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 |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 163 | 163 | 164 | 169 | 224 | 1 | 187 | 234 | 0 |
normalized size | 1 | 1. | 1.01 | 1.04 | 1.37 | 0.01 | 1.15 | 1.44 | 0. |
time (sec) |
N/A |
0.384 |
0.08 |
0.003 |
0.74 |
0.225 |
0.187 |
0.273 |
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 |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 135 | 135 | 135 | 136 | 182 | 1 | 151 | 190 | 0 |
normalized size | 1 | 1. | 1. | 1.01 | 1.35 | 0.01 | 1.12 | 1.41 | 0. |
time (sec) |
N/A |
0.256 |
0.071 |
0.001 |
0.738 |
0.237 |
0.164 |
0.27 |
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 |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 103 | 103 | 104 | 103 | 138 | 1 | 117 | 147 | 0 |
normalized size | 1 | 1. | 1.01 | 1. | 1.34 | 0.01 | 1.14 | 1.43 | 0. |
time (sec) |
N/A |
0.203 |
0.047 |
0.001 |
0.742 |
0.235 |
0.15 |
0.27 |
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 |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 73 | 73 | 73 | 70 | 93 | 1 | 75 | 103 | 0 |
normalized size | 1 | 1. | 1. | 0.96 | 1.27 | 0.01 | 1.03 | 1.41 | 0. |
time (sec) |
N/A |
0.132 |
0.037 |
0.001 |
0.743 |
0.233 |
0.121 |
0.268 |
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 |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 42 | 42 | 42 | 37 | 49 | 1 | 39 | 58 | 0 |
normalized size | 1 | 1. | 1. | 0.88 | 1.17 | 0.02 | 0.93 | 1.38 | 0. |
time (sec) |
N/A |
0.061 |
0.015 |
0.001 |
0.744 |
0.228 |
0.087 |
0.266 |
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) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 188 | 188 | 176 | 313 | 0 | 231 | 175 | 279 | 175 |
normalized size | 1 | 1. | 0.94 | 1.66 | 0. | 1.23 | 0.93 | 1.48 | 0.93 |
time (sec) |
N/A |
0.411 |
0.297 |
0.008 |
0. |
0.29 |
3.723 |
0.285 |
49.891 |
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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(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 213 | 213 | 199 | 345 | 0 | 385 | 206 | 306 | 202 |
normalized size | 1 | 1. | 0.93 | 1.62 | 0. | 1.81 | 0.97 | 1.44 | 0.95 |
time (sec) |
N/A |
0.449 |
0.492 |
0.014 |
0. |
0.292 |
6.965 |
0.279 |
64.426 |
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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(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 242 | 242 | 209 | 362 | 0 | 552 | 246 | 340 | 233 |
normalized size | 1 | 1. | 0.86 | 1.5 | 0. | 2.28 | 1.02 | 1.4 | 0.96 |
time (sec) |
N/A |
0.525 |
0.49 |
0.015 |
0. |
0.263 |
22.238 |
0.28 |
66.666 |
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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(-2) |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 132 | 132 | 126 | 260 | 0 | 1 | 619 | 177 | 0 |
normalized size | 1 | 1. | 0.95 | 1.97 | 0. | 0.01 | 4.69 | 1.34 | 0. |
time (sec) |
N/A |
0.441 |
0.108 |
0.008 |
0. |
0.613 |
46.176 |
0.27 |
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 |
F(-2) |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 97 | 97 | 93 | 175 | 0 | 1 | 434 | 128 | 0 |
normalized size | 1 | 1. | 0.96 | 1.8 | 0. | 0.01 | 4.47 | 1.32 | 0. |
time (sec) |
N/A |
0.256 |
0.113 |
0.005 |
0. |
0.353 |
29.424 |
0.272 |
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 |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 71 | 99 | 0 | 1 | 287 | 95 | 63 |
normalized size | 1 | 1. | 0.99 | 1.38 | 0. | 0.01 | 3.99 | 1.32 | 0.88 |
time (sec) |
N/A |
0.168 |
0.086 |
0.004 |
0. |
0.295 |
13.78 |
0.274 |
23.899 |
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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 |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 80 | 106 | 0 | 1 | 0 | 103 | 73 |
normalized size | 1 | 1. | 1.03 | 1.36 | 0. | 0.01 | 0. | 1.32 | 0.94 |
time (sec) |
N/A |
0.27 |
0.056 |
0.01 |
0. |
0.424 |
0. |
0.275 |
36.073 |
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Problem 13 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
C |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 112 | 112 | 130 | 191 | 0 | 1 | 0 | 173 | 105 |
normalized size | 1 | 1. | 1.16 | 1.71 | 0. | 0.01 | 0. | 1.54 | 0.94 |
time (sec) |
N/A |
0.403 |
0.081 |
0.013 |
0. |
0.826 |
0. |
0.283 |
54.575 |
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Problem 14 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 723 | 723 | 88 | 70 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.12 | 0.1 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.97 |
0.078 |
0.031 |
0. |
0. |
0. |
0. |
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 |
C |
C |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 718 | 718 | 88 | 67 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.12 | 0.09 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
3.448 |
0.082 |
0.007 |
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 |
C |
C |
F |
A |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 634 | 634 | 59 | 49 | 0 | 19340 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.09 | 0.08 | 0. | 30.5 | 0. | 0. | 0. |
time (sec) |
N/A |
1.887 |
0.047 |
0.005 |
0. |
4.371 |
0. |
0. |
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 |
C |
C |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 634 | 634 | 61 | 47 | 0 | 18004 | 0 | 0 | 661 |
normalized size | 1 | 1. | 0.1 | 0.07 | 0. | 28.4 | 0. | 0. | 1.04 |
time (sec) |
N/A |
1.65 |
0.048 |
0.004 |
0. |
1.88 |
0. |
0. |
174.044 |
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Problem 18 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 653 | 653 | 85 | 70 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.13 | 0.11 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.606 |
0.075 |
0.01 |
0. |
0. |
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 |
C |
C |
F |
F(-1) |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 655 | 655 | 89 | 68 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.14 | 0.1 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.514 |
0.078 |
0.01 |
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 |
A |
A |
A |
A |
A |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 46 | 46 | 46 | 38 | 50 | 59 | 42 | 50 | 0 |
normalized size | 1 | 1. | 1. | 0.83 | 1.09 | 1.28 | 0.91 | 1.09 | 0. |
time (sec) |
N/A |
0.124 |
0.025 |
0.004 |
0.817 |
0.257 |
0.286 |
0.269 |
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 |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 31 | 25 | 32 | 38 | 32 | 32 | 29 |
normalized size | 1 | 1. | 1. | 0.81 | 1.03 | 1.23 | 1.03 | 1.03 | 0.94 |
time (sec) |
N/A |
0.083 |
0.012 |
0.004 |
0.817 |
0.272 |
0.269 |
0.271 |
14.248 |
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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 | 39 | 39 | 39 | 33 | 43 | 49 | 37 | 43 | 34 |
normalized size | 1 | 1. | 1. | 0.85 | 1.1 | 1.26 | 0.95 | 1.1 | 0.87 |
time (sec) |
N/A |
0.087 |
0.013 |
0.004 |
0.816 |
0.26 |
0.298 |
0.274 |
13.659 |
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Problem 23 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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grade |
A |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 44 | 35 | 51 | 58 | 41 | 47 | 41 |
normalized size | 1 | 1. | 1.07 | 0.85 | 1.24 | 1.41 | 1. | 1.15 | 1. |
time (sec) |
N/A |
0.115 |
0.02 |
0.008 |
0.819 |
0.27 |
0.34 |
0.288 |
15.463 |
|
|
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Problem 24 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 31 | 31 | 45 | 25 | 32 | 41 | 36 | 32 | 32 |
normalized size | 1 | 1. | 1.45 | 0.81 | 1.03 | 1.32 | 1.16 | 1.03 | 1.03 |
time (sec) |
N/A |
0.102 |
0.02 |
0.006 |
0.817 |
0.254 |
0.376 |
0.275 |
14.516 |
|
|
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Problem 25 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 418 | 418 | 47 | 46 | 0 | 886 | 31 | 867 | 340 |
