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 | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 450 | 1408 | 2083 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 1.04 | 3.25 | 4.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 2.000 | 6.992 | 51.954 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 670 | 675 | 1284 | 2336 | 0 | 0 | 0 | 0 | 98 | 0 |
| N.S. |
1 | 1.01 | 1.92 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 3.416 | 7.685 | 32.501 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 566 | 568 | 1227 | 1803 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 1.00 | 2.17 | 3.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 2.827 | 7.451 | 26.540 | 0.000 | 0.000 | 0.000 | 0.000 | 0.306 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 472 | 475 | 1198 | 1389 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 1.01 | 2.54 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 2.189 | 7.644 | 21.749 | 0.000 | 0.000 | 0.000 | 0.000 | 0.303 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 449 | 461 | 1196 | 1239 | 0 | 0 | 0 | 0 | 92 | 0 |
| N.S. |
1 | 1.03 | 2.66 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 2.153 | 6.937 | 27.581 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 419 | 420 | 1236 | 1363 | 0 | 0 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 1.00 | 2.95 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 1.669 | 6.867 | 31.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 359 | 1314 | 1621 | 0 | 0 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 1.02 | 3.72 | 4.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 1.548 | 7.022 | 38.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 444 | 1407 | 2085 | 0 | 0 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 1.03 | 3.25 | 4.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 2.032 | 7.101 | 54.745 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 522 | 533 | 1515 | 2683 | 0 | 0 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 1.02 | 2.90 | 5.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 2.692 | 7.442 | 77.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 779 | 786 | 1353 | 2992 | 0 | 0 | 0 | 0 | 135 | 0 |
| N.S. |
1 | 1.01 | 1.74 | 3.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 4.304 | 7.973 | 38.848 | 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 | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 664 | 672 | 1287 | 2439 | 0 | 0 | 0 | 0 | 127 | 0 |
| N.S. |
1 | 1.01 | 1.94 | 3.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 3.558 | 7.773 | 31.958 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 564 | 572 | 1251 | 2004 | 0 | 0 | 0 | 0 | 127 | 0 |
| N.S. |
1 | 1.01 | 2.22 | 3.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 2.932 | 8.296 | 30.727 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 547 | 555 | 1241 | 1848 | 0 | 0 | 0 | 0 | 127 | 0 |
| N.S. |
1 | 1.01 | 2.27 | 3.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 2.877 | 7.066 | 31.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 536 | 547 | 1269 | 1831 | 0 | 0 | 0 | 0 | 129 | 0 |
| N.S. |
1 | 1.02 | 2.37 | 3.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 2.884 | 7.013 | 35.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 493 | 499 | 1319 | 1958 | 0 | 0 | 0 | 0 | 137 | 0 |
| N.S. |
1 | 1.01 | 2.68 | 3.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 2.254 | 7.219 | 42.410 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 434 | 445 | 1409 | 2199 | 0 | 0 | 0 | 0 | 137 | 0 |
| N.S. |
1 | 1.03 | 3.25 | 5.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 2.058 | 7.341 | 55.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 522 | 533 | 1517 | 2683 | 0 | 0 | 0 | 0 | 137 | 0 |
| N.S. |
1 | 1.02 | 2.91 | 5.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 2.666 | 7.650 | 80.106 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 622 | 638 | 1640 | 3301 | 0 | 0 | 0 | 0 | 137 | 0 |
