Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 105 | 78 | 0 | 0 | 0 | 76 | 0 | 990 | 0 |
| N.S. |
1 | 1.04 | 0.77 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 9.80 | 0.00 |
| time (sec) |
N/A | 0.258 | 0.562 | 0.000 | 0.000 | 0.000 | 144.144 | 0.000 | 0.374 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 76 | 100 | 0 | 0 | 0 | 65 | 0 | 236 | 68 |
| N.S. |
1 | 1.01 | 1.33 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 3.15 | 0.91 |
| time (sec) |
N/A | 0.200 | 0.304 | 0.000 | 0.000 | 0.000 | 71.382 | 0.000 | 0.247 | 22.994 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 102 | 77 | 0 | 0 | 0 | 76 | 0 | 543 | 0 |
| N.S. |
1 | 1.01 | 0.76 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 5.38 | 0.00 |
| time (sec) |
N/A | 0.250 | 0.557 | 0.000 | 0.000 | 0.000 | 91.711 | 0.000 | 0.331 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 94 | 89 | 0 | 0 | 0 | 68 | 0 | 261 | 0 |
| N.S. |
1 | 1.01 | 0.96 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 | 2.81 | 0.00 |
| time (sec) |
N/A | 0.238 | 0.198 | 0.000 | 0.000 | 0.000 | 70.632 | 0.000 | 0.319 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 100 | 77 | 0 | 0 | 0 | 80 | 0 | 486 | 0 |
| N.S. |
1 | 0.99 | 0.76 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 4.81 | 0.00 |
| time (sec) |
N/A | 0.257 | 0.582 | 0.000 | 0.000 | 0.000 | 104.365 | 0.000 | 0.413 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 95 | 89 | 0 | 0 | 0 | 71 | 0 | 301 | 0 |
| N.S. |
1 | 1.02 | 0.96 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 3.24 | 0.00 |
| time (sec) |
N/A | 0.245 | 0.194 | 0.000 | 0.000 | 0.000 | 113.819 | 0.000 | 0.363 | 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 | 101 | 101 | 78 | 0 | 0 | 0 | 0 | 0 | 980 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 9.70 | 0.00 |
| time (sec) |
N/A | 0.243 | 0.569 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.369 | 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 | 101 | 101 | 78 | 0 | 0 | 0 | 0 | 0 | 552 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.47 | 0.00 |
| time (sec) |
N/A | 0.246 | 0.570 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.318 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 75 | 0 | 0 | 0 | 75 | 0 | 535 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 5.57 | 0.00 |
| time (sec) |
N/A | 0.232 | 0.562 | 0.000 | 0.000 | 0.000 | 144.457 | 0.000 | 0.323 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 77 | 0 | 0 | 0 | 78 | 0 | 581 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 5.87 | 0.00 |
| time (sec) |
N/A | 0.238 | 0.574 | 0.000 | 0.000 | 0.000 | 123.984 | 0.000 | 0.399 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 78 | 0 | 0 | 0 | 78 | 0 | 584 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 | 6.08 | 0.00 |
| time (sec) |
N/A | 0.232 | 0.576 | 0.000 | 0.000 | 0.000 | 123.757 | 0.000 | 0.441 | 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 | 160 | 160 | 109 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.333 | 0.650 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.562 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 134 | 135 | 0 | 0 | 0 | 0 | 0 | 846 | 0 |
| N.S. |
1 | 1.01 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 6.36 | 0.00 |
| time (sec) |
N/A | 0.290 | 1.401 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.301 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 166 | 108 | 0 | 0 | 0 | 121 | 0 | 1531 | 0 |
| N.S. |
1 | 1.04 | 0.68 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 9.63 | 0.00 |
| time (sec) |
N/A | 0.378 | 0.626 | 0.000 | 0.000 | 0.000 | 178.093 | 0.000 | 0.452 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 124 | 103 | 0 | 0 | 0 | 110 | 0 | 489 | 0 |
| N.S. |
1 | 1.02 | 0.84 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 | 4.01 | 0.00 |
| time (sec) |
N/A | 0.278 | 0.297 | 0.000 | 0.000 | 0.000 | 85.045 | 0.000 | 0.435 | 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 | 155 | 156 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.317 | 0.657 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.004 | 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 | 136 | 133 | 140 | 0 | 0 | 0 | 0 | 0 | 656 | 0 |
| N.S. |
1 | 0.98 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.82 | 0.00 |
| time (sec) |
N/A | 0.295 | 0.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.642 | 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 | 157 | 156 | 109 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.298 | 0.616 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.725 | 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 | 157 | 156 | 109 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.301 | 0.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.688 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 0 | 106 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.611 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.497 | 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 | 153 | 154 | 108 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.295 | 0.614 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.662 | 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 | 152 | 152 | 108 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.289 | 0.624 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.780 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 135 | 186 | 0 | 0 | 0 | 0 | 0 | 583 | 0 |
| N.S. |
1 | 1.03 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.45 | 0.00 |
| time (sec) |
N/A | 0.319 | 0.678 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 10.393 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 178 | 0 | 0 | 0 | 0 | 0 | 0 | 535 | 0 |
| N.S. |
1 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.18 | 0.00 |
| time (sec) |