normalized size | 1 | 1. | 0.11 | 0.11 | 0. | 2.12 | 0.07 | 2.07 | 0.81 |
time (sec) |
N/A |
1.124 |
0.019 |
0.009 |
0. |
0.272 |
0.482 |
0.293 |
131.602 |
|
|
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Problem 26 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 382 | 382 | 48 | 44 | 0 | 1447 | 32 | 1 | 340 |
normalized size | 1 | 1. | 0.13 | 0.12 | 0. | 3.79 | 0.08 | 0. | 0.89 |
time (sec) |
N/A |
0.778 |
0.02 |
0.008 |
0. |
0.282 |
0.492 |
0.286 |
125.338 |
|
|
|
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Problem 27 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 378 | 378 | 46 | 41 | 0 | 884 | 24 | 853 | 337 |
normalized size | 1 | 1. | 0.12 | 0.11 | 0. | 2.34 | 0.06 | 2.26 | 0.89 |
time (sec) |
N/A |
0.635 |
0.019 |
0.007 |
0. |
0.277 |
0.478 |
0.286 |
101.496 |
|
|
|
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|
Problem 28 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 55 | 44 | 0 | 1415 | 22 | 1 | 352 |
normalized size | 1 | 1. | 0.13 | 0.11 | 0. | 3.44 | 0.05 | 0. | 0.86 |
time (sec) |
N/A |
0.682 |
0.018 |
0.006 |
0. |
0.276 |
0.489 |
0.285 |
105.392 |
|
|
|
|
|
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|
Problem 29 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 411 | 411 | 57 | 44 | 0 | 873 | 26 | 860 | 352 |
normalized size | 1 | 1. | 0.14 | 0.11 | 0. | 2.12 | 0.06 | 2.09 | 0.86 |
time (sec) |
N/A |
0.693 |
0.017 |
0.007 |
0. |
0.286 |
0.483 |
0.315 |
103.32 |
|
|
|
|
|
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|
Problem 30 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 416 | 416 | 47 | 46 | 0 | 1463 | 31 | 1 | 338 |
normalized size | 1 | 1. | 0.11 | 0.11 | 0. | 3.52 | 0.07 | 0. | 0.81 |
time (sec) |
N/A |
0.697 |
0.02 |
0.01 |
0. |
0.282 |
0.549 |
0.295 |
108.539 |
|
|
|
|
|
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|
|
Problem 31 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 418 | 418 | 47 | 46 | 0 | 930 | 32 | 867 | 342 |
normalized size | 1 | 1. | 0.11 | 0.11 | 0. | 2.22 | 0.08 | 2.07 | 0.82 |
time (sec) |
N/A |
0.854 |
0.02 |
0.009 |
0. |
0.28 |
0.562 |
0.298 |
129.123 |
|
|
|
|
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|
|
Problem 32 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 36 | 36 | 37 | 33 | 43 | 49 | 37 | 43 | 34 |
normalized size | 1 | 1. | 1.03 | 0.92 | 1.19 | 1.36 | 1.03 | 1.19 | 0.94 |
time (sec) |
N/A |
0.091 |
0.014 |
0.003 |
0.827 |
0.259 |
0.285 |
0.279 |
11.439 |
|
|
|
|
|
|
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|
Problem 33 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 55 | 35 | 51 | 58 | 41 | 47 | 41 |
normalized size | 1 | 1. | 1.41 | 0.9 | 1.31 | 1.49 | 1.05 | 1.21 | 1.05 |
time (sec) |
N/A |
0.117 |
0.021 |
0.008 |
0.82 |
0.276 |
0.328 |
0.272 |
16.682 |
|
|
|
|
|
|
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|
Problem 34 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 55 | 35 | 0 | 58 | 41 | 47 | 41 |
normalized size | 1 | 1. | 1.41 | 0.9 | 0. | 1.49 | 1.05 | 1.21 | 1.05 |
time (sec) |
N/A |
0.114 |
0.016 |
0.006 |
0. |
0.253 |
0.326 |
0.273 |
18.013 |
|
|
|
|
|
|
|
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|
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|
|
Problem 35 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 396 | 396 | 279 | 1070 | 0 | 0 | 400 | 0 | 379 |
normalized size | 1 | 1. | 0.7 | 2.7 | 0. | 0. | 1.01 | 0. | 0.96 |
time (sec) |
N/A |
0.774 |
0.582 |
0.203 |
0. |
0. |
25.683 |
0. |
46.905 |
|
|
|
|
|
|
|
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|
|
Problem 36 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 356 | 356 | 249 | 1010 | 0 | 0 | 257 | 0 | 337 |
normalized size | 1 | 1. | 0.7 | 2.84 | 0. | 0. | 0.72 | 0. | 0.95 |
time (sec) |
N/A |
0.602 |
0.524 |
0.045 |
0. |
0. |
13.534 |
0. |
39.809 |
|
|
|
|
|
|
|
|
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|
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|
|
|
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|
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|
|
Problem 37 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 316 | 316 | 219 | 956 | 0 | 0 | 124 | 0 | 294 |
normalized size | 1 | 1. | 0.69 | 3.03 | 0. | 0. | 0.39 | 0. | 0.93 |
time (sec) |
N/A |
0.504 |
0.476 |
0.044 |
0. |
0. |
6.816 |
0. |
33.445 |
|
|
|
|
|
|
|
|
|
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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 |
B |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 194 | 907 | 0 | 0 | 119 | 0 | 253 |
normalized size | 1 | 1. | 0.7 | 3.26 | 0. | 0. | 0.43 | 0. | 0.91 |
time (sec) |
N/A |
0.37 |
0.606 |
0.044 |
0. |
0. |
6.305 |
0. |
27.432 |
|
|
|
|
|
|
|
|
|
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|
|
Problem 39 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
A |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 289 | 289 | 197 | 934 | 0 | 0 | 119 | 0 | 262 |
normalized size | 1 | 1. | 0.68 | 3.23 | 0. | 0. | 0.41 | 0. | 0.91 |
time (sec) |
N/A |
0.402 |
0.456 |
0.06 |
0. |
0. |
59.45 |
0. |
42.235 |
|
|
|
|
|
|
|
|
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|
|
Problem 40 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 309 | 309 | 224 | 1005 | 0 | 0 | 0 | 0 | 286 |
normalized size | 1 | 1. | 0.72 | 3.25 | 0. | 0. | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.438 |
0.674 |
0.07 |
0. |
0. |
0. |
0. |
43.763 |
|
|
|
|
|
|
|
|
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|
|
Problem 41 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 349 | 349 | 262 | 1095 | 0 | 0 | 0 | 0 | 328 |
normalized size | 1 | 1. | 0.75 | 3.14 | 0. | 0. | 0. | 0. | 0.94 |
time (sec) |
N/A |
0.642 |
0.838 |
0.074 |
0. |
0. |
0. |
0. |
50.55 |
|
|
|
|
|
|
|
|
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|
|
Problem 42 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 389 | 389 | 296 | 1182 | 0 | 0 | 0 | 0 | 371 |
normalized size | 1 | 1. | 0.76 | 3.04 | 0. | 0. | 0. | 0. | 0.95 |
time (sec) |
N/A |
0.737 |
1.032 |
0.078 |
0. |
0. |
0. |
0. |
57.496 |
|
|
|
|
|
|
|
|
|
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|
|
Problem 43 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 433 | 433 | 88 | 67 | 0 | 17662 | 0 | 0 | 432 |
normalized size | 1 | 1. | 0.2 | 0.15 | 0. | 40.79 | 0. | 0. | 1. |
time (sec) |
N/A |
2.402 |
0.104 |
0.007 |
0. |
4.467 |
0. |
0. |
169.92 |
|
|
|
|
|
|
|
|
|
|
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|
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|
|
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|
|
Problem 44 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 72 | 72 | 71 | 99 | 0 | 1 | 287 | 95 | 63 |
normalized size | 1 | 1. | 0.99 | 1.38 | 0. | 0.01 | 3.99 | 1.32 | 0.88 |
time (sec) |
N/A |
0.177 |
0.098 |
0.004 |
0. |
0.395 |
24.314 |
0.276 |
24.648 |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 45 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 375 | 375 | 59 | 51 | 0 | 19648 | 0 | 0 | 379 |
normalized size | 1 | 1. | 0.16 | 0.14 | 0. | 52.39 | 0. | 0. | 1.01 |
time (sec) |
N/A |
0.948 |
0.064 |
0.005 |
0. |
16.728 |
0. |
0. |
119.001 |
|
|
|
|
|
|
|
|
|
|
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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 |
B |
F |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 184 | 184 | 179 | 340 | 0 | 2072 | 0 | 1 | 189 |
normalized size | 1 | 1. | 0.97 | 1.85 | 0. | 11.26 | 0. | 0.01 | 1.03 |
time (sec) |
N/A |
0.421 |
0.286 |
0.023 |
0. |
0.398 |
0. |
0.998 |
54.637 |
|
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Problem 47 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 375 | 375 | 61 | 47 | 0 | 12872 | 0 | 0 | 379 |
normalized size | 1 | 1. | 0.16 | 0.13 | 0. | 34.33 | 0. | 0. | 1.01 |
