 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.44 | 4.12 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.512 |
1.403 |
0.02 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
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Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 526 | 526 | 889 | 1945 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.69 | 3.7 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.828 |
2.179 |
0.023 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 618 | 618 | 996 | 2046 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.61 | 3.31 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
5.442 |
3.16 |
0.025 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
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|
Problem 77 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 392 | 392 | 419 | 1817 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.07 | 4.64 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.875 |
2.742 |
0.025 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 78 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 316 | 316 | 397 | 1810 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.26 | 5.73 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.106 |
2.395 |
0.021 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 282 | 282 | 448 | 1667 | 0 | 0 | 0 | 0 | 257 |
normalized size | 1 | 1. | 1.59 | 5.91 | 0. | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
0.735 |
2.172 |
0.019 |
0. |
0. |
0. |
0. |
138.653 |
|
|
|
|
|
|
|
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|
|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 343 | 1669 | 0 | 1 | 0 | 0 | 240 |
normalized size | 1 | 1. | 1.29 | 6.27 | 0. | 0. | 0. | 0. | 0.9 |
time (sec) |
N/A |
0.532 |
0.717 |
0.019 |
0. |
100.791 |
0. |
0. |
89.738 |
|
|
|
|
|
|
|
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|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 473 | 1764 | 0 | 1 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.77 | 6.61 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.693 |
0.525 |
0.023 |
0. |
17.468 |
0. |
0.293 |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 286 | 286 | 379 | 1819 | 0 | 1 | 0 | 0 | 257 |
normalized size | 1 | 1. | 1.33 | 6.36 | 0. | 0. | 0. | 0. | 0.9 |
time (sec) |
N/A |
1.545 |
1.395 |
0.032 |
0. |
25.181 |
0. |
0. |
176.368 |
|
|
|
|
|
|
|
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|
|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 353 | 353 | 505 | 1953 | 0 | 1 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.43 | 5.53 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.939 |
0.79 |
0.026 |
0. |
136.041 |
0. |
0. |
0. |
|
|
|
|
|
|
|
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|
|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 501 | 501 | 536 | 4884 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.07 | 9.75 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.857 |
1.575 |
0.04 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 85 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 417 | 417 | 482 | 4900 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.16 | 11.75 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.215 |
1.263 |
0.025 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 349 | 349 | 416 | 4567 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.19 | 13.09 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.345 |
0.97 |
0.022 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 315 | 315 | 396 | 4574 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.26 | 14.52 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.156 |
1.107 |
0.022 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
|
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|
|
|
Problem 88 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 469 | 469 | 443 | 4765 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.94 | 10.16 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.778 |
