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 | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 627 | 0 | 369 | 498 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.59 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.230 | 8.483 | 0.000 | 0.000 | 0.000 | 0.000 | 41.807 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 867 | 0 | 1369 | 841 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.58 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.585 | 10.557 | 0.000 | 0.000 | 0.000 | 0.000 | 102.558 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 879 | 0 | 514 | 1603 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.58 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.000 | 6.327 | 21.300 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 717 | 0 | 1381 | 1488 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.93 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.602 | 21.676 | 0.000 | 0.000 | 0.000 | 0.000 | 67.714 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 482 | 1030 | 352 | 1075 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 2.14 | 0.73 | 2.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.632 | 4.071 | 5.063 | 0.000 | 0.000 | 0.000 | 0.000 | 31.295 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 881 | 0 | 266 | 1102 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.30 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.912 | 19.741 | 0.000 | 0.000 | 0.000 | 0.000 | 44.505 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1105 | 0 | 443 | 1458 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.40 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 0.000 | 6.413 | 21.021 | 0.000 | 0.000 | 0.000 | 0.000 | 200.035 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1412 | 0 | 480 | 1826 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.34 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
| time (sec) |
N/A | 0.000 | 6.830 | 23.148 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 529 | 0 | 450 | 610 | 0 | 0 | 0 | 0 | 1575 | 0 |
| N.S. |
1 | 0.00 | 0.85 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 2.98 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.668 | 9.385 | 0.000 | 0.000 | 0.000 | 0.000 | 11.471 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1181 | 1451 | 787 | 1468 | 0 | 1206 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.23 | 0.67 | 1.24 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.690 | 6.392 | 23.169 | 0.000 | 0.114 | 0.000 | 0.000 | 1.645 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 862 | 1120 | 586 | 963 | 0 | 886 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.30 | 0.68 | 1.12 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.959 | 5.240 | 19.481 | 0.000 | 0.114 | 0.000 | 0.000 | 1.279 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 621 | 843 | 423 | 646 | 0 | 608 | 0 | 0 | 1140 | 0 |
| N.S. |
1 | 1.36 | 0.68 | 1.04 | 0.00 | 0.98 | 0.00 | 0.00 | 1.84 | 0.00 |
| time (sec) |
N/A | 1.433 | 2.978 | 9.514 | 0.000 | 0.109 | 0.000 | 0.000 | 0.966 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 445 | 826 | 303 | 453 | 0 | 409 | 0 | 0 | 651 | 0 |
| N.S. |
1 | 1.86 | 0.68 | 1.02 | 0.00 | 0.92 | 0.00 | 0.00 | 1.46 | 0.00 |
| time (sec) |
N/A | 1.045 | 2.308 | 7.339 | 0.000 | 0.106 | 0.000 | 0.000 | 0.665 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 532 | 529 | 255 | 373 | 0 | 0 | 0 | 0 | 490 | 0 |
| N.S. |
1 | 0.99 | 0.48 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
| time (sec) |
N/A | 0.887 | 2.164 | 6.833 | 0.000 | 0.000 | 0.000 | 0.000 | 0.783 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 651 | 590 | 282 | 386 | 0 | 0 | 0 | 0 | 1617 | 0 |
| N.S. |
1 | 0.91 | 0.43 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 2.48 | 0.00 |
| time (sec) |
N/A | 0.999 | 2.402 | 6.849 | 0.000 | 0.000 | 0.000 | 0.000 | 1.462 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 532 | 479 | 366 | 582 | 0 | 499 | 0 | 0 | 906 | 0 |
| N.S. |
1 | 0.90 | 0.69 | 1.09 | 0.00 | 0.94 | 0.00 | 0.00 | 1.70 | 0.00 |
| time (sec) |
N/A | 0.744 | 2.577 | 8.799 | 0.000 | 0.103 | 0.000 | 0.000 | 0.792 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 388 | 356 | 270 | 417 | 0 | 324 | 0 | 0 | 521 | 0 |
| N.S. |