time (sec) |
N/A |
0.804 |
0.066 |
0.009 |
0. |
1.842 |
0. |
0. |
113.172 |
|
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Problem 48 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 78 | 78 | 80 | 106 | 0 | 1 | 0 | 105 | 73 |
normalized size | 1 | 1. | 1.03 | 1.36 | 0. | 0.01 | 0. | 1.35 | 0.94 |
time (sec) |
N/A |
0.278 |
0.057 |
0.009 |
0. |
0.862 |
0. |
0.282 |
36.743 |
|
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Problem 49 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 392 | 392 | 85 | 72 | 0 | 0 | 0 | 0 | 391 |
normalized size | 1 | 1. | 0.22 | 0.18 | 0. | 0. | 0. | 0. | 1. |
time (sec) |
N/A |
1.458 |
0.089 |
0.01 |
0. |
0. |
0. |
0. |
160.037 |
|
|
|
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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) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 199 | 199 | 89 | 365 | 0 | 3742 | 0 | 1 | 201 |
normalized size | 1 | 1. | 0.45 | 1.83 | 0. | 18.8 | 0. | 0.01 | 1.01 |
time (sec) |
N/A |
0.697 |
0.074 |
0.025 |
0. |
0.835 |
0. |
0.495 |
84.805 |
|
|
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Problem 51 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
F(-1) |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 394 | 394 | 86 | 68 | 0 | 0 | 0 | 0 | 394 |
normalized size | 1 | 1. | 0.22 | 0.17 | 0. | 0. | 0. | 0. | 1. |
time (sec) |
N/A |
1.386 |
0.099 |
0.009 |
0. |
0. |
0. |
0. |
153.716 |
|
|
|
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Problem 52 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 278 | 278 | 46 | 34 | 0 | 261 | 170 | 281 | 530 |
normalized size | 1 | 1. | 0.17 | 0.12 | 0. | 0.94 | 0.61 | 1.01 | 1.91 |
time (sec) |
N/A |
0.662 |
0.025 |
0.01 |
0. |
0.263 |
0.652 |
0.279 |
80.625 |
|
|
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Problem 53 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 39 | 39 | 39 | 33 | 43 | 49 | 37 | 43 | 34 |
normalized size | 1 | 1. | 1. | 0.85 | 1.1 | 1.26 | 0.95 | 1.1 | 0.87 |
time (sec) |
N/A |
0.092 |
0.02 |
0.005 |
0.826 |
0.253 |
0.329 |
0.273 |
14.054 |
|
|
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|
Problem 54 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 355 | 355 | 55 | 46 | 0 | 1223 | 27 | 342 | 481 |
normalized size | 1 | 1. | 0.15 | 0.13 | 0. | 3.45 | 0.08 | 0.96 | 1.35 |
time (sec) |
N/A |
0.717 |
0.024 |
0.01 |
0. |
0.282 |
4.618 |
0.283 |
102.214 |
|
|
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Problem 55 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 50 | 50 | 44 | 39 | 0 | 59 | 42 | 42 | 42 |
normalized size | 1 | 1. | 0.88 | 0.78 | 0. | 1.18 | 0.84 | 0.84 | 0.84 |
time (sec) |
N/A |
0.08 |
0.026 |
0.015 |
0. |
0.248 |
0.289 |
0.286 |
20.258 |
|
|
|
|
|
|
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|
Problem 56 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 355 | 355 | 57 | 44 | 0 | 1223 | 26 | 342 | 495 |
normalized size | 1 | 1. | 0.16 | 0.12 | 0. | 3.45 | 0.07 | 0.96 | 1.39 |
time (sec) |
N/A |
0.506 |
0.021 |
0.001 |
0. |
0.28 |
4.641 |
0.306 |
78.633 |
|
|
|
|
|
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Problem 57 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 41 | 41 | 44 | 35 | 51 | 58 | 41 | 51 | 41 |
normalized size | 1 | 1. | 1.07 | 0.85 | 1.24 | 1.41 | 1. | 1.24 | 1. |
time (sec) |
N/A |
0.117 |
0.021 |
0.009 |
0.822 |
0.251 |
0.386 |
0.303 |
16.454 |
|
|
|
|
|
|
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|
|
Problem 58 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 280 | 280 | 47 | 38 | 0 | 284 | 168 | 284 | 512 |
normalized size | 1 | 1. | 0.17 | 0.14 | 0. | 1.01 | 0.6 | 1.01 | 1.83 |
time (sec) |
N/A |
0.536 |
0.023 |
0.013 |
0. |
0.274 |
0.696 |
0.312 |
84.449 |
|
|
|
|
|
|
|
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|
|
Problem 59 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
A |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 89 | 89 | 49 | 70 | 0 | 188 | 76 | 348 | 76 |
normalized size | 1 | 1. | 0.55 | 0.79 | 0. | 2.11 | 0.85 | 3.91 | 0.85 |
time (sec) |
N/A |
0.189 |
0.024 |
0.007 |
0. |
0.268 |
0.698 |
0.349 |
40.017 |
|
|
|
|
|
|
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|
|
Problem 60 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
C |
F |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 370 | 370 | 47 | 46 | 0 | 1197 | 32 | 348 | 318 |
normalized size | 1 | 1. | 0.13 | 0.12 | 0. | 3.24 | 0.09 | 0.94 | 0.86 |
time (sec) |
N/A |
0.612 |
0.022 |
0.014 |
0. |
0.299 |
4.69 |
0.294 |
77.103 |
|
|
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|
Problem 61 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
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 | 280 | 280 | 283 | 662 | 0 | 1 | 0 | 398 | 0 |
normalized size | 1 | 1. | 1.01 | 2.36 | 0. | 0. | 0. | 1.42 | 0. |
time (sec) |
N/A |
1.207 |
0.405 |
0.018 |
0. |
28.978 |
0. |
0.291 |
0. |
|
|
|
|
|
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|
Problem 62 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
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 | 218 | 218 | 218 | 512 | 0 | 1 | 0 | 302 | 0 |
normalized size | 1 | 1. | 1. | 2.35 | 0. | 0. | 0. | 1.39 | 0. |
time (sec) |
N/A |
0.794 |
0.308 |
0.012 |
0. |
17.944 |
0. |
0.296 |
0. |
|
|
|
|
|
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|
Problem 63 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 176 | 176 | 178 | 388 | 0 | 1 | 0 | 250 | 0 |
normalized size | 1 | 1. | 1.01 | 2.2 | 0. | 0.01 | 0. | 1.42 | 0. |
time (sec) |
N/A |
0.535 |
0.32 |
0.011 |
0. |
5.411 |
0. |
0.314 |
0. |
|
|
|
|
|
|
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|
Problem 64 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 149 | 149 | 132 | 275 | 0 | 1 | 0 | 201 | 129 |
normalized size | 1 | 1. | 0.89 | 1.85 | 0. | 0.01 | 0. | 1.35 | 0.87 |
time (sec) |
N/A |
0.399 |
0.211 |
0.009 |
0. |
1.627 |
0. |
0.301 |
80.285 |
|
|
|
|
|
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|
Problem 65 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 124 | 124 | 107 | 169 | 0 | 1 | 0 | 171 | 112 |
normalized size | 1 | 1. | 0.86 | 1.36 | 0. | 0.01 | 0. | 1.38 | 0.9 |
time (sec) |
N/A |
0.323 |
0.129 |
0.007 |
0. |
0.528 |
0. |
0.299 |
62.253 |
|
|
|
|
|
|
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|
Problem 66 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 123 | 123 | 105 | 168 | 0 | 1 | 0 | 170 | 112 |
normalized size | 1 | 1. | 0.85 | 1.37 | 0. | 0.01 | 0. | 1.38 | 0.91 |
time (sec) |
N/A |
0.28 |
0.135 |
0.007 |
0. |
0.546 |
0. |
0.297 |
60.69 |
|
|
|
|
|
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|
|
Problem 67 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
F(-1) |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 159 | 152 | 285 | 0 | 0 | 0 | 221 | 136 |
normalized size | 1 | 1.01 | 0.96 | 1.8 | 0. | 0. | 0. | 1.4 | 0.86 |
time (sec) |
N/A |
0.553 |
0.34 |
0.011 |
0. |
0. |
0. |
0.294 |
99.804 |
|
|
|
|
|
|
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|
|
Problem 68 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
F(-1) |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 193 | 193 | 194 | 412 | 0 | 0 | 0 | 284 | 178 |
normalized size | 1 | 1. | 1.01 | 2.13 | 0. | 0. | 0. | 1.47 | 0.92 |
time (sec) |
N/A |
0.714 |
0.286 |
0.017 |
0. |
0. |
0. |
0.302 |
137.446 |
|
|
|
|
|
|
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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(-2) |
F(-1) |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 252 | 252 | 252 | 562 | 0 | 0 | 0 | 377 | 0 |
normalized size | 1 | 1. | 1. | 2.23 | 0. | 0. | 0. | 1.5 | 0. |
time (sec) |
N/A |
0.913 |
0.377 |
0.018 |
0. |
0. |
0. |
0.3 |
0. |
|
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Problem 70 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