| N.S. |
1 | 1.03 | 2.64 | 5.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 3.375 | 8.023 | 102.977 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 418 | 423 | 1236 | 1387 | 0 | 0 | 0 | 0 | 207 | 0 |
| N.S. |
1 | 1.01 | 2.96 | 3.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 1.853 | 25.305 | 35.356 | 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 | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 479 | 480 | 1175 | 1087 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 1.00 | 2.45 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
| time (sec) |
N/A | 2.161 | 19.535 | 25.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 436 | 402 | 476 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.02 | 0.94 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 1.803 | 13.854 | 16.753 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 228 | 231 | 173 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.642 | 15.051 | 17.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 299 | 480 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 1.00 | 1.30 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.709 | 15.718 | 23.937 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 294 | 416 | 934 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 1.01 | 1.43 | 3.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.021 | 17.491 | 34.377 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 363 | 375 | 1319 | 1507 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 1.03 | 3.63 | 4.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 1.502 | 6.974 | 46.755 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 500 | 527 | 1234 | 1628 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.05 | 2.47 | 3.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 2.470 | 7.429 | 25.306 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 416 | 420 | 1012 | 1173 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 1.01 | 2.43 | 2.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 1.494 | 19.016 | 17.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 307 | 1223 | 957 | 0 | 0 | 0 | 0 | 42 | 0 |
| N.S. |
1 | 1.08 | 4.31 | 3.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 1.067 | 6.944 | 18.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 331 | 1281 | 1293 | 0 | 0 | 0 | 0 | 44 | 0 |
| N.S. |
1 | 1.09 | 4.20 | 4.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 1.165 | 7.064 | 30.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 393 | 412 | 1357 | 1932 | 0 | 0 | 0 | 0 | 44 | 0 |
| N.S. |
1 | 1.05 | 3.45 | 4.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 1.739 | 7.362 | 40.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 674 | 698 | 1396 | 4190 | 0 | 0 | 0 | 0 | 57 | 0 |
| N.S. |
1 | 1.04 | 2.07 | 6.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 3.461 | 7.948 | 32.499 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 545 | 569 | 1342 | 2848 | 0 | 0 | 0 | 0 | 55 | 0 |
| N.S. |
1 | 1.04 | 2.46 | 5.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 2.476 | 7.477 | 27.513 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 410 | 1335 | 2072 | 0 | 0 | 0 | 0 | 49 | 0 |
| N.S. |
1 | 1.05 | 3.41 | 5.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 1.569 | 7.395 | 22.655 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 444 | 1384 | 2442 | 0 | 0 | 0 | 0 | 58 | 0 |
| N.S. |
1 | 1.03 | 3.23 | 5.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 1.730 | 7.196 | 29.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 456 | 477 | 1431 | 2956 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 1.05 | 3.14 | 6.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 1.934 | 7.335 | 37.220 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 567 | 581 | 1499 | 3720 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 1.02 | 2.64 | 6.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 2.702 | 7.615 | 46.709 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 419 | 426 | 225 | 388 | 0 | 0 | 0 | 0 | 41 | 0 |