1 | 0.92 | 0.70 | 1.07 | 0.00 | 0.84 | 0.00 | 0.00 | 1.34 | 0.00 |
| time (sec) |
N/A | 0.528 | 1.731 | 7.071 | 0.000 | 0.099 | 0.000 | 0.000 | 0.600 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 265 | 215 | 312 | 0 | 214 | 0 | 0 | 273 | 0 |
| N.S. |
1 | 0.93 | 0.76 | 1.10 | 0.00 | 0.75 | 0.00 | 0.00 | 0.96 | 0.00 |
| time (sec) |
N/A | 0.365 | 1.396 | 5.178 | 0.000 | 0.090 | 0.000 | 0.000 | 0.421 | 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 | 262 | 256 | 206 | 298 | 0 | 0 | 0 | 0 | 224 | 0 |
| N.S. |
1 | 0.98 | 0.79 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
| time (sec) |
N/A | 0.383 | 1.409 | 5.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.504 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 326 | 247 | 360 | 0 | 192 | 0 | 0 | 1015 | 0 |
| N.S. |
1 | 1.15 | 0.87 | 1.27 | 0.00 | 0.68 | 0.00 | 0.00 | 3.57 | 0.00 |
| time (sec) |
N/A | 0.491 | 1.757 | 6.205 | 0.000 | 0.096 | 0.000 | 0.000 | 1.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 430 | 342 | 476 | 0 | 320 | 0 | 0 | 970 | 0 |
| N.S. |
1 | 1.10 | 0.87 | 1.22 | 0.00 | 0.82 | 0.00 | 0.00 | 2.48 | 0.00 |
| time (sec) |
N/A | 0.687 | 2.279 | 8.316 | 0.000 | 0.096 | 0.000 | 0.000 | 1.880 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 531 | 583 | 464 | 640 | 0 | 488 | 0 | 0 | 910 | 0 |
| N.S. |
1 | 1.10 | 0.87 | 1.21 | 0.00 | 0.92 | 0.00 | 0.00 | 1.71 | 0.00 |
| time (sec) |
N/A | 0.979 | 3.796 | 10.562 | 0.000 | 0.097 | 0.000 | 0.000 | 2.913 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 555 | 0 | 433 | 543 | 0 | 0 | 0 | 0 | 1495 | 0 |
| N.S. |
1 | 0.00 | 0.78 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 2.69 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.288 | 10.615 | 0.000 | 0.000 | 0.000 | 0.000 | 11.696 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 399 | 0 | 323 | 600 | 0 | 0 | 0 | 0 | 604 | 0 |
| N.S. |
1 | 0.00 | 0.81 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 1.51 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.217 | 10.948 | 0.000 | 0.000 | 0.000 | 0.000 | 5.040 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 316 | 0 | 187 | 274 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 0.00 | 0.59 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.000 | 1.868 | 4.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.590 | 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 | 102 | 102 | 143 | 191 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.00 | 1.40 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.207 | 1.596 | 4.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.350 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 387 | 0 | 373 | 302 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 0.00 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.000 | 2.387 | 8.276 | 0.000 | 0.000 | 0.000 | 0.000 | 7.643 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 498 | 0 | 345 | 448 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 0.00 | 0.69 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.722 | 8.648 | 0.000 | 0.000 | 0.000 | 0.000 | 25.131 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 702 | 0 | 1020 | 799 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 0.00 | 1.45 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.193 | 10.756 | 0.000 | 0.000 | 0.000 | 0.000 | 36.996 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 643 | 0 | 438 | 1554 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.68 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.909 | 23.783 | 0.000 | 0.000 | 0.000 | 0.000 | 89.808 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 538 | 0 | 359 | 1214 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.67 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.967 | 6.740 | 0.000 | 0.000 | 0.000 | 0.000 | 19.004 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 496 | 0 | 253 | 812 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.00 | 0.51 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.000 | 2.720 | 6.746 | 0.000 | 0.000 | 0.000 | 0.000 | 9.669 | 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 | 440 | 565 | 496 | 725 | 0 | 0 | 0 | 0 | 67 | 0 |
| N.S. |