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 | 343 | 343 | 338 | 943 | 0 | 1 | 0 | 763 | 0 |
normalized size | 1 | 1. | 0.99 | 2.75 | 0. | 0. | 0. | 2.22 | 0. |
time (sec) |
N/A |
1.804 |
0.658 |
0.02 |
0. |
118.759 |
0. |
0.303 |
0. |
|
|
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Problem 71 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
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 | 274 | 274 | 269 | 765 | 0 | 1 | 0 | 643 | 0 |
normalized size | 1 | 1. | 0.98 | 2.79 | 0. | 0. | 0. | 2.35 | 0. |
time (sec) |
N/A |
1.104 |
0.545 |
0.016 |
0. |
50.476 |
0. |
0.3 |
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) |
A |
F(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 246 | 246 | 207 | 580 | 0 | 1 | 0 | 556 | 0 |
normalized size | 1 | 1. | 0.84 | 2.36 | 0. | 0. | 0. | 2.26 | 0. |
time (sec) |
N/A |
0.834 |
0.407 |
0.014 |
0. |
17.632 |
0. |
0.284 |
0. |
|
|
|
|
|
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Problem 73 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 159 | 389 | 0 | 1 | 0 | 455 | 177 |
normalized size | 1 | 1. | 0.82 | 2.01 | 0. | 0.01 | 0. | 2.35 | 0.91 |
time (sec) |
N/A |
0.559 |
0.406 |
0.013 |
0. |
6.045 |
0. |
0.273 |
146.522 |
|
|
|
|
|
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Problem 74 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 183 | 183 | 148 | 328 | 0 | 1 | 0 | 441 | 167 |
normalized size | 1 | 1. | 0.81 | 1.79 | 0. | 0.01 | 0. | 2.41 | 0.91 |
time (sec) |
N/A |
0.508 |
0.441 |
0.012 |
0. |
5.23 |
0. |
0.277 |
103.401 |
|
|
|
|
|
|
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Problem 75 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 189 | 189 | 151 | 386 | 0 | 1 | 0 | 447 | 177 |
normalized size | 1 | 1. | 0.8 | 2.04 | 0. | 0.01 | 0. | 2.37 | 0.94 |
time (sec) |
N/A |
0.648 |
0.384 |
0.013 |
0. |
2.751 |
0. |
0.29 |
150.937 |
|
|
|
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Problem 76 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
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 | 248 | 249 | 246 | 589 | 0 | 0 | 0 | 528 | 0 |
normalized size | 1 | 1. | 0.99 | 2.38 | 0. | 0. | 0. | 2.13 | 0. |
time (sec) |
N/A |
0.849 |
0.477 |
0.019 |
0. |
0. |
0. |
0.297 |
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(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 291 | 291 | 287 | 791 | 0 | 0 | 0 | 657 | 0 |
normalized size | 1 | 1. | 0.99 | 2.72 | 0. | 0. | 0. | 2.26 | 0. |
time (sec) |
N/A |
1.202 |
0.658 |
0.023 |
0. |
0. |
0. |
0.284 |
0. |
|
|
|
|
|
|
|
|
|
|
|
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|
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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(-1) |
A |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 372 | 372 | 370 | 993 | 0 | 0 | 0 | 792 | 0 |
normalized size | 1 | 1. | 0.99 | 2.67 | 0. | 0. | 0. | 2.13 | 0. |
time (sec) |
N/A |
1.887 |
0.779 |
0.026 |
0. |
0. |
0. |
0.29 |
0. |
|
|
|
|
|
|
|
|
|
|
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|
Problem 79 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 981 | 981 | 10904 | 11938 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 11.12 | 12.17 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
10.135 |
14.785 |
0.169 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 80 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 778 | 778 | 7531 | 9182 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 9.68 | 11.8 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
4.665 |
14.221 |
0.074 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 81 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 636 | 636 | 5350 | 6302 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 8.41 | 9.91 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.514 |
13.577 |
0.06 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
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|
Problem 82 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F |
F(-1) |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 550 | 550 | 3390 | 4361 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 6.16 | 7.93 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.735 |
13.161 |
0.059 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 83 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 955 | 955 | 758 | 3023 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0.79 | 3.17 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
7.743 |
13.112 |
0.06 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
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|
Problem 84 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
C |
B |
F |
F(-1) |
F |
F(-1) |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 929 | 929 | 4893 | 3553 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 5.27 | 3.82 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
7.193 |
13.119 |
0.066 |
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 |
C |
B |
F |
F(-1) |
F(-1) |
F(-1) |
F |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 1287 | 1287 | 6206 | 4957 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 4.82 | 3.85 | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
13.636 |
13.607 |
0.071 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
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|
Problem 86 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.053 |
0.245 |
0.647 |
0. |
0. |
0. |
0. |
0. |
|
|
|
|
|
|
|
|
|
|
|
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|
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|
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|
|
Problem 87 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 358 | 358 | 249 | 0 | 0 | 0 | 0 | 0 | 320 |
normalized size | 1 | 1. | 0.7 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
0.507 |
0.686 |
0.113 |
0. |
0. |
0. |
0. |
65.938 |
|
|
|
|
|
|
|
|
|
|
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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 |
F |
F |
F |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 189 | 0 | 0 | 0 | 0 | 0 | 228 |
normalized size | 1 | 1. | 0.72 | 0. | 0. | 0. | 0. | 0. | 0.87 |
time (sec) |
N/A |
0.348 |
0.335 |
0.119 |
0. |
0. |
0. |
0. |
46.79 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
Problem 89 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 166 | 166 | 136 | 0 | 0 | 0 | 0 | 0 | 136 |
normalized size | 1 | 1. | 0.82 | 0. | 0. | 0. | 0. | 0. | 0.82 |
time (sec) |
N/A |
0.216 |
0.148 |
0.105 |
0. |
0. |
0. |
0. |
27.471 |
|
|
|
|
|
|
|
|
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|
|
Problem 90 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 0 | 0 | 0 | 0 | 0 | 0 | 162 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.84 |
time (sec) |
N/A |
0.504 |
0.096 |
0.131 |
0. |
0. |
0. |
0. |
88.172 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Problem 91 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 302 | 302 | 0 | 0 | 0 | 0 | 0 | 0 | 258 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.85 |
time (sec) |
N/A |
0.763 |
0.195 |
0.131 |
0. |
0. |
0. |
0. |
155.763 |
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Problem 92 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 412 | 412 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
1.054 |
0.879 |
0.131 |
0. |
0. |
0. |
0. |
0. |
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Problem 93 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 201 | 46548 | 19 | 1 | 1326 | 1 | 12 |
normalized size | 1 | 1. | 12.56 | 2909.25 | 1.19 | 0.06 | 82.88 | 0.06 | 0.75 |
time (sec) |
N/A |
0.035 |
0.273 |
0.007 |
0.767 |
0.264 |
0.967 |
0.267 |
3.672 |
