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 | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 405 | 706 | 817 | 434 | 0 | 0 | 0 | 0 | 613 | 0 |
| N.S. |
1 | 1.74 | 2.02 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 1.51 | 0.00 |
| time (sec) |
N/A | 0.934 | 11.911 | 5.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.400 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 554 | 362 | 368 | 0 | 0 | 0 | 0 | 386 | 0 |
| N.S. |
1 | 1.65 | 1.08 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 |
| time (sec) |
N/A | 0.801 | 11.620 | 2.309 | 0.000 | 0.000 | 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 | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 375 | 497 | 456 | 0 | 0 | 0 | 0 | 249 | 0 |
| N.S. |
1 | 1.37 | 1.81 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
| time (sec) |
N/A | 0.562 | 11.093 | 2.340 | 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 | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 259 | 398 | 490 | 385 | 0 | 0 | 0 | 0 | 253 | 0 |
| N.S. |
1 | 1.54 | 1.89 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
| time (sec) |
N/A | 0.695 | 11.059 | 2.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.311 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 293 | 377 | 613 | 404 | 0 | 0 | 0 | 0 | 270 | 0 |
| N.S. |
1 | 1.29 | 2.09 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
| time (sec) |
N/A | 0.626 | 11.220 | 4.392 | 0.000 | 0.000 | 0.000 | 0.000 | 0.417 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 355 | 523 | 781 | 455 | 0 | 0 | 0 | 0 | 462 | 0 |
| N.S. |
1 | 1.47 | 2.20 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 1.30 | 0.00 |
| time (sec) |
N/A | 0.801 | 11.635 | 4.948 | 0.000 | 0.000 | 0.000 | 0.000 | 0.502 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 330 | 346 | 352 | 357 | 0 | 0 | 0 | 0 | 389 | 0 |
| N.S. |
1 | 1.05 | 1.07 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
| time (sec) |
N/A | 1.248 | 11.484 | 5.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.371 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 268 | 276 | 367 | 430 | 0 | 0 | 0 | 0 | 206 | 0 |
| N.S. |
1 | 1.03 | 1.37 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
| time (sec) |
N/A | 0.888 | 10.983 | 4.679 | 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 | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 212 | 215 | 193 | 329 | 0 | 0 | 0 | 0 | 89 | 0 |
| N.S. |
1 | 1.01 | 0.91 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.639 | 10.518 | 1.128 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 129 | 173 | 0 | 0 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.373 | 10.385 | 0.669 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 208 | 318 | 214 | 0 | 0 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 1.00 | 1.53 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 0.480 | 10.554 | 1.618 | 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 | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 314 | 460 | 314 | 0 | 0 | 0 | 0 | 212 | 0 |
| N.S. |
1 | 1.14 | 1.67 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
| time (sec) |
N/A | 0.578 | 10.961 | 2.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.378 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 494 | 650 | 441 | 0 | 0 | 0 | 0 | 336 | 0 |
| N.S. |
1 | 1.40 | 1.84 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
| time (sec) |
N/A | 0.765 | 11.519 | 3.824 | 0.000 | 0.000 | 0.000 | 0.000 | 0.454 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 405 | 597 | 577 | 704 | 0 | 0 | 0 | 0 | 1571 | 0 |
| N.S. |
1 | 1.47 | 1.42 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 3.88 | 0.00 |
| time (sec) |
N/A | 0.995 | 11.771 | 12.373 | 0.000 | 0.000 | 0.000 | 0.000 | 1.355 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 367 | 493 | 358 | 975 | 0 | 0 | 0 | 0 | 919 | 0 |
| N.S. |
1 | 1.34 | 0.98 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 2.50 | 0.00 |
| time (sec) |
N/A | 0.841 | 11.624 | 2.362 | 0.000 | 0.000 | 0.000 | 0.000 | 1.067 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 319 | 366 | 417 | 850 | 0 | 0 | 0 | 0 | 587 | 0 |
| N.S. |
1 | 1.15 | 1.31 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 1.84 | 0.00 |
| time (sec) |
N/A | 0.689 | 11.199 | 1.728 | 0.000 | 0.000 | 0.000 | 0.000 | 0.836 | 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 | 311 | 311 | 307 | 742 | 0 | 0 | 0 | 0 | 131 | 0 |
| N.S. |
1 | 1.00 | 0.99 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.624 | 11.522 | 1.158 | 0.000 | 0.000 | 0.000 | 0.000 | 0.696 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 306 | 306 | 407 | 530 | 0 | 0 | 0 | 0 | 128 | 0 |
| N.S. |
1 | 1.00 | 1.33 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.585 | 11.032 | 0.663 | 0.000 | 0.000 | 0.000 | 0.000 | 0.721 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 388 | 448 | 534 | 486 | 0 | 0 | 0 | 0 | 579 | 0 |
| N.S. |
1 | 1.15 | 1.38 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
| time (sec) |
N/A | 0.806 | 11.279 | 4.950 | 0.000 | 0.000 | 0.000 | 0.000 | 0.695 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 460 | 546 | 727 | 663 | 0 | 0 | 0 | 0 | 909 | 0 |
| N.S. |
1 | 1.19 | 1.58 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 1.98 | 0.00 |
| time (sec) |
N/A | 0.889 | 11.683 | 7.480 | 0.000 | 0.000 | 0.000 | 0.000 | 0.602 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 272 | 226 | 295 | 0 | 0 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.07 | 0.89 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 1.318 | 1.113 | 0.937 | 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 | A | F | F(-1) | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 202 | 184 | 243 | 0 | 0 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.06 | 0.96 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.954 | 0.801 | 0.761 | 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 | A | F | A | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 142 | 144 | 198 | 0 | 863 | 0 | 0 | 101 | 0 |
| N.S. |
1 | 1.03 | 1.04 | 1.43 | 0.00 | 6.25 | 0.00 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.627 | 0.623 | 0.630 | 0.000 | 46.114 | 0.000 | 0.000 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 164 | 208 | 0 | 0 | 0 | 0 | 98 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.484 | 1.015 | 0.518 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 155 | 209 | 0 | 902 | 0 | 153 | 97 | 0 |
| N.S. |
1 | 1.00 | 1.12 | 1.51 | 0.00 | 6.54 | 0.00 | 1.11 | 0.70 | 0.00 |
| time (sec) |
N/A | 0.454 | 0.724 | 0.654 | 0.000 | 0.828 | 0.000 | 0.154 | 0.280 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 207 | 190 | 252 | 0 | 1266 | 0 | 311 | 98 | 0 |
| N.S. |
1 | 1.10 | 1.01 | 1.33 | 0.00 | 6.70 | 0.00 | 1.65 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.544 | 1.377 | 0.763 | 0.000 | 1.867 | 0.000 | 0.181 | 0.327 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 282 | 246 | 309 | 0 | 1609 | 0 | 556 | 100 | 0 |
