Detailed conclusion table per each integral is given by the 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 as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 234 | 92 | 0 | 0 | 0 | 6574 | 0 | 458 | 0 |
N.S. |
1 | 1.24 | 0.49 | 0.00 | 0.00 | 0.00 | 34.78 | 0.00 | 2.42 | 0.00 |
time (sec) |
N/A | 0.447 | 0.023 | 0.000 | 0.000 | 0.000 | 91.733 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 243 | 92 | 0 | 0 | 0 | 0 | 0 | 647 | 0 |
N.S. |
1 | 1.17 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.13 | 0.00 |
time (sec) |
N/A | 0.459 | 0.126 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 343 | 302 | 2232 | 795 | 2166 | 35984 | 3713 | 2557 | 1796 |
N.S. |
1 | 1.00 | 0.88 | 6.51 | 2.32 | 6.31 | 104.91 | 10.83 | 7.45 | 5.24 |
time (sec) |
N/A | 0.557 | 0.122 | 0.411 | 0.054 | 0.117 | 8.816 | 0.160 | 0.269 | 9.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 282 | 773 | 1210 | 625 | 1684 | 24687 | 2851 | 1950 | 1459 |
N.S. |
1 | 1.00 | 2.74 | 4.29 | 2.22 | 5.97 | 87.54 | 10.11 | 6.91 | 5.17 |
time (sec) |
N/A | 0.467 | 1.176 | 0.397 | 0.053 | 0.104 | 5.596 | 0.153 | 0.228 | 9.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 223 | 379 | 954 | 472 | 1250 | 15990 | 2085 | 1411 | 1144 |
N.S. |
1 | 1.00 | 1.70 | 4.28 | 2.12 | 5.61 | 71.70 | 9.35 | 6.33 | 5.13 |
time (sec) |
N/A | 0.382 | 0.468 | 0.368 | 0.047 | 0.098 | 4.285 | 0.149 | 0.224 | 9.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 246 | 226 | 0 | 0 | 0 | 5622 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 22.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.110 | 0.000 | 0.000 | 0.000 | 4.797 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 232 | 170 | 0 | 0 | 0 | 3213 | 0 | 1204 | 0 |
N.S. |
1 | 1.17 | 0.86 | 0.00 | 0.00 | 0.00 | 16.23 | 0.00 | 6.08 | 0.00 |
time (sec) |
N/A | 0.472 | 0.040 | 0.000 | 0.000 | 0.000 | 3.301 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 243 | 168 | 0 | 0 | 0 | 2419 | 0 | 1220 | 0 |
N.S. |
1 | 1.10 | 0.76 | 0.00 | 0.00 | 0.00 | 10.95 | 0.00 | 5.52 | 0.00 |
time (sec) |
N/A | 0.623 | 0.134 | 0.000 | 0.000 | 0.000 | 4.577 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 259 | 152 | 0 | 0 | 0 | 3628 | 0 | 1033 | 0 |
N.S. |
1 | 1.34 | 0.79 | 0.00 | 0.00 | 0.00 | 18.80 | 0.00 | 5.35 | 0.00 |
time (sec) |
N/A | 0.775 | 0.060 | 0.000 | 0.000 | 0.000 | 12.298 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 304 | 167 | 0 | 0 | 0 | 6803 | 0 | 1108 | 0 |
N.S. |
1 | 1.24 | 0.68 | 0.00 | 0.00 | 0.00 | 27.77 | 0.00 | 4.52 | 0.00 |
time (sec) |
N/A | 0.854 | 0.042 | 0.000 | 0.000 | 0.000 | 87.545 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 363 | 108 | 0 | 0 | 0 | 0 | 0 | 1028 | 0 |
N.S. |
1 | 1.51 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.27 | 0.00 |
time (sec) |
N/A | 0.866 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 436 | 122 | 0 | 0 | 0 | 0 | 0 | 1066 | 0 |
N.S. |
1 | 1.23 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.01 | 0.00 |
time (sec) |
N/A | 0.936 | 0.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.415 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 445 | 122 | 0 | 0 | 0 | 0 | 0 | 1433 | 0 |
N.S. |
1 | 1.16 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.72 | 0.00 |
time (sec) |
N/A | 0.927 | 0.177 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 276 | 217 | 0 | 0 | 0 | 0 | 0 | 345 | 0 |
N.S. |
1 | 1.15 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.761 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 232 | 168 | 0 | 0 | 0 | 0 | 0 | 383 | 0 |
N.S. |
1 | 1.21 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.01 | 0.00 |
time (sec) |
N/A | 0.504 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 195 | 170 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.08 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.331 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 163 | 151 | 0 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.12 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.263 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 167 | 145 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.08 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.270 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 207 | 189 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.13 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.340 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 207 | 167 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.05 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.374 | 0.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 342 | 413 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.659 | 0.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 292 | 247 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.516 | 0.528 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 295 | 403 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.485 | 0.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 263 | 230 | 0 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.57 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.415 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 299 | 253 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.98 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.502 | 0.170 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 484 | 391 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.38 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.808 | 0.522 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 504 | 513 | 437 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.02 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.801 | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 145 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.284 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 145 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 0.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 143 | 108 | 0 | 0 | 0 | 58 | 0 | 962 | 0 |