1 | 1.28 | 1.13 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.871 | 3.377 | 6.612 | 0.000 | 0.000 | 0.000 | 0.000 | 9.938 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 648 | 0 | 293 | 1058 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.00 | 0.45 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.690 | 20.564 | 0.000 | 0.000 | 0.000 | 0.000 | 21.409 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 840 | 0 | 392 | 1401 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.47 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.213 | 21.854 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1095 | 0 | 470 | 1785 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.43 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.930 | 22.353 | 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 | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 630 | 962 | 488 | 964 | 0 | 1047 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.53 | 0.77 | 1.53 | 0.00 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.688 | 4.946 | 20.312 | 0.000 | 0.112 | 0.000 | 0.000 | 2.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 443 | 745 | 363 | 718 | 0 | 708 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.68 | 0.82 | 1.62 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.314 | 3.941 | 11.047 | 0.000 | 0.104 | 0.000 | 0.000 | 1.641 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 306 | 595 | 281 | 532 | 0 | 423 | 0 | 0 | 1420 | 0 |
| N.S. |
1 | 1.94 | 0.92 | 1.74 | 0.00 | 1.38 | 0.00 | 0.00 | 4.64 | 0.00 |
| time (sec) |
N/A | 0.786 | 3.348 | 8.972 | 0.000 | 0.111 | 0.000 | 0.000 | 1.192 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 576 | 270 | 478 | 0 | 0 | 0 | 0 | 1342 | 0 |
| N.S. |
1 | 1.34 | 0.63 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 3.13 | 0.00 |
| time (sec) |
N/A | 0.983 | 3.404 | 9.516 | 0.000 | 0.000 | 0.000 | 0.000 | 1.812 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 569 | 701 | 331 | 530 | 0 | 429 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.23 | 0.58 | 0.93 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.281 | 4.210 | 10.405 | 0.000 | 0.116 | 0.000 | 0.000 | 2.948 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 879 | 881 | 441 | 675 | 0 | 664 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.50 | 0.77 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.609 | 4.714 | 19.520 | 0.000 | 0.104 | 0.000 | 0.000 | 5.650 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 392 | 414 | 305 | 609 | 0 | 556 | 0 | 0 | 1483 | 0 |
| N.S. |
1 | 1.06 | 0.78 | 1.55 | 0.00 | 1.42 | 0.00 | 0.00 | 3.78 | 0.00 |
| time (sec) |
N/A | 0.656 | 3.607 | 11.028 | 0.000 | 0.106 | 0.000 | 0.000 | 1.232 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 283 | 323 | 232 | 444 | 0 | 354 | 0 | 0 | 1048 | 0 |
| N.S. |
1 | 1.14 | 0.82 | 1.57 | 0.00 | 1.25 | 0.00 | 0.00 | 3.70 | 0.00 |
| time (sec) |
N/A | 0.505 | 2.689 | 8.954 | 0.000 | 0.115 | 0.000 | 0.000 | 0.961 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 259 | 208 | 378 | 0 | 237 | 0 | 0 | 840 | 0 |
| N.S. |
1 | 1.26 | 1.01 | 1.83 | 0.00 | 1.15 | 0.00 | 0.00 | 4.08 | 0.00 |
| time (sec) |
N/A | 0.364 | 2.450 | 4.665 | 0.000 | 0.094 | 0.000 | 0.000 | 0.741 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 309 | 217 | 382 | 0 | 214 | 0 | 0 | 797 | 0 |
| N.S. |
1 | 1.44 | 1.01 | 1.78 | 0.00 | 1.00 | 0.00 | 0.00 | 3.71 | 0.00 |
| time (sec) |
N/A | 0.483 | 2.806 | 10.286 | 0.000 | 0.087 | 0.000 | 0.000 | 1.092 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 289 | 384 | 274 | 460 | 0 | 326 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.33 | 0.95 | 1.59 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.612 | 3.358 | 9.864 | 0.000 | 0.090 | 0.000 | 0.000 | 1.910 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 489 | 383 | 587 | 0 | 552 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.25 | 0.98 | 1.50 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.808 | 4.223 | 19.500 | 0.000 | 0.097 | 0.000 | 0.000 | 3.051 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 379 | 0 | 303 | 637 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.80 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.745 | 6.762 | 0.000 | 0.000 | 0.000 | 0.000 | 17.509 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 0 | 275 | 390 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.00 | 1.09 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.527 | 6.339 | 0.000 | 0.000 | 0.000 | 0.000 | 9.632 | 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 | 209 | 209 | 207 | 286 | 0 | 0 | 0 | 0 | 67 | 0 |