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Problem 94 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 233 | 46552 | 1674 | 1 | 1384 | 1 | 14 |
normalized size | 1 | 1. | 12.94 | 2586.22 | 93. | 0.06 | 76.89 | 0.06 | 0.78 |
time (sec) |
N/A |
0.066 |
0.287 |
0.004 |
0.793 |
0.277 |
0.916 |
0.275 |
4.946 |
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Problem 95 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 233 | 46552 | 1674 | 1 | 1394 | 1 | 14 |
normalized size | 1 | 1. | 12.94 | 2586.22 | 93. | 0.06 | 77.44 | 0.06 | 0.78 |
time (sec) |
N/A |
0.07 |
0.287 |
0.004 |
0.78 |
0.266 |
0.924 |
0.277 |
4.991 |
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Problem 96 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 260 | 2042 | 0 | 1751 | 0 | 1 | 17 |
normalized size | 1 | 1. | 11.3 | 88.78 | 0. | 76.13 | 0. | 0.04 | 0.74 |
time (sec) |
N/A |
0.069 |
0.727 |
0.099 |
0. |
0.334 |
0. |
0.326 |
14.23 |
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Problem 97 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 201 | 47685 | 22 | 1 | 1326 | 1 | 12 |
normalized size | 1 | 1. | 11.17 | 2649.17 | 1.22 | 0.06 | 73.67 | 0.06 | 0.67 |
time (sec) |
N/A |
0.035 |
0.302 |
0.007 |
0.77 |
0.259 |
0.956 |
0.269 |
4.022 |
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Problem 98 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 233 | 47688 | 1677 | 1 | 1384 | 1 | 14 |
normalized size | 1 | 1. | 11.65 | 2384.4 | 83.85 | 0.05 | 69.2 | 0.05 | 0.7 |
time (sec) |
N/A |
0.066 |
0.304 |
0.004 |
0.787 |
0.259 |
0.947 |
0.275 |
5.445 |
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Problem 99 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 233 | 47688 | 1677 | 1 | 1394 | 1 | 14 |
normalized size | 1 | 1. | 11.65 | 2384.4 | 83.85 | 0.05 | 69.7 | 0.05 | 0.7 |
time (sec) |
N/A |
0.07 |
0.315 |
0.004 |
0.791 |
0.259 |
0.948 |
0.274 |
5.487 |
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Problem 100 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 260 | 2046 | 0 | 1754 | 0 | 1 | 17 |
normalized size | 1 | 1. | 10.4 | 81.84 | 0. | 70.16 | 0. | 0.04 | 0.68 |
time (sec) |
N/A |
0.072 |
0.661 |
0.097 |
0. |
0.329 |
0. |
0.327 |
15.756 |
|
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Problem 101 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 172 | 155 | 18 | 1 | 175 | 208 | 10 |
normalized size | 1 | 1. | 11.47 | 10.33 | 1.2 | 0.07 | 11.67 | 13.87 | 0.67 |
time (sec) |
N/A |
0.013 |
0.009 |
0.004 |
0.771 |
0.255 |
0.267 |
0.262 |
3.189 |
|
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Problem 102 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 182 | 157 | 211 | 1 | 182 | 211 | 12 |
normalized size | 1 | 1. | 10.71 | 9.24 | 12.41 | 0.06 | 10.71 | 12.41 | 0.71 |
time (sec) |
N/A |
0.02 |
0.009 |
0.004 |
0.765 |
0.253 |
0.278 |
0.263 |
13.301 |
|
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Problem 103 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 186 | 157 | 211 | 1 | 185 | 211 | 12 |
normalized size | 1 | 1. | 10.94 | 9.24 | 12.41 | 0.06 | 10.88 | 12.41 | 0.71 |
time (sec) |
N/A |
0.021 |
0.01 |
0.004 |
0.771 |
0.269 |
0.283 |
0.269 |
12.684 |
|
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Problem 104 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 21 | 230 | 0 | 255 | 0 | 255 | 15 |
normalized size | 1 | 1. | 1. | 10.95 | 0. | 12.14 | 0. | 12.14 | 0.71 |
time (sec) |
N/A |
0.062 |
0.054 |
0.057 |
0. |
0.316 |
0. |
0.27 |
12.011 |
|
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Problem 105 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 11 | 11 | 10 | 12 | 15 | 15 | 10 | 15 | 10 |
normalized size | 1 | 1. | 0.91 | 1.09 | 1.36 | 1.36 | 0.91 | 1.36 | 0.91 |
time (sec) |
N/A |
0.008 |
0.005 |
0.002 |
0.773 |
0.279 |
1.164 |
0.265 |
3.699 |
|
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Problem 106 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 16 | 20 | 20 | 14 | 20 | 14 |
normalized size | 1 | 1. | 1. | 0.94 | 1.18 | 1.18 | 0.82 | 1.18 | 0.82 |
time (sec) |
N/A |
0.011 |
0.01 |
0.002 |
0.768 |
0.271 |
1.593 |
0.291 |
4.943 |
|
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Problem 107 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 17 | 16 | 20 | 20 | 14 | 20 | 14 |
normalized size | 1 | 1. | 1. | 0.94 | 1.18 | 1.18 | 0.82 | 1.18 | 0.82 |
time (sec) |
N/A |
0.011 |
0.011 |
0.002 |
0.772 |
0.282 |
1.989 |
0.266 |
4.995 |
|
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Problem 108 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 26 | 24 | 31 | 26 | 0 | 26 | 15 |
normalized size | 1 | 1. | 1.37 | 1.26 | 1.63 | 1.37 | 0. | 1.37 | 0.79 |
time (sec) |
N/A |
0.067 |
0.049 |
0.033 |
0.826 |
0.297 |
0. |
0.266 |
12.138 |
|
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Problem 109 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 15 | 15 | 19 | 473 | 0 | 19 | 15 |
normalized size | 1 | 1. | 0.94 | 0.94 | 1.19 | 29.56 | 0. | 1.19 | 0.94 |
time (sec) |
N/A |
0.009 |
0.018 |
0.001 |
0.763 |
0.328 |
0. |
0.275 |
3.666 |
|
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Problem 110 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 18 | 17 | 475 | 475 | 0 | 0 | 17 |
normalized size | 1 | 1. | 1. | 0.94 | 26.39 | 26.39 | 0. | 0. | 0.94 |
time (sec) |
N/A |
0.012 |
0.02 |
0.002 |
0.858 |
0.372 |
0. |
0. |
4.957 |
|
|
|
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|
Problem 111 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 18 | 17 | 475 | 475 | 0 | 22 | 17 |
normalized size | 1 | 1. | 1. | 0.94 | 26.39 | 26.39 | 0. | 1.22 | 0.94 |
time (sec) |
N/A |
0.013 |
0.021 |
0.001 |
0.877 |
0.363 |
0. |
0.359 |
5.006 |
|
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Problem 112 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 23 | 23 | 23 | 22 | 562 | 532 | 0 | 28 | 20 |
normalized size | 1 | 1. | 1. | 0.96 | 24.43 | 23.13 | 0. | 1.22 | 0.87 |
time (sec) |
N/A |
0.072 |
0.082 |
0.095 |
1.214 |
0.363 |
0. |
0.282 |
12.267 |
|
|
|
|
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|
Problem 113 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 13 | 13 | 12 | 14 | 18 | 18 | 10 | 18 | 10 |
normalized size | 1 | 1. | 0.92 | 1.08 | 1.38 | 1.38 | 0.77 | 1.38 | 0.77 |
time (sec) |
N/A |
0.009 |
0.008 |
0.002 |
0.751 |
0.274 |
1.185 |
0.265 |
4.012 |
|
|
|
|
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Problem 114 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 18 | 23 | 23 | 14 | 23 | 14 |
normalized size | 1 | 1. | 1. | 0.95 | 1.21 | 1.21 | 0.74 | 1.21 | 0.74 |
time (sec) |
N/A |
0.01 |
0.01 |
0.001 |
0.744 |
0.254 |
1.597 |
0.291 |
5.4 |
|
|
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Problem 115 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 19 | 18 | 23 | 23 | 14 | 23 | 14 |
normalized size | 1 | 1. | 1. | 0.95 | 1.21 | 1.21 | 0.74 | 1.21 | 0.74 |
time (sec) |
N/A |
0.01 |
0.011 |
0.002 |
0.759 |
0.256 |
1.938 |
0.267 |
5.427 |
|
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Problem 116 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 29 | 26 | 34 | 28 | 0 | 28 | 15 |
normalized size | 1 | 1. | 1.38 | 1.24 | 1.62 | 1.33 | 0. | 1.33 | 0.71 |
time (sec) |
N/A |
0.073 |
0.048 |
0.033 |
0.853 |
0.312 |
0. |
0.267 |
12.904 |
|
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Problem 117 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 18 | 18 | 16 | 17 | 22 | 478 | 0 | 22 | 15 |
normalized size | 1 | 1. | 0.89 | 0.94 | 1.22 | 26.56 | 0. | 1.22 | 0.83 |
time (sec) |
N/A |
0.011 |
0.021 |
0.001 |
0.757 |
0.322 |
0. |
0.275 |
4.02 |
|
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Problem 118 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
F(-2) |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 19 | 481 | 481 | 0 | 0 | 15 |
normalized size | 1 | 1. | 1. | 0.95 | 24.05 | 24.05 | 0. | 0. | 0.75 |