| N.S. |
1 | 1.02 | 0.54 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.703 | 4.894 | 22.106 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 131 | 138 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 1.00 | 1.12 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.309 | 1.593 | 15.704 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 110 | 171 | 112 | 0 | 0 | 0 | 0 | 44 | 0 |
| N.S. |
1 | 1.00 | 1.55 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 0.305 | 2.044 | 12.839 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 226 | 212 | 380 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.672 | 6.744 | 28.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 0 | 234 | 0 | 0 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
| time (sec) |
N/A | 0.282 | 0.000 | 13.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 0 | 216 | 0 | 0 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 3.09 | 0.00 | 0.00 | 0.00 | 0.00 | 1.24 | 0.00 |
| time (sec) |
N/A | 0.296 | 0.000 | 11.938 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 0 | 225 | 0 | 0 | 0 | 0 | 91 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
| time (sec) |
N/A | 0.473 | 0.000 | 13.572 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 0 | 160 | 0 | 0 | 0 | 0 | 91 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 |
| time (sec) |
N/A | 0.458 | 0.000 | 13.938 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 0 | 236 | 0 | 0 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 3.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
| time (sec) |
N/A | 0.283 | 0.000 | 13.901 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 0 | 242 | 0 | 0 | 0 | 0 | 91 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
| time (sec) |
N/A | 0.295 | 0.000 | 12.611 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 98 | 0 | 154 | 0 | 0 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
| time (sec) |
N/A | 0.463 | 0.000 | 14.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 0 | 166 | 0 | 0 | 0 | 0 | 91 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
| time (sec) |
N/A | 0.452 | 0.000 | 14.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 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 | 33 | 33 | 35 | 33 | 35 | 35 | 32 | 35 | 61 | 35 |
| N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.97 | 1.06 | 1.85 | 1.06 |
| time (sec) |
N/A | 0.262 | 26.449 | 0.970 | 3.746 | 0.117 | 121.208 | 0.823 | 0.197 | 25.524 |
| 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 | 595 | 614 | 479 | 0 | 0 | 0 | 0 | 0 | 144 | 0 |
| N.S. |
1 | 1.03 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 3.007 | 6.236 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 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 | 406 | 408 | 263 | 0 | 0 | 0 | 0 | 0 | 117 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 1.768 | 3.247 | 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 | 287 | 291 | 211 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 1.01 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
| time (sec) |
N/A | 1.097 | 1.792 | 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 | 196 | 193 | 162 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.98 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.641 | 0.911 | 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 | B | F | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 281 | 10482 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 0.98 | 36.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 0.887 | 34.999 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 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 | 35 | 35 | 37 | 33 | 35 | 54 | 34 | 35 | 97 | 35 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.54 | 0.97 | 1.00 | 2.77 | 1.00 |
| time (sec) |
N/A | 0.842 | 107.894 | 0.943 | 3.205 | 0.116 | 139.351 | 16.684 | 0.226 | 25.731 |