| N.S. |
1 | 1.00 | 0.99 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.312 | 3.274 | 6.588 | 0.000 | 0.000 | 0.000 | 0.000 | 8.918 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 463 | 0 | 493 | 586 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.00 | 1.06 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.522 | 19.754 | 0.000 | 0.000 | 0.000 | 0.000 | 22.446 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 626 | 0 | 446 | 772 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.00 | 0.71 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.533 | 21.519 | 0.000 | 0.000 | 0.000 | 0.000 | 36.646 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 887 | 0 | 1430 | 1123 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.00 | 1.61 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.000 | 6.000 | 23.886 | 0.000 | 0.000 | 0.000 | 0.000 | 52.986 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 542 | 0 | 359 | 972 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.66 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.258 | 8.820 | 0.000 | 0.000 | 0.000 | 0.000 | 63.864 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 514 | 0 | 266 | 866 | 0 | 0 | 0 | 0 | 111 | 0 |
| N.S. |
1 | 0.00 | 0.52 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.512 | 9.209 | 0.000 | 0.000 | 0.000 | 0.000 | 35.527 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 415 | 1179 | 277 | 873 | 0 | 0 | 0 | 0 | 108 | 0 |
| N.S. |
1 | 2.84 | 0.67 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 1.700 | 4.446 | 8.895 | 0.000 | 0.000 | 0.000 | 0.000 | 33.431 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 766 | 0 | 355 | 1228 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.46 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.401 | 25.255 | 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 | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 974 | 0 | 472 | 1678 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.48 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.771 | 27.420 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1300 | 0 | 669 | 2108 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.51 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 0.000 | 6.693 | 28.908 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 0 | 275 | 390 | 0 | 0 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 0.00 | 1.09 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.217 | 6.448 | 0.000 | 0.000 | 0.000 | 0.000 | 9.595 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 357 | 0 | 354 | 382 | 0 | 0 | 0 | 0 | 71 | 0 |
| N.S. |
1 | 0.00 | 0.99 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.571 | 6.378 | 0.000 | 0.000 | 0.000 | 0.000 | 9.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 248 | 198 | 283 | 0 | 125 | 0 | 0 | 94 | 0 |
| N.S. |
1 | 1.19 | 0.95 | 1.35 | 0.00 | 0.60 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.370 | 3.271 | 5.505 | 0.000 | 0.115 | 0.000 | 0.000 | 0.299 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 228 | 207 | 282 | 0 | 124 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 1.03 | 0.93 | 1.27 | 0.00 | 0.56 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.404 | 3.238 | 6.224 | 0.000 | 0.097 | 0.000 | 0.000 | 0.300 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 228 | 204 | 282 | 0 | 124 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 1.03 | 0.92 | 1.27 | 0.00 | 0.56 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.401 | 3.352 | 6.323 | 0.000 | 0.093 | 0.000 | 0.000 | 0.304 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 225 | 231 | 209 | 283 | 0 | 123 | 0 | 0 | 102 | 0 |
| N.S. |
1 | 1.03 | 0.93 | 1.26 | 0.00 | 0.55 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.406 | 3.286 | 5.955 | 0.000 | 0.093 | 0.000 | 0.000 | 0.319 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 587 | 862 | 450 | 617 | 0 | 601 | 0 | 0 | 1140 | 0 |
| N.S. |
1 | 1.47 | 0.77 | 1.05 | 0.00 | 1.02 | 0.00 | 0.00 | 1.94 | 0.00 |