time (sec) |
N/A |
0.012 |
0.027 |
0.001 |
0.84 |
0.334 |
0. |
0. |
5.426 |
|
|
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Problem 119 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 20 | 19 | 481 | 481 | 0 | 24 | 15 |
normalized size | 1 | 1. | 1. | 0.95 | 24.05 | 24.05 | 0. | 1.2 | 0.75 |
time (sec) |
N/A |
0.014 |
0.028 |
0.001 |
0.875 |
0.335 |
0. |
0.363 |
5.482 |
|
|
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Problem 120 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 25 | 24 | 566 | 536 | 0 | 31 | 19 |
normalized size | 1 | 1. | 1. | 0.96 | 22.64 | 21.44 | 0. | 1.24 | 0.76 |
time (sec) |
N/A |
0.076 |
0.091 |
0.096 |
1.228 |
0.348 |
0. |
0.281 |
13.299 |
|
|
|
|
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Problem 121 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 10 | 10 | 9 | 9 | 14 | 14 | 8 | 15 | 8 |
normalized size | 1 | 1. | 0.9 | 0.9 | 1.4 | 1.4 | 0.8 | 1.5 | 0.8 |
time (sec) |
N/A |
0.008 |
0.006 |
0.002 |
0.741 |
0.256 |
1.071 |
0.263 |
3.172 |
|
|
|
|
|
|
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|
Problem 122 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 15 | 14 | 23 | 18 | 12 | 20 | 15 |
normalized size | 1 | 1. | 0.94 | 0.88 | 1.44 | 1.12 | 0.75 | 1.25 | 0.94 |
time (sec) |
N/A |
0.009 |
0.01 |
0.007 |
0.751 |
0.282 |
1.234 |
0.264 |
11.581 |
|
|
|
|
|
|
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|
Problem 123 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 16 | 16 | 15 | 14 | 23 | 18 | 12 | 20 | 15 |
normalized size | 1 | 1. | 0.94 | 0.88 | 1.44 | 1.12 | 0.75 | 1.25 | 0.94 |
time (sec) |
N/A |
0.01 |
0.011 |
0.007 |
0.746 |
0.259 |
1.296 |
0.265 |
10.867 |
|
|
|
|
|
|
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|
Problem 124 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 15 | 18 | 63 | 23 | 0 | 23 | 36 |
normalized size | 1 | 1. | 1. | 1.2 | 4.2 | 1.53 | 0. | 1.53 | 2.4 |
time (sec) |
N/A |
0.071 |
0.018 |
0.03 |
0.766 |
0.295 |
0. |
0.265 |
13.224 |
|
|
|
|
|
|
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|
Problem 125 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 15 | 15 | 14 | 177 | 18 | 109 | 87 | 18 | 14 |
normalized size | 1 | 1. | 0.93 | 11.8 | 1.2 | 7.27 | 5.8 | 1.2 | 0.93 |
time (sec) |
N/A |
0.008 |
0.034 |
0.028 |
0.745 |
0.259 |
17.628 |
0.267 |
3.184 |
|
|
|
|
|
|
|
|
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|
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|
Problem 126 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 16 | 197 | 109 | 109 | 0 | 20 | 15 |
normalized size | 1 | 1. | 0.94 | 11.59 | 6.41 | 6.41 | 0. | 1.18 | 0.88 |
time (sec) |
N/A |
0.011 |
0.049 |
0.028 |
0.764 |
0.279 |
0. |
0.268 |
13.029 |
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 127 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
B |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 17 | 17 | 16 | 197 | 109 | 109 | 0 | 20 | 15 |
normalized size | 1 | 1. | 0.94 | 11.59 | 6.41 | 6.41 | 0. | 1.18 | 0.88 |
time (sec) |
N/A |
0.011 |
0.059 |
0.021 |
0.767 |
0.274 |
0. |
0.269 |
13.166 |
|
|
|
|
|
|
|
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|
Problem 128 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
B |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 21 | 21 | 127 | 203 | 826 | 142 | 0 | 27 | 19 |
normalized size | 1 | 1. | 6.05 | 9.67 | 39.33 | 6.76 | 0. | 1.29 | 0.9 |
time (sec) |
N/A |
0.063 |
0.079 |
0.086 |
0.798 |
0.354 |
0. |
0.272 |
11.025 |
|
|
|
|
|
|
|
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|
Problem 129 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 20 | 20 | 19 | 21 | 0 | 38 | 0 | 80 | 15 |
normalized size | 1 | 1. | 0.95 | 1.05 | 0. | 1.9 | 0. | 4. | 0.75 |
time (sec) |
N/A |
0.013 |
0.03 |
0.004 |
0. |
0.3 |
0. |
0.269 |
3.991 |
|
|
|
|
|
|
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|
Problem 130 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 24 | 45 | 45 | 0 | 92 | 19 |
normalized size | 1 | 1. | 0.96 | 0.96 | 1.8 | 1.8 | 0. | 3.68 | 0.76 |
time (sec) |
N/A |
0.014 |
0.034 |
0.005 |
0.856 |
0.278 |
0. |
0.272 |
5.556 |
|
|
|
|
|
|
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|
|
Problem 131 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 25 | 25 | 24 | 24 | 45 | 45 | 0 | 92 | 19 |
normalized size | 1 | 1. | 0.96 | 0.96 | 1.8 | 1.8 | 0. | 3.68 | 0.76 |
time (sec) |
N/A |
0.014 |
0.033 |
0.008 |
0.849 |
0.276 |
0. |
0.281 |
5.63 |
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 132 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 26 | 40 | 53 | 51 | 0 | 36 | 20 |
normalized size | 1 | 1. | 0.96 | 1.48 | 1.96 | 1.89 | 0. | 1.33 | 0.74 |
time (sec) |
N/A |
0.069 |
0.087 |
0.089 |
1.035 |
0.285 |
0. |
0.288 |
12.312 |
|
|
|
|
|
|
|
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|
|
Problem 133 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 22 | 22 | 21 | 23 | 0 | 43 | 0 | 89 | 15 |
normalized size | 1 | 1. | 0.95 | 1.05 | 0. | 1.95 | 0. | 4.05 | 0.68 |
time (sec) |
N/A |
0.011 |
0.031 |
0.004 |
0. |
0.281 |
0. |
0.266 |
4.385 |
|
|
|
|
|
|
|
|
|
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|
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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(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 26 | 26 | 50 | 50 | 0 | 101 | 19 |
normalized size | 1 | 1. | 0.96 | 0.96 | 1.85 | 1.85 | 0. | 3.74 | 0.7 |
time (sec) |
N/A |
0.013 |
0.038 |
0.005 |
0.831 |
0.287 |
0. |
0.273 |
6.069 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
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|
|
Problem 135 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 27 | 27 | 26 | 26 | 50 | 50 | 0 | 101 | 19 |
normalized size | 1 | 1. | 0.96 | 0.96 | 1.85 | 1.85 | 0. | 3.74 | 0.7 |
time (sec) |
N/A |
0.014 |
0.038 |
0.007 |
0.844 |
0.279 |
0. |
0.275 |
6.138 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
Problem 136 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 29 | 29 | 28 | 45 | 58 | 57 | 0 | 39 | 20 |
normalized size | 1 | 1. | 0.97 | 1.55 | 2. | 1.97 | 0. | 1.34 | 0.69 |
time (sec) |
N/A |
0.069 |
0.088 |
0.094 |
1.05 |
0.307 |
0. |
0.287 |
13.298 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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|
|
|
|
Problem 137 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
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|
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|
|
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|
|
grade |
A |
A |
A |
A |
F(-2) |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 19 | 19 | 17 | 24 | 0 | 35 | 46 | 55 | 14 |
normalized size | 1 | 1. | 0.89 | 1.26 | 0. | 1.84 | 2.42 | 2.89 | 0.74 |
time (sec) |
N/A |
0.01 |
0.032 |
0.006 |
0. |
0.299 |
1.723 |
0.264 |
3.517 |
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Problem 138 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
|
grade |
A |
A |
A |
A |
A |
A |
A |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 24 | 31 | 47 | 42 | 85 | 65 | 17 |
normalized size | 1 | 1. | 1. | 1.29 | 1.96 | 1.75 | 3.54 | 2.71 | 0.71 |
time (sec) |
N/A |
0.012 |
0.044 |
0.005 |
0.906 |
0.28 |
61.081 |
0.268 |
4.972 |
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Problem 139 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
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|
|
grade |
A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 24 | 24 | 24 | 31 | 47 | 42 | 0 | 65 | 17 |
normalized size | 1 | 1. | 1. | 1.29 | 1.96 | 1.75 | 0. | 2.71 | 0.71 |
time (sec) |
N/A |
0.013 |
0.045 |
0.005 |
0.923 |
0.281 |
0. |
0.271 |
5.019 |
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Problem 140 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