| 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 | 35 | 35 | 37 | 33 | 35 | 35 | 34 | 35 | 59 | 35 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.97 | 1.00 | 1.69 | 1.00 |
| time (sec) |
N/A | 0.304 | 46.623 | 0.967 | 2.170 | 0.103 | 7.321 | 0.869 | 0.228 | 25.448 |
| 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 | 35 | 35 | 37 | 33 | 35 | 35 | 34 | 35 | 26 | 35 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.97 | 1.00 | 0.74 | 1.00 |
| time (sec) |
N/A | 0.312 | 43.028 | 1.085 | 2.027 | 0.100 | 3.687 | 0.607 | 0.168 | 25.742 |
| 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 | 35 | 35 | 37 | 33 | 35 | 63 | 34 | 35 | 38 | 35 |
| N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.80 | 0.97 | 1.00 | 1.09 | 1.00 |
| time (sec) |
N/A | 0.873 | 40.026 | 1.110 | 2.241 | 0.115 | 9.048 | 1.137 | 0.184 | 26.497 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 166 | 292 | 634 | 0 | 219 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 0.97 | 1.70 | 3.69 | 0.00 | 1.27 | 0.00 | 0.00 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.874 | 3.359 | 35.451 | 0.000 | 0.094 | 0.000 | 0.000 | 0.299 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 137 | 225 | 399 | 0 | 188 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.01 | 1.67 | 2.96 | 0.00 | 1.39 | 0.00 | 0.00 | 0.76 | 0.00 |
| time (sec) |
N/A | 0.804 | 1.986 | 35.011 | 0.000 | 0.095 | 0.000 | 0.000 | 0.344 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 157 | 242 | 0 | 141 | 0 | 0 | 95 | 0 |
| N.S. |
1 | 1.00 | 1.48 | 2.28 | 0.00 | 1.33 | 0.00 | 0.00 | 0.90 | 0.00 |
| time (sec) |
N/A | 0.698 | 2.235 | 5.701 | 0.000 | 0.102 | 0.000 | 0.000 | 0.275 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 113 | 148 | 321 | 0 | 142 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 1.03 | 1.35 | 2.92 | 0.00 | 1.29 | 0.00 | 0.00 | 0.64 | 0.00 |
| time (sec) |
N/A | 0.703 | 2.547 | 6.522 | 0.000 | 0.093 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 143 | 148 | 355 | 0 | 169 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.01 | 1.05 | 2.52 | 0.00 | 1.20 | 0.00 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.804 | 2.798 | 10.063 | 0.000 | 0.096 | 0.000 | 0.000 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 170 | 182 | 383 | 0 | 187 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 0.99 | 1.06 | 2.23 | 0.00 | 1.09 | 0.00 | 0.00 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.887 | 3.494 | 15.069 | 0.000 | 0.101 | 0.000 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 196 | 299 | 714 | 0 | 239 | 0 | 0 | 163 | 0 |
| N.S. |
1 | 0.98 | 1.50 | 3.59 | 0.00 | 1.20 | 0.00 | 0.00 | 0.82 | 0.00 |
| time (sec) |
N/A | 1.187 | 4.284 | 62.869 | 0.000 | 0.093 | 0.000 | 0.000 | 0.402 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 164 | 188 | 513 | 0 | 202 | 0 | 0 | 163 | 0 |
| N.S. |
1 | 1.02 | 1.18 | 3.21 | 0.00 | 1.26 | 0.00 | 0.00 | 1.02 | 0.00 |
| time (sec) |
N/A | 1.038 | 3.255 | 62.822 | 0.000 | 0.120 | 0.000 | 0.000 | 0.396 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 164 | 152 | 244 | 0 | 166 | 0 | 0 | 151 | 0 |
| N.S. |
1 | 1.02 | 0.95 | 1.52 | 0.00 | 1.04 | 0.00 | 0.00 | 0.94 | 0.00 |
| time (sec) |
N/A | 1.003 | 3.388 | 7.583 | 0.000 | 0.120 | 0.000 | 0.000 | 0.343 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 172 | 153 | 357 | 0 | 187 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 1.04 | 0.92 | 2.15 | 0.00 | 1.13 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 1.022 | 3.704 | 10.599 | 0.000 | 0.108 | 0.000 | 0.000 | 0.225 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 202 | 193 | 385 | 0 | 211 | 0 | 0 | 163 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 1.92 | 0.00 | 1.05 | 0.00 | 0.00 | 0.81 | 0.00 |
| time (sec) |
N/A | 1.197 | 4.189 | 15.770 | 0.000 | 0.115 | 0.000 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 246 | 435 | 902 | 0 | 263 | 0 | 0 | 221 | 0 |
| N.S. |