0.866 |
0.026 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 463 | 463 | 433 | 4799 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.94 | 10.37 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.6 |
0.78 |
0.027 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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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 |
B |
F |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 614 | 614 | 429 | 5056 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.7 | 8.23 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.195 |
0.974 |
0.029 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 207 | 1346 | 0 | 1 | 0 | 0 | 170 |
normalized size | 1 | 1. | 1.1 | 7.12 | 0. | 0.01 | 0. | 0. | 0.9 |
time (sec) |
N/A |
0.67 |
0.694 |
0.027 |
0. |
166.762 |
0. |
0. |
98.292 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
|
Problem 92 |
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 | 75 | 75 | 79 | 102 | 112 | 95 | 0 | 99 | 56 |
normalized size | 1 | 1. | 1.05 | 1.36 | 1.49 | 1.27 | 0. | 1.32 | 0.75 |
time (sec) |
N/A |
0.143 |
0.021 |
0.02 |
0.795 |
0.299 |
0. |
0.275 |
37.494 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 93 |
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 | 130 | 130 | 124 | 789 | 0 | 1806 | 0 | 0 | 141 |
normalized size | 1 | 1. | 0.95 | 6.07 | 0. | 13.89 | 0. | 0. | 1.08 |
time (sec) |
N/A |
0.382 |
0.2 |
0.08 |
0. |
0.336 |
0. |
0. |
39.476 |
|
|
|
|
|
|
|
|
|
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|
|
|
|
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|
|
|
Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 369 | 369 | 399 | 516 | 0 | 0 | 0 | 0 | 338 |
normalized size | 1 | 1. | 1.08 | 1.4 | 0. | 0. | 0. | 0. | 0.92 |
time (sec) |
N/A |
1.576 |
4.762 |
0.025 |
0. |
0. |
0. |
0. |
144.552 |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 287 | 287 | 404 | 410 | 0 | 0 | 0 | 0 | 260 |
normalized size | 1 | 1. | 1.41 | 1.43 | 0. | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
1.271 |
2.784 |
0.021 |
0. |
0. |
0. |
0. |
124.668 |
|
|
|
|
|
|
|
|
|
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|
|
Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 266 | 266 | 353 | 399 | 0 | 0 | 0 | 0 | 241 |
normalized size | 1 | 1. | 1.33 | 1.5 | 0. | 0. | 0. | 0. | 0.91 |
time (sec) |
N/A |
0.533 |
0.788 |
0.02 |
0. |
0. |
0. |
0. |
78.789 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 289 | 354 | 0 | 3717 | 0 | 0 | 202 |
normalized size | 1 | 1. | 1.31 | 1.61 | 0. | 16.9 | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.341 |
0.486 |
0.019 |
0. |
0.641 |
0. |
0. |
57.718 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 220 | 220 | 301 | 358 | 0 | 3565 | 0 | 0 | 202 |
normalized size | 1 | 1. | 1.37 | 1.63 | 0. | 16.2 | 0. | 0. | 0.92 |
time (sec) |
N/A |
0.334 |
0.455 |
0.02 |
0. |
0.702 |
0. |
0. |
55.761 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 267 | 267 | 351 | 391 | 0 | 1 | 0 | 1 | 241 |
normalized size | 1 | 1. | 1.31 | 1.46 | 0. | 0. | 0. | 0. | 0.9 |
time (sec) |
N/A |
1.319 |
1.031 |
0.022 |
0. |
71.979 |
0. |
0.281 |
124.81 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-1) |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 432 | 427 | 0 | 0 | 0 | 4 | 262 |
normalized size | 1 | 1. | 1.48 | 1.47 | 0. | 0. | 0. | 0.01 | 0.9 |
time (sec) |
N/A |
1.364 |
2.273 |
0.024 |
0. |
0. |
0. |
0.658 |
131.872 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
F(-1) |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 376 | 376 | 418 | 519 | 0 | 0 | 0 | 4 | 342 |
normalized size | 1 | 1. | 1.11 | 1.38 | 0. | 0. | 0. | 0.01 | 0.91 |
time (sec) |
N/A |
1.593 |
2.714 |
0.026 |
0. |
0. |
0. |
0.677 |