C |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 26 | 26 | 24 | 155 | 54 | 49 | 0 | 35 | 19 |
normalized size | 1 | 1. | 0.92 | 5.96 | 2.08 | 1.88 | 0. | 1.35 | 0.73 |
time (sec) |
N/A |
0.126 |
0.084 |
0.14 |
1.107 |
0.288 |
0. |
0.281 |
15.945 |
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Problem 141 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 196 | 196 | 318 | 0 | 0 | 0 | 0 | 0 | 182 |
normalized size | 1 | 1. | 1.62 | 0. | 0. | 0. | 0. | 0. | 0.93 |
time (sec) |
N/A |
0.549 |
1.538 |
0.047 |
0. |
0. |
0. |
0. |
50.056 |
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Problem 142 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
|
|
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|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 374 | 374 | 5363 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 14.34 | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
2.73 |
6.592 |
0.06 |
0. |
0. |
0. |
0. |
0. |
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Problem 143 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
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|
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|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
F(-1) |
verified |
N/A |
Yes |
Yes |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 816 | 816 | 20515 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 1. | 25.14 | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
9.342 |
7.917 |
0.082 |
0. |
0. |
0. |
0. |
0. |
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Problem 144 |
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 | 47 | 47 | 47 | 36 | 46 | 46 | 0 | 46 | 48 |
normalized size | 1 | 1. | 1. | 0.77 | 0.98 | 0.98 | 0. | 0.98 | 1.02 |
time (sec) |
N/A |
0.102 |
0.04 |
0.005 |
0.768 |
0.274 |
0. |
0.297 |
30.678 |
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Problem 145 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 245 | 245 | 0 | 0 | 0 | 0 | 0 | 0 | 199 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.81 |
time (sec) |
N/A |
1.15 |
0.112 |
0.11 |
0. |
0. |
0. |
0. |
110.144 |
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Problem 146 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 210 | 210 | 0 | 0 | 0 | 0 | 0 | 0 | 173 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.82 |
time (sec) |
N/A |
1.151 |
0.151 |
0.077 |
0. |
0. |
0. |
0. |
91.364 |
|
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Problem 147 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 206 | 206 | 0 | 0 | 0 | 0 | 0 | 0 | 167 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.81 |
time (sec) |
N/A |
0.862 |
0.137 |
0.076 |
0. |
0. |
0. |
0. |
78.156 |
|
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Problem 148 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 194 | 194 | 0 | 0 | 0 | 0 | 0 | 0 | 167 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.62 |
0.067 |
0.075 |
0. |
0. |
0. |
0. |
100.184 |
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Problem 149 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 262 | 262 | 0 | 0 | 0 | 0 | 0 | 0 | 243 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.93 |
time (sec) |
N/A |
1.436 |
0.086 |
0.108 |
0. |
0. |
0. |
0. |
121.827 |
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Problem 150 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 212 | 212 | 0 | 0 | 0 | 0 | 0 | 0 | 168 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.79 |
time (sec) |
N/A |
1.071 |
0.092 |
0.077 |
0. |
0. |
0. |
0. |
91.44 |
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Problem 151 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
A |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 210 | 210 | 0 | 0 | 0 | 0 | 0 | 0 | 168 |
normalized size | 1 | 1. | 0. | 0. | 0. | 0. | 0. | 0. | 0.8 |
time (sec) |
N/A |
1.053 |
0.091 |
0.076 |
0. |
0. |
0. |
0. |
91.395 |
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Problem 152 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F(-2) |
A |
verified |
N/A |
NO |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 498 | 498 | 1615 | 0 | 0 | 0 | 0 | 0 | 442 |
normalized size | 1 | 1. | 3.24 | 0. | 0. | 0. | 0. | 0. | 0.89 |
time (sec) |
N/A |
1.387 |
17.638 |
0.09 |
0. |
0. |
0. |
0. |
140.812 |
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Problem 153 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 323 | 323 | 922 | 0 | 0 | 0 | 0 | 0 | 279 |
normalized size | 1 | 1. | 2.85 | 0. | 0. | 0. | 0. | 0. | 0.86 |
time (sec) |
N/A |
0.825 |
2.487 |
0.079 |
0. |
0. |
0. |
0. |
86.806 |
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Problem 154 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
A |
A |
B |
F |
F |
F |
F(-1) |
F |
A |
verified |
N/A |
Yes |
NO |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 158 | 158 | 534 | 0 | 0 | 0 | 0 | 0 | 129 |
normalized size | 1 | 1. | 3.38 | 0. | 0. | 0. | 0. | 0. | 0.82 |
time (sec) |
N/A |
0.328 |
0.92 |
0.079 |
0. |
0. |
0. |
0. |
34.908 |
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Problem 155 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
|
|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.072 |
0.126 |
0.108 |
0. |
0. |
0. |
0. |
0. |
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Problem 156 |
Optimal |
Rubi |
Mathematica |
Maple |
Maxima |
Fricas |
Sympy |
Giac |
Rubi in Sympy |
|
|
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|
|
|
|
|
|
|
grade |
N/A |
A |
A |
A |
A |
A |
F(-1) |
A |
A |
verified |
N/A |
N/A |
N/A |
TBD |
TBD |
TBD |
TBD |
TBD |
TBD |
size | 34 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
normalized size | 1 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. |
time (sec) |
N/A |
0.07 |
0.264 |
0.122 |
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 [83] had the largest ratio of [ 0.4231
]
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| Table 1: Rubi specific breakdown of results for each integral
|
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|
# |
grade |
|
|
normalized | antiderivative |
leaf size |
|
|
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\) |
|
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|
1 |
A |
2 |
1 |
1. |
22 |
0.045 |
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|
|
|
2 |
A |
2 |
1 |
1. |
22 |
0.045 |
|
|
|
|
|
|
|
3 |
A |
2 |
1 |
1. |
22 |
0.045 |
|
|
|
|
|
|
|
4 |
A |
2 |
1 |
1. |
22 |
0.045 |
|
|
|
|
|
|
|
5 |
A |
2 |
1 |
1. |
20 |
0.05 |
|
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|
|
|
|
|
6 |
A |
8 |
8 |
1. |
22 |
0.364 |
|
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|
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|
|
7 |
A |
8 |
8 |
1. |
22 |
0.364 |
|
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8 |
A |
8 |
8 |
1. |
22 |
0.364 |
|
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|
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9 |
A |
7 |
6 |
1. |
25 |
0.24 |
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10 |
A |
6 |
6 |
1. |
25 |
0.24 |
|
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11 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
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|
|
12 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
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|
|
13 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
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|
|
14 |
A |
14 |
8 |
1. |
25 |
0.32 |
|
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15 |
A |
14 |
8 |
1. |
25 |
0.32 |
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|
16 |
A |
13 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
17 |
A |
13 |
7 |
1. |
22 |
0.318 |
|
|
|
|
|
|
|
18 |
A |
14 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
19 |