| N.S. |
1 | 1.11 | 0.97 | 1.22 | 0.00 | 6.36 | 0.00 | 2.20 | 0.40 | 0.00 |
| time (sec) |
N/A | 0.605 | 1.712 | 1.102 | 0.000 | 2.328 | 0.000 | 0.209 | 0.400 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 702 | 675 | 406 | 405 | 0 | 0 | 0 | 0 | 363 | 0 |
| N.S. |
1 | 0.96 | 0.58 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 1.815 | 11.740 | 6.059 | 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 | C | C | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 581 | 591 | 456 | 546 | 0 | 0 | 0 | 0 | 186 | 0 |
| N.S. |
1 | 1.02 | 0.78 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 1.258 | 11.111 | 5.199 | 0.000 | 0.000 | 0.000 | 0.000 | 0.315 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 516 | 529 | 211 | 370 | 0 | 0 | 0 | 0 | 121 | 0 |
| N.S. |
1 | 1.03 | 0.41 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.875 | 10.598 | 1.156 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 534 | 554 | 422 | 317 | 0 | 0 | 0 | 0 | 121 | 0 |
| N.S. |
1 | 1.04 | 0.79 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 1.118 | 10.938 | 1.856 | 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 | C | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 593 | 613 | 549 | 345 | 0 | 0 | 0 | 0 | 201 | 0 |
| N.S. |
1 | 1.03 | 0.93 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 1.669 | 11.148 | 3.979 | 0.000 | 0.000 | 0.000 | 0.000 | 0.427 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | C | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 723 | 0 | 822 | 494 | 0 | 0 | 0 | 0 | 316 | 0 |
| N.S. |
1 | 0.00 | 1.14 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
| time (sec) |
N/A | 0.000 | 11.680 | 4.448 | 0.000 | 0.000 | 0.000 | 0.000 | 0.615 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 874 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1029 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.584 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 737 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 737 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.205 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 623 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 458 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.937 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 530 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 482 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.143 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 524 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 454 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.659 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 551 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1526 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.77 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 6.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 488 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 8.081 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 583 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 18.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 700 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 105.305 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 874 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1029 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.051 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 732 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 737 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.01 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.886 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 620 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 690 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.662 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 569 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 806 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.238 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 592 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 7.971 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 637 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 16.342 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 582 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 23.670 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 700 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 126.287 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 825 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 738 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 737 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.274 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 629 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 459 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.991 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 538 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 291 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.731 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 488 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 244 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.898 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 486 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 308 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.311 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 413 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1063 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.57 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.619 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 492 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 8.644 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 588 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 18.494 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 673 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1491 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.22 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.861 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 580 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1070 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.84 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.567 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 546 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 679 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.24 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.227 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 518 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 855 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.278 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 431 