N.S. |
1 | 0.98 | 0.74 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 | 6.59 | 0.00 |
time (sec) |
N/A | 0.258 | 0.199 | 0.000 | 0.000 | 0.000 | 72.289 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 129 | 108 | 0 | 0 | 0 | 60 | 0 | 1031 | 0 |
N.S. |
1 | 1.02 | 0.85 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 | 8.12 | 0.00 |
time (sec) |
N/A | 0.243 | 0.293 | 0.000 | 0.000 | 0.000 | 73.223 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 123 | 110 | 0 | 0 | 0 | 0 | 0 | 1047 | 0 |
N.S. |
1 | 0.95 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.12 | 0.00 |
time (sec) |
N/A | 0.245 | 0.245 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 129 | 110 | 0 | 0 | 0 | 0 | 0 | 1081 | 0 |
N.S. |
1 | 0.98 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.25 | 0.00 |
time (sec) |
N/A | 0.246 | 0.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 129 | 110 | 0 | 0 | 0 | 0 | 0 | 1081 | 0 |
N.S. |
1 | 1.06 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.86 | 0.00 |
time (sec) |
N/A | 0.247 | 0.279 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 305 | 272 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.552 | 0.370 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 305 | 272 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.543 | 0.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 302 | 270 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.542 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 270 | 270 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.493 | 0.373 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 240 | 272 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.482 | 0.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 250 | 272 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.479 | 0.364 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 264 | 272 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.505 | 0.433 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 267 | 272 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.508 | 0.477 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 1201 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 9.38 | 0.00 |
time (sec) |
N/A | 0.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.068 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 176 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.416 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.562 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.410 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.381 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 255 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.724 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.549 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 255 | 0 | 0 | 0 | 0 | 0 | 0 | 572 | 0 |
N.S. |
1 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.692 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.895 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 392 | 255 | 0 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.721 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 255 | 0 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.640 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 255 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.699 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 478 | 255 | 0 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.716 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.396 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 439 | 425 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.759 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.516 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 360 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.448 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.396 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 297 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 154 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.244 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 19 | 23 | 22 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.83 | 1.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.160 | 0.660 | 0.007 | 0.070 | 0.090 | 2.874 | 0.124 | 0.302 | 8.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 20 | 23 | 22 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.87 | 1.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.161 | 0.518 | 0.000 | 0.078 | 0.100 | 2.600 | 0.126 | 0.281 | 8.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 439 | 425 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.693 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 360 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 297 | 0 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.883 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 0 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.244 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.833 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 33 | 19 | 23 | 48 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.43 | 0.83 | 1.00 | 2.09 | 1.00 |
time (sec) |
N/A | 0.172 | 0.186 | 0.006 | 0.072 | 0.089 | 10.049 | 0.148 | 0.560 | 8.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 33 | 20 | 23 | 47 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.43 | 0.87 | 1.00 | 2.04 | 1.00 |
time (sec) |