A |
14 |
8 |
1. |
25 |
0.32 |
|
|
|
|
|
|
|
20 |
A |
7 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
|
21 |
A |
4 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
22 |
A |
5 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
23 |
A |
7 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
24 |
A |
5 |
4 |
1. |
23 |
0.174 |
|
|
|
|
|
|
|
25 |
A |
15 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
26 |
A |
15 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
27 |
A |
14 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
28 |
A |
13 |
7 |
1. |
21 |
0.333 |
|
|
|
|
|
|
|
29 |
A |
13 |
7 |
1. |
20 |
0.35 |
|
|
|
|
|
|
|
30 |
A |
14 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
31 |
A |
15 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
32 |
A |
5 |
5 |
1. |
21 |
0.238 |
|
|
|
|
|
|
|
33 |
A |
7 |
6 |
1. |
21 |
0.286 |
|
|
|
|
|
|
|
34 |
A |
8 |
7 |
1. |
18 |
0.389 |
|
|
|
|
|
|
|
35 |
A |
6 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
36 |
A |
5 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
37 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
38 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
39 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
40 |
A |
3 |
3 |
1. |
24 |
0.125 |
|
|
|
|
|
|
|
|
41 |
A |
4 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
42 |
A |
5 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
43 |
A |
8 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
44 |
A |
5 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
45 |
A |
7 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
46 |
A |
4 |
3 |
1. |
23 |
0.13 |
|
|
|
|
|
|
|
47 |
A |
7 |
4 |
1. |
22 |
0.182 |
|
|
|
|
|
|
|
48 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
49 |
A |
8 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
50 |
A |
5 |
4 |
1. |
25 |
0.16 |
|
|
|
|
|
|
|
51 |
A |
8 |
5 |
1. |
25 |
0.2 |
|
|
|
|
|
|
|
52 |
A |
20 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
53 |
A |
5 |
5 |
1. |
23 |
0.217 |
|
|
|
|
|
|
|
54 |
A |
21 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
55 |
A |
4 |
3 |
1. |
21 |
0.143 |
|
|
|
|
|
|
|
56 |
A |
19 |
6 |
1. |
20 |
0.3 |
|
|
|
|
|
|
|
57 |
A |
7 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
58 |
A |
20 |
7 |
1. |
23 |
0.304 |
|
|
|
|
|
|
|
59 |
A |
11 |
8 |
1. |
23 |
0.348 |
|
|
|
|
|
|
|
60 |
A |
21 |
9 |
1. |
23 |
0.391 |
|
|
|
|
|
|
|
|
61 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
62 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
63 |
A |
7 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
64 |
A |
7 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
65 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
66 |
A |
7 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
67 |
A |
7 |
6 |
1.01 |
25 |
0.24 |
|
|
|
|
|
|
|
68 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
69 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
70 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
71 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
72 |
A |
7 |
6 |
1. |
23 |
0.261 |
|
|
|
|
|
|
|
73 |
A |
7 |
6 |
1. |
22 |
0.273 |
|
|
|
|
|
|
|
74 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
75 |
A |
8 |
7 |
1. |
25 |
0.28 |
|
|
|
|
|
|
|
76 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
77 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
78 |
A |
7 |
6 |
1. |
25 |
0.24 |
|
|
|
|
|
|
|
79 |
A |
11 |
7 |
1. |
29 |
0.241 |
|
|
|
|
|
|
|
80 |
A |
10 |
7 |
1. |
29 |
0.241 |
|
|
|
|
|
|
|
|
81 |
A |
8 |
7 |
1. |
29 |
0.241 |
|
|
|
|
|
|
|
82 |
A |
8 |
7 |
1. |
27 |
0.259 |
|
|
|
|
|
|
|
83 |
A |
16 |
11 |
1. |
26 |
0.423 |
|
|
|
|
|
|
|
84 |
A |
16 |
11 |
1. |
29 |
0.379 |
|
|
|
|
|
|
|
85 |
A |
24 |
12 |
1. |
29 |
0.414 |
|
|
|
|
|
|
|
86 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
87 |
A |
13 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
88 |
A |
10 |
4 |
1. |
26 |
0.154 |
|
|
|
|
|
|
|
89 |
A |
7 |
4 |
1. |
24 |
0.167 |
|
|
|
|
|
|
|
90 |
A |
6 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
91 |
A |
8 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
92 |
A |
10 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
93 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
94 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
95 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
96 |
A |
2 |
2 |
1. |
30 |
0.067 |
|
|
|
|
|
|
|
97 |
A |
1 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
98 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
99 |
A |
1 |
1 |
1. |
28 |
0.036 |
|
|
|
|
|
|
|
100 |
A |
2 |
2 |
1. |
32 |
0.062 |
|
|
|
|
|
|
|
|
101 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
102 |
A |
1 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
103 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
104 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
105 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
106 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
107 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
108 |
A |
2 |
2 |
1. |
30 |
0.067 |
|
|
|
|
|
|
|
109 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
110 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
111 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
112 |
A |
2 |
2 |
1. |
30 |
0.067 |
|
|
|
|
|
|
|
113 |
A |
1 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
114 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
115 |
A |
1 |
1 |
1. |
28 |
0.036 |
|
|
|
|
|
|
|
116 |
A |
2 |
2 |
1. |
32 |
0.062 |
|
|
|
|
|
|
|
117 |
A |
1 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
118 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
119 |
A |
1 |
1 |
1. |
28 |
0.036 |
|
|
|
|
|
|
|
120 |
A |
2 |
2 |
1. |
32 |
0.062 |
|
|
|
|
|
|
|
|
121 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
122 |
A |
1 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
123 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
124 |
A |
4 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
125 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
126 |
A |
1 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
127 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
128 |
A |
3 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
129 |
A |
1 |
1 |
1. |
19 |
0.053 |
|
|
|
|
|
|
|
130 |
A |
1 |
1 |
1. |
24 |
0.042 |
|
|
|
|
|
|
|
131 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
132 |
A |
2 |
2 |
1. |
30 |
0.067 |
|
|
|
|
|
|
|
133 |
A |
1 |
1 |
1. |
21 |
0.048 |
|
|
|
|
|
|
|
134 |
A |
1 |
1 |
1. |
26 |
0.038 |
|
|
|
|
|
|
|
135 |
A |
1 |
1 |
1. |
28 |
0.036 |
|
|
|
|
|
|
|
136 |
A |
2 |
2 |
1. |
32 |
0.062 |
|
|
|
|
|
|
|
137 |
A |
1 |
1 |
1. |
18 |
0.056 |
|
|
|
|
|
|
|
138 |
A |
1 |
1 |
1. |
23 |
0.043 |
|
|
|
|
|
|
|
139 |
A |
1 |
1 |
1. |
25 |
0.04 |
|
|
|
|
|
|
|
140 |
A |
2 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
|
141 |
A |
4 |
2 |
1. |
29 |
0.069 |
|
|
|
|
|
|
|
142 |
A |
5 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
143 |
A |
6 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
144 |
A |
3 |
3 |
1. |
59 |
0.051 |
|
|
|
|
|
|
|
145 |
A |
5 |
3 |
1. |
31 |
0.097 |
|
|
|
|
|
|
|
146 |
A |
5 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
147 |
A |
5 |
3 |
1. |
27 |
0.111 |
|
|
|
|
|
|
|
148 |
A |
5 |
3 |
1. |
26 |
0.115 |
|
|
|
|
|
|
|
149 |
A |
8 |
5 |
1. |
29 |
0.172 |
|
|
|
|
|
|
|
150 |
A |
5 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
151 |
A |
5 |
3 |
1. |
29 |
0.103 |
|
|
|
|
|
|
|
152 |
A |
10 |
4 |
1. |
31 |
0.129 |
|
|
|
|
|
|
|
153 |
A |
7 |
4 |
1. |
29 |
0.138 |
|
|
|
|
|
|
|
154 |
A |
2 |
2 |
1. |
22 |
0.091 |
|
|
|
|
|
|
|
155 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
156 |
A |
0 |
0 |
0. |
0 |
0. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|