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.848 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 503 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 6.617 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 593 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 19.154 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 668 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 461 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.119 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 551 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 234 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.792 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 476 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 151 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.429 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 131 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.617 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 368 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 254 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.432 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 445 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1063 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.39 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.157 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 546 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 7.610 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 662 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 17.122 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 815 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 933 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.864 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 676 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 517 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.295 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 558 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 350 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.951 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 501 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 185 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.085 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 497 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 311 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.074 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 452 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.475 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 561 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 11.869 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 691 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 29.875 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 842 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1657 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.97 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.885 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 717 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1418 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.98 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.378 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 658 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 669 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.499 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 547 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 503 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.343 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 529 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.503 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 669 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 10.317 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 840 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 25.513 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | A | B | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 114 | 81 | 81 | 0 | 150 | 0 | 80 | 268 | 397 |
| N.S. |
1 | 1.48 | 1.05 | 1.05 | 0.00 | 1.95 | 0.00 | 1.04 | 3.48 | 5.16 |
| time (sec) |
N/A | 0.368 | 0.199 | 0.481 | 0.000 | 0.066 | 0.000 | 0.114 | 0.235 | 0.788 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 273 | 310 | 366 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.416 | 0.286 | 0.970 | 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 | C | A | F(-2) | F(-1) | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 421 | 438 | 310 | 364 | 0 | 0 | 0 | 0 | 115 | 0 |
| N.S. |
1 | 1.04 | 0.74 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.610 | 10.694 | 0.990 | 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 | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 88 | 72 | 69 | 0 | 81 | 0 | 81 | 67 | 0 |
| N.S. |
1 | 1.07 | 0.88 | 0.84 | 0.00 | 0.99 | 0.00 | 0.99 | 0.82 | 0.00 |
| time (sec) |
N/A | 0.567 | 0.247 | 0.026 | 0.000 | 0.079 | 0.000 | 0.142 | 0.264 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 64 | 63 | 49 | 0 | 74 | 0 | 74 | 67 | 0 |
| N.S. |
1 | 1.02 | 1.00 | 0.78 | 0.00 | 1.17 | 0.00 | 1.17 | 1.06 | 0.00 |
| time (sec) |
N/A | 0.465 | 0.178 | 0.410 | 0.000 | 0.077 | 0.000 | 0.130 | 0.262 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 45 | 49 | 37 | 0 | 62 | 0 | 62 | 65 | 0 |
| N.S. |
1 | 0.96 | 1.04 | 0.79 | 0.00 | 1.32 | 0.00 | 1.32 | 1.38 | 0.00 |
| time (sec) |
N/A | 0.274 | 0.163 | 0.171 | 0.000 | 0.083 | 0.000 | 0.119 | 0.248 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 42 | 42 | 0 | 78 | 0 | 78 | 102 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.79 | 0.00 | 1.47 | 0.00 | 1.47 | 1.92 | 0.00 |
| time (sec) |
N/A | 0.295 | 0.179 | 0.212 | 0.000 | 0.081 | 0.000 | 0.130 | 0.291 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 40 | 42 | 0 | 67 | 0 | 80 | 137 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.91 | 0.00 | 1.46 | 0.00 | 1.74 | 2.98 | 0.00 |
| time (sec) |
N/A | 0.323 | 0.192 | 0.163 | 0.000 | 0.073 | 0.000 | 0.123 | 0.249 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 68 | 79 | 0 | 119 | 0 | 163 | 67 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 0.85 | 0.00 | 1.28 | 0.00 | 1.75 | 0.72 | 0.00 |
| time (sec) |
N/A | 0.387 | 0.255 | 0.431 | 0.000 | 0.082 | 0.000 | 0.151 | 0.227 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 154 | 159 | 239 | 0 | 124 | 0 | 0 | 111 | 0 |
| N.S. |
1 | 1.01 | 1.05 | 1.57 | 0.00 | 0.82 | 0.00 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.592 | 10.339 | 1.175 | 0.000 | 0.109 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 140 | 126 | 308 | 0 | 119 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 1.01 | 0.91 | 2.23 | 0.00 | 0.86 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 0.489 | 10.238 | 0.574 | 0.000 | 0.110 | 0.000 | 0.000 | 0.179 | 0.000 |