1 | 1.01 | 1.78 | 3.70 | 0.00 | 1.08 | 0.00 | 0.00 | 0.91 | 0.00 |
| time (sec) |
N/A | 1.547 | 5.896 | 184.507 | 0.000 | 0.103 | 0.000 | 0.000 | 0.498 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 215 | 268 | 916 | 0 | 243 | 0 | 0 | 221 | 0 |
| N.S. |
1 | 1.02 | 1.27 | 4.34 | 0.00 | 1.15 | 0.00 | 0.00 | 1.05 | 0.00 |
| time (sec) |
N/A | 1.320 | 4.983 | 186.372 | 0.000 | 0.118 | 0.000 | 0.000 | 0.501 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 201 | 202 | 654 | 0 | 215 | 0 | 0 | 221 | 0 |
| N.S. |
1 | 1.01 | 1.02 | 3.29 | 0.00 | 1.08 | 0.00 | 0.00 | 1.11 | 0.00 |
| time (sec) |
N/A | 1.301 | 3.579 | 185.510 | 0.000 | 0.117 | 0.000 | 0.000 | 0.518 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 215 | 207 | 337 | 0 | 197 | 0 | 0 | 205 | 0 |
| N.S. |
1 | 1.02 | 0.98 | 1.60 | 0.00 | 0.93 | 0.00 | 0.00 | 0.97 | 0.00 |
| time (sec) |
N/A | 1.364 | 3.116 | 11.595 | 0.000 | 0.110 | 0.000 | 0.000 | 0.494 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 222 | 194 | 385 | 0 | 211 | 0 | 0 | 156 | 0 |
| N.S. |
1 | 1.05 | 0.92 | 1.82 | 0.00 | 1.00 | 0.00 | 0.00 | 0.74 | 0.00 |
| time (sec) |
N/A | 1.390 | 4.613 | 15.724 | 0.000 | 0.105 | 0.000 | 0.000 | 0.358 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 250 | 196 | 413 | 0 | 231 | 0 | 0 | 221 | 0 |
| N.S. |
1 | 1.02 | 0.80 | 1.69 | 0.00 | 0.95 | 0.00 | 0.00 | 0.91 | 0.00 |
| time (sec) |
N/A | 1.629 | 4.798 | 18.198 | 0.000 | 0.139 | 0.000 | 0.000 | 0.335 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 185 | 650 | 466 | 0 | 308 | 0 | 0 | 71 | 0 |
| N.S. |
1 | 0.96 | 3.37 | 2.41 | 0.00 | 1.60 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 0.992 | 8.999 | 7.348 | 0.000 | 0.116 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 157 | 400 | 319 | 0 | 250 | 0 | 0 | 67 | 0 |
| N.S. |
1 | 0.99 | 2.52 | 2.01 | 0.00 | 1.57 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.924 | 6.449 | 3.756 | 0.000 | 0.106 | 0.000 | 0.000 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 129 | 200 | 243 | 0 | 241 | 0 | 0 | 55 | 0 |
| N.S. |
1 | 1.05 | 1.63 | 1.98 | 0.00 | 1.96 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.759 | 3.020 | 3.044 | 0.000 | 0.106 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 130 | 422 | 244 | 0 | 237 | 0 | 0 | 79 | 0 |
| N.S. |
1 | 1.04 | 3.38 | 1.95 | 0.00 | 1.90 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.753 | 4.638 | 4.632 | 0.000 | 0.114 | 0.000 | 0.000 | 0.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 159 | 444 | 262 | 0 | 261 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 0.98 | 2.72 | 1.61 | 0.00 | 1.60 | 0.00 | 0.00 | 0.53 | 0.00 |
| time (sec) |
N/A | 0.933 | 7.581 | 5.697 | 0.000 | 0.164 | 0.000 | 0.000 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 196 | 187 | 518 | 281 | 0 | 278 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 0.95 | 2.64 | 1.43 | 0.00 | 1.42 | 0.00 | 0.00 | 0.44 | 0.00 |
| time (sec) |
N/A | 0.952 | 5.522 | 7.024 | 0.000 | 0.114 | 0.000 | 0.000 | 0.178 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 208 | 303 | 494 | 0 | 367 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.00 | 1.46 | 2.38 | 0.00 | 1.76 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 1.282 | 4.774 | 4.484 | 0.000 | 0.108 | 0.000 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 171 | 256 | 350 | 0 | 326 | 0 | 0 | 75 | 0 |
| N.S. |
1 | 1.06 | 1.59 | 2.17 | 0.00 | 2.02 | 0.00 | 0.00 | 0.47 | 0.00 |
| time (sec) |
N/A | 1.075 | 3.438 | 4.398 | 0.000 | 0.102 | 0.000 | 0.000 | 0.176 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 175 | 256 | 350 | 0 | 324 | 0 | 0 | 111 | 0 |
| N.S. |
1 | 1.04 | 1.52 | 2.08 | 0.00 | 1.93 | 0.00 | 0.00 | 0.66 | 0.00 |
| time (sec) |
N/A | 1.080 | 4.082 | 4.868 | 0.000 | 0.107 | 0.000 | 0.000 | 0.182 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 182 | 732 | 421 | 0 | 362 | 0 | 0 | 123 | 0 |
| N.S. |
1 | 1.03 | 4.16 | 2.39 | 0.00 | 2.06 | 0.00 | 0.00 | 0.70 | 0.00 |
| time (sec) |