| time (sec) |
N/A | 1.601 | 9.162 | 12.234 | 0.000 | 0.103 | 0.000 | 0.000 | 0.981 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 411 | 638 | 318 | 436 | 0 | 368 | 0 | 0 | 599 | 0 |
| N.S. |
1 | 1.55 | 0.77 | 1.06 | 0.00 | 0.90 | 0.00 | 0.00 | 1.46 | 0.00 |
| time (sec) |
N/A | 1.089 | 6.210 | 8.532 | 0.000 | 0.108 | 0.000 | 0.000 | 0.670 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 302 | 483 | 236 | 325 | 0 | 224 | 0 | 0 | 288 | 0 |
| N.S. |
1 | 1.60 | 0.78 | 1.08 | 0.00 | 0.74 | 0.00 | 0.00 | 0.95 | 0.00 |
| time (sec) |
N/A | 0.612 | 4.182 | 6.154 | 0.000 | 0.100 | 0.000 | 0.000 | 0.464 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 463 | 225 | 304 | 0 | 0 | 0 | 0 | 187 | 0 |
| N.S. |
1 | 1.69 | 0.82 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
| time (sec) |
N/A | 0.761 | 3.756 | 5.978 | 0.000 | 0.000 | 0.000 | 0.000 | 0.557 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 581 | 272 | 374 | 0 | 228 | 0 | 0 | 998 | 0 |
| N.S. |
1 | 1.95 | 0.91 | 1.26 | 0.00 | 0.77 | 0.00 | 0.00 | 3.35 | 0.00 |
| time (sec) |
N/A | 1.038 | 5.022 | 7.625 | 0.000 | 0.116 | 0.000 | 0.000 | 1.334 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 423 | 771 | 401 | 523 | 0 | 369 | 0 | 0 | 994 | 0 |
| N.S. |
1 | 1.82 | 0.95 | 1.24 | 0.00 | 0.87 | 0.00 | 0.00 | 2.35 | 0.00 |
| time (sec) |
N/A | 1.369 | 6.624 | 10.708 | 0.000 | 0.090 | 0.000 | 0.000 | 1.930 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 608 | 1038 | 575 | 755 | 0 | 598 | 0 | 0 | 932 | 0 |
| N.S. |
1 | 1.71 | 0.95 | 1.24 | 0.00 | 0.98 | 0.00 | 0.00 | 1.53 | 0.00 |
| time (sec) |
N/A | 1.866 | 9.656 | 19.594 | 0.000 | 0.093 | 0.000 | 0.000 | 3.097 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 524 | 489 | 382 | 575 | 0 | 494 | 0 | 0 | 906 | 0 |
| N.S. |
1 | 0.93 | 0.73 | 1.10 | 0.00 | 0.94 | 0.00 | 0.00 | 1.73 | 0.00 |
| time (sec) |
N/A | 0.832 | 7.400 | 10.667 | 0.000 | 0.097 | 0.000 | 0.000 | 0.783 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 381 | 365 | 287 | 414 | 0 | 319 | 0 | 0 | 522 | 0 |
| N.S. |
1 | 0.96 | 0.75 | 1.09 | 0.00 | 0.84 | 0.00 | 0.00 | 1.37 | 0.00 |
| time (sec) |
N/A | 0.574 | 5.612 | 8.375 | 0.000 | 0.093 | 0.000 | 0.000 | 0.616 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 265 | 218 | 302 | 0 | 186 | 0 | 0 | 229 | 0 |
| N.S. |
1 | 0.94 | 0.78 | 1.07 | 0.00 | 0.66 | 0.00 | 0.00 | 0.81 | 0.00 |
| time (sec) |
N/A | 0.383 | 3.362 | 5.608 | 0.000 | 0.101 | 0.000 | 0.000 | 0.430 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 207 | 131 | 158 | 0 | 130 | 0 | 0 | 94 | 0 |
| N.S. |
1 | 1.00 | 0.64 | 0.77 | 0.00 | 0.63 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 0.297 | 2.192 | 3.725 | 0.000 | 0.082 | 0.000 | 0.000 | 0.237 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 248 | 198 | 283 | 0 | 125 | 0 | 0 | 94 | 0 |
| N.S. |
1 | 1.19 | 0.95 | 1.35 | 0.00 | 0.60 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.373 | 0.221 | 5.530 | 0.000 | 0.094 | 0.000 | 0.000 | 0.291 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 325 | 256 | 333 | 0 | 188 | 0 | 0 | 132 | 0 |
| N.S. |
1 | 1.14 | 0.90 | 1.16 | 0.00 | 0.66 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 0.486 | 4.045 | 7.229 | 0.000 | 0.091 | 0.000 | 0.000 | 0.851 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 438 | 355 | 481 | 0 | 319 | 0 | 0 | 287 | 0 |
| N.S. |
1 | 1.12 | 0.91 | 1.23 | 0.00 | 0.82 | 0.00 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.702 | 5.892 | 9.748 | 0.000 | 0.093 | 0.000 | 0.000 | 1.648 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 597 | 0 | 419 | 528 | 0 | 0 | 0 | 0 | 1496 | 0 |
| N.S. |
1 | 0.00 | 0.70 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 2.51 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.533 | 20.188 | 0.000 | 0.000 | 0.000 | 0.000 | 11.647 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 438 | 0 | 315 | 510 | 0 | 0 | 0 | 0 | 608 | 0 |
| N.S. |
1 | 0.00 | 0.72 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 1.39 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.898 | 20.434 | 0.000 | 0.000 | 0.000 | 0.000 | 5.098 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 334 | 0 | 172 | 202 | 0 | 0 | 0 | 0 | 78 | 0 |
| N.S. |