N/A | 0.159 | 0.202 | 0.009 | 0.074 | 0.097 | 17.443 | 0.148 | 0.488 | 8.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 431 | 422 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.666 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 359 | 260 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.423 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 297 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 154 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.239 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 33 | 19 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.43 | 0.83 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.162 | 0.674 | 0.007 | 0.077 | 0.080 | 2.352 | 0.126 | 0.255 | 9.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 35 | 20 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.52 | 0.87 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.162 | 0.593 | 0.007 | 0.073 | 0.094 | 2.716 | 0.131 | 0.283 | 9.648 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 394 | 0 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.494 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 385 | 246 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.10 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.499 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 365 | 0 | 0 | 0 | 0 | 0 | 0 | 1428 | 0 |
N.S. |
1 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.76 | 0.00 |
time (sec) |
N/A | 0.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.361 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 154 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.238 | 0.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 42 | 19 | 23 | 40 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.83 | 0.83 | 1.00 | 1.74 | 1.00 |
time (sec) |
N/A | 0.152 | 0.993 | 0.007 | 0.075 | 0.088 | 23.979 | 0.137 | 0.384 | 9.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 44 | 20 | 23 | 42 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.91 | 0.87 | 1.00 | 1.83 | 1.00 |
time (sec) |
N/A | 0.153 | 0.632 | 0.007 | 0.074 | 0.102 | 52.561 | 0.140 | 0.427 | 10.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 378 | 378 | 275 | 0 | 0 | 0 | 128 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.727 | 0.054 | 0.000 | 0.000 | 0.000 | 17.606 | 0.000 | 0.416 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 157 | 113 | 0 | 0 | 0 | 80 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.75 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.280 | 0.026 | 0.000 | 0.000 | 0.000 | 6.638 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 0 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 295 | 0 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.543 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 24 | 0 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.162 | 1.489 | 0.182 | 0.082 | 0.124 | 0.000 | 0.136 | 200.049 | 8.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 24 | 22 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.92 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.163 | 1.728 | 0.181 | 0.077 | 0.126 | 21.035 | 0.132 | 200.038 | 8.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 24 | 22 | 24 | 27 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.92 | 1.00 | 1.12 | 1.00 |
time (sec) |
N/A | 0.166 | 1.866 | 0.184 | 0.076 | 0.121 | 11.120 | 0.133 | 0.517 | 9.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 44 | 22 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.83 | 0.92 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.159 | 2.295 | 0.182 | 0.078 | 0.157 | 24.389 | 0.142 | 200.048 | 8.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 291 | 182 | 0 | 0 | 0 | 230 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.72 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.640 | 0.138 | 0.000 | 0.000 | 0.000 | 116.294 | 0.000 | 0.488 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 214 | 158 | 0 | 0 | 0 | 168 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.81 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 0.054 | 0.000 | 0.000 | 0.000 | 78.516 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 106 | 0 | 0 | 0 | 107 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.239 | 0.032 | 0.000 | 0.000 | 0.000 | 37.863 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 64 | 0 | 0 | 0 | 54 | 0 | 174 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.180 | 0.009 | 0.000 | 0.000 | 0.000 | 9.702 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 164 | 0 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.328 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 242 | 0 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.458 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 338 | 227 | 0 | 0 | 0 | 274 | 0 | 835 | 0 |
N.S. |
1 | 1.04 | 0.70 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 | 2.58 | 0.00 |
time (sec) |
N/A | 0.823 | 0.278 | 0.000 | 0.000 | 0.000 | 155.043 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 260 | 189 | 0 | 0 | 0 | 223 | 0 | 591 | 0 |
N.S. |
1 | 1.04 | 0.75 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 2.35 | 0.00 |
time (sec) |
N/A | 0.512 | 0.147 | 0.000 | 0.000 | 0.000 | 98.256 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 207 | 164 | 0 | 0 | 0 | 156 | 0 | 343 | 0 |
N.S. |
1 | 1.03 | 0.82 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.333 | 0.056 | 0.000 | 0.000 | 0.000 | 61.401 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 115 | 0 | 0 | 0 | 104 | 0 | 202 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.247 | 0.035 | 0.000 | 0.000 | 0.000 | 35.426 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 65 | 0 | 0 | 0 | 46 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.183 | 0.017 | 0.000 | 0.000 | 0.000 | 8.575 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 230 | 0 | 0 | 0 | 0 | 0 | 0 | 339 | 0 |
N.S. |
1 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 360 | 0 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.706 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 408 | 404 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.727 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.678 | 0.000 |