159.291 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 466 | 466 | 480 | 1648 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.03 | 3.54 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.904 |
5.486 |
0.025 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 341 | 341 | 414 | 1480 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.21 | 4.34 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.181 |
3.658 |
0.023 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 297 | 297 | 583 | 1427 | 0 | 0 | 0 | 0 | 338 |
normalized size | 1 | 1. | 1.96 | 4.8 | 0. | 0. | 0. | 0. | 1.14 |
time (sec) |
N/A |
0.935 |
1.373 |
0.023 |
0. |
0. |
0. |
0. |
167.761 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 299 | 299 | 407 | 1360 | 0 | 0 | 0 | 0 | 342 |
normalized size | 1 | 1. | 1.36 | 4.55 | 0. | 0. | 0. | 0. | 1.14 |
time (sec) |
N/A |
0.862 |
2.447 |
0.021 |
0. |
0. |
0. |
0. |
156.897 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 310 | 310 | 584 | 1376 | 0 | 0 | 0 | 0 | 352 |
normalized size | 1 | 1. | 1.88 | 4.44 | 0. | 0. | 0. | 0. | 1.14 |
time (sec) |
N/A |
0.927 |
1.403 |
0.02 |
0. |
0. |
0. |
0. |
151.232 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 394 | 394 | 742 | 1518 | 0 | 0 | 0 | 1 | 0 |
normalized size | 1 | 1. | 1.88 | 3.85 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.334 |
6.481 |
0.024 |
0. |
0. |
0. |
0.295 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 454 | 454 | 537 | 1656 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.18 | 3.65 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.75 |
3.392 |
0.025 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 761 | 761 | 1546 | 14815 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.03 | 19.47 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
8.377 |
6.305 |
0.028 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 549 | 549 | 1112 | 10138 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.03 | 18.47 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
14.046 |
2.863 |
0.022 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 431 | 431 | 699 | 6019 | 0 | 0 | 0 | 0 | 420 |
normalized size | 1 | 1. | 1.62 | 13.97 | 0. | 0. | 0. | 0. | 0.97 |
time (sec) |
N/A |
1.636 |
4.703 |
0. |
0. |
0. |
0. |
0. |
157.719 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 523 | 521 | 903 | 6460 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.73 | 12.35 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
7.14 |
1.868 |
0.025 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 736 | 736 | 972 | 6765 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.32 | 9.19 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
8.042 |
3.755 |
0.028 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
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Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 545 | 545 | 918 | 3131 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.68 | 5.74 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
7.745 |
2.058 |
0.026 |
0. |
0. |
0. |
0. |
0. |
|
|
|
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Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 463 | 463 | 815 | 2321 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.76 | 5.01 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
7.394 |
1.39 |
0.023 |
0. |
0. |
0. |
0. |
0. |
|
|
|
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Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 402 | 402 | 874 | 1516 | 0 | 15270 | 0 | 0 | 384 |
normalized size | 1 | 1. | 2.17 | 3.77 | 0. | 37.99 | 0. | 0. | 0.96 |
time (sec) |
N/A |
2.555 |
6.179 |
0.02 |
0. |
5.157 |
0. |
0. |
127.151 |
|
|
|
|
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Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 633 | 761 | 0 | 15237 | 0 | 0 | 357 |
normalized size | 1 | 1. | 1.69 | 2.03 | 0. | 40.74 | 0. | 0. | 0.95 |
time (sec) |
N/A |
0.791 |
4.572 |
0. |
0. |
6.795 |
0. |
0. |
107.217 |
|
|
|
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Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F |