N/A | 1.117 | 8.394 | 5.820 | 0.000 | 0.125 | 0.000 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 211 | 777 | 435 | 0 | 376 | 0 | 0 | 123 | 0 |
| N.S. |
1 | 1.02 | 3.77 | 2.11 | 0.00 | 1.83 | 0.00 | 0.00 | 0.60 | 0.00 |
| time (sec) |
N/A | 1.351 | 8.787 | 6.504 | 0.000 | 0.144 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 267 | 358 | 685 | 0 | 481 | 0 | 0 | 107 | 0 |
| N.S. |
1 | 1.02 | 1.37 | 2.62 | 0.00 | 1.84 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 1.727 | 7.328 | 5.948 | 0.000 | 0.102 | 0.000 | 0.000 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 237 | 793 | 451 | 0 | 476 | 0 | 0 | 95 | 0 |
| N.S. |
1 | 1.07 | 3.57 | 2.03 | 0.00 | 2.14 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 1.505 | 8.608 | 5.879 | 0.000 | 0.113 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 231 | 792 | 451 | 0 | 472 | 0 | 0 | 143 | 0 |
| N.S. |
1 | 1.07 | 3.67 | 2.09 | 0.00 | 2.19 | 0.00 | 0.00 | 0.66 | 0.00 |
| time (sec) |
N/A | 1.519 | 8.566 | 6.388 | 0.000 | 0.112 | 0.000 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 237 | 793 | 451 | 0 | 474 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.07 | 3.57 | 2.03 | 0.00 | 2.14 | 0.00 | 0.00 | 0.72 | 0.00 |
| time (sec) |
N/A | 1.465 | 9.452 | 6.499 | 0.000 | 0.130 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 243 | 817 | 451 | 0 | 478 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.07 | 3.58 | 1.98 | 0.00 | 2.10 | 0.00 | 0.00 | 0.70 | 0.00 |
| time (sec) |
N/A | 1.507 | 10.021 | 7.148 | 0.000 | 0.108 | 0.000 | 0.000 | 0.194 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 259 | 269 | 589 | 465 | 0 | 489 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.04 | 2.27 | 1.80 | 0.00 | 1.89 | 0.00 | 0.00 | 0.61 | 0.00 |
| time (sec) |
N/A | 1.718 | 8.860 | 7.786 | 0.000 | 0.122 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 220 | 235 | 124 | 366 | 659 | 121 | 0 | 0 | 68 | 479 |
| N.S. |
1 | 1.07 | 0.56 | 1.66 | 3.00 | 0.55 | 0.00 | 0.00 | 0.31 | 2.18 |
| time (sec) |
N/A | 1.155 | 0.630 | 21.129 | 0.240 | 0.091 | 0.000 | 0.000 | 0.230 | 32.966 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 192 | 102 | 327 | 568 | 104 | 0 | 0 | 68 | 441 |
| N.S. |
1 | 1.10 | 0.58 | 1.87 | 3.25 | 0.59 | 0.00 | 0.00 | 0.39 | 2.52 |
| time (sec) |
N/A | 0.948 | 0.499 | 18.292 | 0.255 | 0.093 | 0.000 | 0.000 | 0.244 | 29.042 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 149 | 78 | 288 | 475 | 86 | 0 | 0 | 68 | 196 |
| N.S. |
1 | 1.15 | 0.60 | 2.22 | 3.65 | 0.66 | 0.00 | 0.00 | 0.52 | 1.51 |
| time (sec) |
N/A | 0.757 | 0.307 | 16.435 | 0.218 | 0.096 | 0.000 | 0.000 | 0.238 | 1.773 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 106 | 57 | 249 | 380 | 65 | 0 | 0 | 68 | 114 |
| N.S. |
1 | 1.25 | 0.67 | 2.93 | 4.47 | 0.76 | 0.00 | 0.00 | 0.80 | 1.34 |
| time (sec) |
N/A | 0.607 | 0.202 | 15.547 | 0.224 | 0.089 | 0.000 | 0.000 | 0.240 | 0.664 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 97 | 86 | 319 | 906 | 91 | 0 | 0 | 64 | 0 |
| N.S. |
1 | 1.01 | 0.90 | 3.32 | 9.44 | 0.95 | 0.00 | 0.00 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.609 | 0.206 | 15.219 | 0.477 | 0.099 | 0.000 | 0.000 | 0.214 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 99 | 103 | 457 | 939 | 97 | 0 | 0 | 52 | 0 |
| N.S. |
1 | 1.01 | 1.05 | 4.66 | 9.58 | 0.99 | 0.00 | 0.00 | 0.53 | 0.00 |
| time (sec) |
N/A | 0.600 | 0.249 | 14.910 | 0.352 | 0.132 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | B | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 144 | 120 | 0 | 1851 | 127 | 0 | 0 | 68 | 0 |
| N.S. |
1 | 0.95 | 0.79 | 0.00 | 12.26 | 0.84 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.764 | 0.457 | 0.000 | 0.447 | 0.128 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 196 | 187 | 138 | 740 | 2981 | 146 | 0 | 0 | 68 | 0 |
| N.S. |
1 | 0.95 | 0.70 | 3.78 | 15.21 | 0.74 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.918 | 0.804 | 16.971 | 0.751 | 0.133 | 0.000 | 0.000 | 0.184 | 0.000 |