1 | 0.00 | 0.51 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.138 | 5.747 | 0.000 | 0.000 | 0.000 | 0.000 | 0.681 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 0 | 130 | 143 | 0 | 0 | 0 | 0 | 78 | 0 |
| N.S. |
1 | 0.00 | 0.63 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.000 | 2.144 | 5.819 | 0.000 | 0.000 | 0.000 | 0.000 | 0.474 | 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 | 100 | 101 | 118 | 0 | 0 | 0 | 0 | 75 | 0 |
| N.S. |
1 | 0.47 | 0.48 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.272 | 1.952 | 5.770 | 0.000 | 0.000 | 0.000 | 0.000 | 0.366 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 379 | 0 | 297 | 302 | 0 | 0 | 0 | 0 | 78 | 0 |
| N.S. |
1 | 0.00 | 0.78 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.095 | 8.981 | 0.000 | 0.000 | 0.000 | 0.000 | 1.066 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 441 | 0 | 341 | 445 | 0 | 0 | 0 | 0 | 626 | 0 |
| N.S. |
1 | 0.00 | 0.77 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.854 | 10.641 | 0.000 | 0.000 | 0.000 | 0.000 | 12.609 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 601 | 0 | 962 | 792 | 0 | 0 | 0 | 0 | 1538 | 0 |
| N.S. |
1 | 0.00 | 1.60 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 2.56 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.196 | 20.853 | 0.000 | 0.000 | 0.000 | 0.000 | 56.550 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 719 | 0 | 537 | 1454 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.75 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.728 | 25.770 | 0.000 | 0.000 | 0.000 | 0.000 | 127.903 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 544 | 0 | 397 | 1269 | 0 | 0 | 0 | 0 | 130 | 0 |
| N.S. |
1 | 0.00 | 0.73 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.612 | 6.961 | 0.000 | 0.000 | 0.000 | 0.000 | 9.580 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 482 | 0 | 887 | 1061 | 0 | 0 | 0 | 0 | 130 | 0 |
| N.S. |
1 | 0.00 | 1.84 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.359 | 8.063 | 0.000 | 0.000 | 0.000 | 0.000 | 9.925 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 452 | 0 | 425 | 710 | 0 | 0 | 0 | 0 | 130 | 0 |
| N.S. |
1 | 0.00 | 0.94 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.892 | 8.552 | 0.000 | 0.000 | 0.000 | 0.000 | 8.551 | 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 | 426 | 448 | 587 | 973 | 0 | 0 | 0 | 0 | 127 | 0 |
| N.S. |
1 | 1.05 | 1.38 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.639 | 4.208 | 8.598 | 0.000 | 0.000 | 0.000 | 0.000 | 0.791 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 531 | 0 | 434 | 1214 | 0 | 0 | 0 | 0 | 1418 | 0 |
| N.S. |
1 | 0.00 | 0.82 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 2.67 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.044 | 22.639 | 0.000 | 0.000 | 0.000 | 0.000 | 18.644 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 705 | 0 | 476 | 1391 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.68 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.621 | 24.068 | 0.000 | 0.000 | 0.000 | 0.000 | 55.807 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1080 | 0 | 730 | 3361 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 0.00 | 0.68 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 0.000 | 6.100 | 30.414 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 852 | 0 | 559 | 2927 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.66 | 3.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 5.089 | 11.052 | 0.000 | 0.000 | 0.000 | 0.000 | 108.548 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 666 | 0 | 458 | 2712 | 0 | 0 | 0 | 0 | 182 | 0 |
| N.S. |
1 | 0.00 | 0.69 | 4.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.704 | 11.073 | 0.000 | 0.000 | 0.000 | 0.000 | 18.430 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 582 | 0 | 392 | 2074 | 0 | 0 | 0 | 0 | 182 | 0 |
| N.S. |
1 | 0.00 | 0.67 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
| time (sec) |
N/A | 0.000 | 4.354 | 9.879 | 0.000 | 0.000 | 0.000 | 0.000 | 21.109 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 583 | 0 | 391 | 1952 | 0 | 0 | 0 | 0 | 182 | 0 |
| N.S. |
1 | 0.00 | 0.67 | 3.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.933 | 11.151 | 0.000 | 0.000 | 0.000 | 0.000 | 19.051 | 0.000 |