F(-1) |
F |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 451 | 451 | 994 | 859 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 2.2 | 1.9 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
5.868 |
6.246 |
0.022 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
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Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 543 | 543 | 866 | 983 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.59 | 1.81 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
10.059 |
1.872 |
0.026 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
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|
Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 679 | 679 | 1008 | 1296 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.48 | 1.91 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
17.187 |
3.369 |
0.029 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
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Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
NO |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 779 | 779 | 1066 | 13951 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.37 | 17.91 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
24.266 |
5.97 |
0.034 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 609 | 609 | 897 | 10781 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.47 | 17.7 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
13.191 |
4.724 |
0.028 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
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|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 609 | 609 | 868 | 6813 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.43 | 11.19 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
12.776 |
3.99 |
0.024 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 666 | 666 | 906 | 3889 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.36 | 5.84 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.165 |
4.528 |
0. |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
F(-1) |
F(-1) |
F(-2) |
F(-1) |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 816 | 814 | 1331 | 4384 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 1.63 | 5.37 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
24.85 |
5.879 |
0.026 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 140 | 140 | 1101 | 159 | 0 | 242 | 0 | 254 | 153 |
normalized size | 1 | 1. | 7.86 | 1.14 | 0. | 1.73 | 0. | 1.81 | 1.09 |
time (sec) |
N/A |
1.034 |
6.294 |
0.024 |
0. |
0.308 |
0. |
0.29 |
121.949 |
|
|
|
|
|
|
|
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|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 115 | 115 | 1093 | 144 | 0 | 236 | 0 | 250 | 129 |
normalized size | 1 | 1. | 9.5 | 1.25 | 0. | 2.05 | 0. | 2.17 | 1.12 |
time (sec) |
N/A |
0.887 |
6.284 |
0.019 |
0. |
0.3 |
0. |
0.275 |
115.126 |
|
|
|
|
|
|
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|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 98 | 98 | 1087 | 130 | 0 | 213 | 0 | 231 | 116 |
normalized size | 1 | 1. | 11.09 | 1.33 | 0. | 2.17 | 0. | 2.36 | 1.18 |
time (sec) |
N/A |
0.484 |
6.269 |
0.009 |
0. |
0.305 |
0. |
0.275 |
83.245 |
|
|
|
|
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Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 68 | 69 | 891 | 92 | 0 | 54 | 0 | 92 | 71 |
normalized size | 1 | 1.01 | 13.1 | 1.35 | 0. | 0.79 | 0. | 1.35 | 1.04 |
time (sec) |
N/A |
0.151 |
6.362 |
0.011 |
0. |
0.292 |
0. |
0.271 |
25.026 |
|
|
|
|
|
|
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|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 95 | 95 | 800 | 121 | 0 | 167 | 0 | 223 | 88 |
normalized size | 1 | 1. | 8.42 | 1.27 | 0. | 1.76 | 0. | 2.35 | 0.93 |
time (sec) |
N/A |
0.26 |
4.356 |
0.009 |
0. |
0.294 |
0. |
0.272 |
52.695 |
|
|
|
|
|
|
|
|
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|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 130 | 130 | 1068 | 152 | 0 | 221 | 0 | 269 | 129 |
normalized size | 1 | 1. | 8.22 | 1.17 | 0. | 1.7 | 0. | 2.07 | 0.99 |
time (sec) |
N/A |
0.865 |
6.25 |
0.023 |
0. |
0.3 |
0. |
0.272 |
124.364 |
|
|
|
|
|
|
|
|
|
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|
|
|
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|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 151 | 151 | 1135 | 169 | 0 | 258 | 0 | 363 | 150 |
normalized size | 1 | 1. | 7.52 | 1.12 | 0. | 1.71 | 0. | 2.4 | 0.99 |
time (sec) |
N/A |
1.001 |
6.298 |
0.023 |
0. |
0.306 |
0. |
0.274 |
118.371 |
|
|
|
|
|
|
|
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|
|
Problem 133 |
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 | 149 | 149 | 111 | 147 | 209 | 128 | 0 | 115 | 138 |
normalized size | 1 | 1. | 0.74 | 0.99 | 1.4 | 0.86 | 0. | 0.77 | 0.93 |
time (sec) |
N/A |
0.232 |
0.157 |
0.022 |
0.789 |
0.287 |
0. |
0.271 |
28.563 |
|
|
|
|
|
|
|
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|
|
Problem 134 |
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 | 103 | 103 | 70 | 96 | 140 | 108 | 0 | 95 | 94 |
normalized size | 1 | 1. | 0.68 | 0.93 | 1.36 | 1.05 | 0. | 0.92 | 0.91 |
time (sec) |
N/A |
0.113 |
0.084 |
0.009 |
0.78 |
0.283 |
0. |
0.268 |
17.707 |
|
|
|
|
|
|
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|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 28 | 28 | 37 | 163 | 0 | 72 | 0 | 85 | 26 |
normalized size | 1 | 1. | 1.32 | 5.82 | 0. | 2.57 | 0. | 3.04 | 0.93 |
time (sec) |
N/A |
0.118 |
0.027 |
0.021 |
0. |
0.295 |
0. |
0.281 |
23.149 |
|
|
|
|
|
|
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|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 84 | 84 | 93 | 245 | 0 | 170 | 0 | 215 | 71 |
normalized size | 1 | 1. | 1.11 | 2.92 | 0. | 2.02 | 0. | 2.56 | 0.85 |
time (sec) |
N/A |
0.209 |
0.24 |
0.027 |
0. |
0.29 |
0. |
0.29 |
32.086 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F |
A |
F |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 139 | 139 | 129 | 306 | 0 | 251 | 0 | 313 | 126 |
normalized size | 1 | 1. | 0.93 | 2.2 | 0. | 1.81 | 0. | 2.25 | 0.91 |
time (sec) |
N/A |
0.357 |
0.187 |
0.032 |
0. |
0.295 |
0. |
0.289 |
47.051 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 13 | 16 | 15 | 15 | 31 | 15 | 12 |
normalized size | 1 | 1. | 0.87 | 1.07 | 1. | 1. | 2.07 | 1. | 0.8 |
time (sec) |
N/A |
0.008 |
0.017 |
0.005 |
0.715 |
0.276 |
0.407 |
0.271 |
2.594 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 139 |
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 | 13 | 14 | 12 | 15 | 10 | 15 | 10 |
normalized size | 1 | 1. | 0.81 | 0.88 | 0.75 | 0.94 | 0.62 | 0.94 | 0.62 |
time (sec) |
N/A |
0.008 |
0.009 |
0.004 |
0.702 |
0.274 |
15.185 |
0.271 |
1.904 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 13 | 20 | 0 | 15 | 0 | 0 | 12 |
normalized size | 1 | 1. | 0.87 | 1.33 | 0. | 1. | 0. | 0. | 0.8 |
time (sec) |
N/A |
0.045 |
0.014 |
0.005 |
0. |
0.27 |
0. |
0. |
9.685 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
F |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 13 | 18 | 0 | 15 | 0 | 0 | 12 |
normalized size | 1 | 1. | 0.87 | 1.2 | 0. | 1. | 0. | 0. | 0.8 |
time (sec) |
N/A |
0.093 |
0.01 |
0.005 |
0. |
0.279 |
0. |
0. |
11.966 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 142 |
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 | 242 | 242 | 331 | 0 | 0 | 0 | 0 | 0 | 224 |
normalized size | 1 | 1. | 1.37 | 0. | 0. | 0. | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.344 |
1.038 |
0.314 |
0. |
0. |
0. |
0. |
29.789 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 488 | 488 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.378 |
0.93 |
0.668 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
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 [63] had the largest ratio of [ 0.5556
]
|
|
|
|
|
|
|
|
|
| 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 |
5 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
2 |
A |
5 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
3 |
A |
5 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
4 |
A |
8 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
5 |
A |
9 |
8 |
1. |
27 |
0.296 |
|
|
|
|
|
|
|
6 |
A |
9 |
6 |
1. |
30 |
0.2 |
|
|
|
|
|
|
|
7 |
A |
5 |
3 |
1. |
30 |
0.1 |
|
|
|
|
|
|
|
8 |
A |
6 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
9 |
A |
7 |
5 |
1. |
30 |
0.167 |
|
|
|
|
|
|
|
10 |
A |
5 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
11 |
A |
5 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
12 |
A |
5 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
13 |
A |
6 |
5 |
0.99 |
28 |
0.179 |
|
|
|
|
|
|
|
14 |
A |
6 |
5 |
1. |
30 |
0.167 |
|
|
|
|
|
|
|
15 |
A |
9 |
5 |
0.98 |
30 |
0.167 |
|
|
|
|
|
|
|
16 |
A |
10 |
6 |
0.99 |
30 |
0.2 |
|
|
|
|
|
|
|
17 |
A |
5 |
5 |
1. |
34 |
0.147 |
|
|
|
|
|
|
|
18 |
A |
5 |
5 |
1. |
34 |
0.147 |
|
|
|
|
|
|
|
19 |
A |
9 |
6 |
1. |
32 |
0.188 |
|
|
|
|
|
|
|
20 |
A |
10 |
7 |
1. |
32 |
0.219 |
|
|
|
|
|
|
|
|
21 |
A |
5 |
3 |
1. |
32 |
0.094 |
|
|
|
|
|
|
|
22 |
A |
5 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
23 |
A |
5 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
24 |
A |
6 |
6 |
1. |
26 |
0.231 |
|
|
|
|
|
|
|
25 |
A |
5 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
26 |
A |
7 |
6 |
1. |
30 |
0.2 |
|
|
|
|
|
|
|
27 |
A |
7 |
6 |
1. |
30 |
0.2 |
|
|
|
|
|
|
|
28 |
A |
5 |
3 |
1. |
30 |
0.1 |
|
|
|
|
|
|
|
29 |
A |
6 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
30 |
A |
7 |
5 |
1. |
30 |
0.167 |
|
|
|
|
|
|
|
31 |
A |
2 |
2 |
1. |
26 |
0.077 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1. |
26 |
0.192 |
|
|
|
|
|
|
|
33 |
A |
2 |
2 |
1. |
24 |
0.083 |
|
|
|
|
|
|
|
34 |
A |
5 |
5 |
1. |
20 |
0.25 |
|
|
|
|
|
|
|
35 |
A |
6 |
5 |
1. |
36 |
0.139 |
|
|
|
|
|
|
|
36 |
A |
2 |
2 |
1. |
36 |
0.056 |
|
|
|
|
|
|
|
37 |
A |
2 |
2 |
1. |
32 |
0.062 |
|
|
|
|
|
|
|
38 |
A |
13 |
9 |
1. |
32 |
0.281 |
|
|
|
|
|
|
|
39 |
A |
5 |
5 |
1. |
38 |
0.132 |
|
|
|
|
|
|
|
40 |
A |
6 |
6 |
1. |
35 |
0.171 |
|
|
|
|
|
|
|
|
41 |
A |
5 |
5 |
1. |
33 |
0.152 |
|
|
|
|
|
|
|
42 |
A |
5 |
5 |
1. |
32 |
0.156 |
|
|
|
|
|
|
|
43 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
44 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
45 |
A |
8 |
8 |
1. |
35 |
0.229 |
|
|
|
|
|
|
|
46 |
A |
6 |
6 |
1. |
38 |
0.158 |
|
|
|
|
|
|
|
47 |
A |
5 |
5 |
1. |
36 |
0.139 |
|
|
|
|
|
|
|
48 |
A |
5 |
5 |
1. |
35 |
0.143 |
|
|
|
|
|
|
|
49 |
A |
7 |
6 |
1. |
38 |
0.158 |
|
|
|
|
|
|
|
50 |
A |
7 |
6 |
1. |
38 |
0.158 |
|
|
|
|
|
|
|
51 |
A |
7 |
6 |
1. |
38 |
0.158 |
|
|
|
|
|
|
|
52 |
A |
9 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
53 |
A |
11 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
54 |
A |
8 |
5 |
1. |
24 |
0.208 |
|
|
|
|
|
|
|
55 |
A |
12 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
56 |
A |
18 |
12 |
1. |
27 |
0.444 |
|
|
|
|
|
|
|
57 |
A |
22 |
13 |
1. |
27 |
0.482 |
|
|
|
|
|
|
|
58 |
A |
10 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
59 |
A |
16 |
9 |
1. |
25 |
0.36 |
|
|
|
|
|
|
|
60 |
A |
9 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
|
61 |
A |
17 |
11 |
1. |
27 |
0.407 |
|
|
|
|
|
|
|
62 |
A |
21 |
14 |
1. |
27 |
0.518 |
|
|
|
|
|
|
|
63 |
A |
26 |
15 |
1. |
27 |
0.556 |
|
|
|
|
|
|
|
64 |
A |
10 |
6 |
1. |
27 |
0.222 |
|
|
|
|
|
|
|
65 |
A |
8 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
66 |
A |
5 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
67 |
A |
5 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
68 |
A |
10 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
69 |
A |
11 |
8 |
1. |
27 |
0.296 |
|
|
|
|
|
|
|
70 |
A |
15 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
71 |
A |
10 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
72 |
A |
6 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
73 |
A |
6 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
74 |
A |
6 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
75 |
A |
12 |
9 |
1. |
27 |
0.333 |
|
|
|
|
|
|
|
76 |
A |
14 |
11 |
1. |
27 |
0.407 |
|
|
|
|
|
|
|
77 |
A |
15 |
9 |
1. |
28 |
0.321 |
|
|
|
|
|
|
|
78 |
A |
9 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
79 |
A |
9 |
6 |
1. |
26 |
0.231 |
|
|
|
|
|
|
|
80 |
A |
8 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
|
81 |
A |
17 |
9 |
1. |
28 |
0.321 |
|
|
|
|
|
|
|
82 |
A |
16 |
8 |
1. |
28 |
0.286 |
|
|
|
|
|
|
|
83 |
A |
20 |
10 |
1. |
28 |
0.357 |
|
|
|
|
|
|
|
84 |
A |
17 |
10 |
1. |
28 |
0.357 |
|
|
|
|
|
|
|
85 |
A |
10 |
7 |
1. |
28 |
0.25 |
|
|
|
|
|
|
|
86 |
A |
10 |
7 |
1. |
26 |
0.269 |
|
|
|
|
|
|
|
87 |
A |
9 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
88 |
A |
19 |
11 |
1. |
28 |
0.393 |
|
|
|
|
|
|
|
89 |
A |
18 |
10 |
1. |
28 |
0.357 |
|
|
|
|
|
|
|
90 |
A |
26 |
13 |
1. |
28 |
0.464 |
|
|
|
|
|
|
|
91 |
A |
9 |
6 |
1. |
24 |
0.25 |
|
|
|
|
|
|
|
92 |
A |
8 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
93 |
A |
10 |
9 |
1. |
17 |
0.529 |
|
|
|
|
|
|
|
94 |
A |
13 |
7 |
1. |
28 |
0.25 |
|
|
|
|
|
|
|
95 |
A |
10 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
96 |
A |
8 |
5 |
1. |
28 |
0.179 |
|
|
|
|
|
|
|
97 |
A |
5 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
98 |
A |
5 |
3 |
1. |
25 |
0.12 |
|
|
|
|
|
|
|
99 |
A |
9 |
4 |
1. |
28 |
0.143 |
|
|
|
|
|
|
|
100 |
A |
10 |
5 |
1. |
28 |
0.179 |
|
|
|
|
|
|
|
|
101 |
A |
13 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
102 |
A |
13 |
9 |
1. |
28 |
0.321 |
|
|
|
|
|
|
|
103 |
A |
9 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
104 |
A |
6 |
4 |
1. |
28 |
0.143 |
|
|
|
|
|
|
|
105 |
A |
6 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
106 |
A |
6 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
107 |
A |
12 |
7 |
1. |
28 |
0.25 |
|
|
|
|
|
|
|
108 |
A |
12 |
7 |
1. |
28 |
0.25 |
|
|
|
|
|
|
|
109 |
A |
9 |
6 |
1. |
30 |
0.2 |
|
|
|
|
|
|
|
110 |
A |
9 |
6 |
1. |
28 |
0.214 |
|
|
|
|
|
|
|
111 |
A |
8 |
5 |
1. |
27 |
0.185 |
|
|
|
|
|
|
|
112 |
A |
17 |
9 |
1. |
30 |
0.3 |
|
|
|
|
|
|
|
113 |
A |
23 |
10 |
1. |
30 |
0.333 |
|
|
|
|
|
|
|
114 |
A |
12 |
6 |
1. |
30 |
0.2 |
|
|
|
|
|
|
|
115 |
A |
8 |
5 |
1. |
30 |
0.167 |
|
|
|
|
|
|
|
116 |
A |
5 |
3 |
1. |
28 |
0.107 |
|
|
|
|
|
|
|
117 |
A |
5 |
3 |
1. |
27 |
0.111 |
|
|
|
|
|
|
|
118 |
A |
9 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
119 |
A |
12 |
5 |
1. |
30 |
0.167 |
|
|
|
|
|
|
|
120 |
A |
16 |
7 |
1. |
30 |
0.233 |
|
|
|
|
|
|
|
|
121 |
A |
10 |
7 |
1. |
30 |
0.233 |
|
|
|
|
|
|
|
122 |
A |
6 |
4 |
1. |
30 |
0.133 |
|
|
|
|
|
|
|
123 |
A |
6 |
4 |
1. |
28 |
0.143 |
|
|
|
|
|
|
|
124 |
A |
6 |
4 |
1. |
27 |
0.148 |
|
|
|
|
|
|
|
125 |
A |
12 |
7 |
1. |
30 |
0.233 |
|
|
|
|
|
|
|
126 |
A |
24 |
14 |
1. |
30 |
0.467 |
|
|
|
|
|
|
|
127 |
A |
20 |
13 |
1. |
30 |
0.433 |
|
|
|
|
|
|
|
128 |
A |
16 |
12 |
1. |
30 |
0.4 |
|
|
|
|
|
|
|
129 |
A |
6 |
4 |
1.01 |
28 |
0.143 |
|
|
|
|
|
|
|
130 |
A |
10 |
8 |
1. |
27 |
0.296 |
|
|
|
|
|
|
|
131 |
A |
17 |
11 |
1. |
30 |
0.367 |
|
|
|
|
|
|
|
132 |
A |
20 |
12 |
1. |
30 |
0.4 |
|
|
|
|
|
|
|
133 |
A |
8 |
6 |
1. |
34 |
0.176 |
|
|
|
|
|
|
|
134 |
A |
6 |
5 |
1. |
30 |
0.167 |
|
|
|
|
|
|
|
135 |
A |
3 |
3 |
1. |
34 |
0.088 |
|
|
|
|
|
|
|
136 |
A |
5 |
5 |
1. |
34 |
0.147 |
|
|
|
|
|
|
|
137 |
A |
7 |
7 |
1. |
34 |
0.206 |
|
|
|
|
|
|
|
138 |
A |
1 |
1 |
1. |
17 |
0.059 |
|
|
|
|
|
|
|
139 |
A |
1 |
1 |
1. |
15 |
0.067 |
|
|
|
|
|
|
|
140 |
A |
2 |
2 |
1. |
23 |
0.087 |
|
|
|
|
|
|
|
|
141 |
A |
3 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
142 |
A |
2 |
2 |
1. |
40 |
0.05 |
|
|
|
|
|
|
|
143 |
A |
2 |
2 |
1. |
104 |
0.019 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|