N/A | 0.382 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 6.406 | 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 | 130 | 131 | 143 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.01 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.303 | 0.566 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.455 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 129 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.336 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.775 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 183 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.356 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.388 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 183 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.117 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 182 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.380 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.438 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 530 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.14 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 6.610 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.777 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 123 | 0 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.307 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.772 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.020 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.775 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 287 | 259 | 243 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.453 | 0.786 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 78.809 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 322 | 0 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.610 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 11.634 | 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 | 198 | 197 | 158 | 0 | 0 | 0 | 0 | 0 | 1055 | 0 |
| N.S. |
1 | 0.99 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.33 | 0.00 |
| time (sec) |
N/A | 0.431 | 0.699 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 40.331 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 195 | 0 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.417 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 11.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 312 | 0 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.625 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 15.827 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 377 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.661 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 25.455 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 302 | 341 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 0.97 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.623 | 2.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 66.499 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 11.793 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 12.225 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 189 | 0 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.396 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 11.534 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 22.669 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 71.399 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 131 | 126 | 136 | 0 | 430 | 0 | 125 | 27 | 8521 |
| N.S. |
1 | 0.99 | 0.95 | 1.03 | 0.00 | 3.26 | 0.00 | 0.95 | 0.20 | 64.55 |
| time (sec) |
N/A | 0.368 | 0.084 | 0.136 | 0.000 | 0.988 | 0.000 | 1.020 | 200.020 | 24.714 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 95 | 93 | 98 | 0 | 305 | 434 | 91 | 27 | 6587 |
| N.S. |
1 | 0.98 | 0.96 | 1.01 | 0.00 | 3.14 | 4.47 | 0.94 | 0.28 | 67.91 |
| time (sec) |
N/A | 0.291 | 0.092 | 0.087 | 0.000 | 0.377 | 38.895 | 1.020 | 200.036 | 24.310 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 74 | 71 | 66 | 0 | 216 | 287 | 68 | 27 | 3704 |
| N.S. |
1 | 1.03 | 0.99 | 0.92 | 0.00 | 3.00 | 3.99 | 0.94 | 0.38 | 51.44 |
| time (sec) |
N/A | 0.249 | 0.065 | 0.088 | 0.000 | 0.182 | 10.548 | 1.031 | 200.031 | 23.410 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 81 | 80 | 74 | 0 | 240 | 0 | 77 | 27 | 8454 |
| N.S. |
1 | 1.04 | 1.03 | 0.95 | 0.00 | 3.08 | 0.00 | 0.99 | 0.35 | 108.38 |
| time (sec) |
N/A | 0.290 | 0.050 | 0.083 | 0.000 | 0.471 | 0.000 | 1.020 | 200.025 | 24.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 114 | 130 | 125 | 0 | 385 | 0 | 125 | 27 | 14100 |
| N.S. |
1 | 1.02 | 1.16 | 1.12 | 0.00 | 3.44 | 0.00 | 1.12 | 0.24 | 125.89 |
| time (sec) |
N/A | 0.355 | 0.061 | 0.115 | 0.000 | 1.248 | 0.000 | 1.014 | 200.017 | 43.396 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 193 | 179 | 0 | 533 | 0 | 181 | 27 | 19687 |
| N.S. |
1 | 1.00 | 1.25 | 1.15 | 0.00 | 3.44 | 0.00 | 1.17 | 0.17 | 127.01 |
| time (sec) |
N/A | 0.435 | 0.098 | 0.154 | 0.000 | 3.373 | 0.000 | 1.012 | 200.038 | 63.283 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 280 | 333 | 298 | 0 | 4744 | 0 | 4524 | 27 | 26868 |
| N.S. |
1 | 1.03 | 1.22 | 1.09 | 0.00 | 17.38 | 0.00 | 16.57 | 0.10 | 98.42 |
| time (sec) |
N/A | 0.631 | 0.547 | 0.119 | 0.000 | 2.565 | 0.000 | 1.276 | 200.020 | 27.389 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 224 | 259 | 219 | 0 | 2520 | 0 | 2966 | 27 | 17577 |
| N.S. |
1 | 1.01 | 1.17 | 0.99 | 0.00 | 11.40 | 0.00 | 13.42 | 0.12 | 79.53 |
| time (sec) |
N/A | 0.461 | 0.181 | 0.095 | 0.000 | 0.364 | 0.000 | 1.275 | 200.022 | 27.963 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 182 | 179 | 168 | 0 | 1535 | 0 | 1404 | 25 | 4501 |
| N.S. |
1 | 0.99 | 0.97 | 0.91 | 0.00 | 8.34 | 0.00 | 7.63 | 0.14 | 24.46 |
| time (sec) |
N/A | 0.339 | 0.150 | 0.091 | 0.000 | 0.207 | 0.000 | 1.563 | 200.018 | 26.531 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 195 | 89 | 177 | 0 | 2772 | 0 | 3003 | 27 | 15013 |
| N.S. |
1 | 0.98 | 0.45 | 0.89 | 0.00 | 13.93 | 0.00 | 15.09 | 0.14 | 75.44 |
| time (sec) |
N/A | 0.418 | 0.048 | 0.105 | 0.000 | 0.728 | 0.000 | 1.392 | 200.014 | 26.218 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 247 | 136 | 236 | 0 | 4924 | 0 | 4428 | 27 | 24353 |
| N.S. |
1 | 0.96 | 0.53 | 0.92 | 0.00 | 19.16 | 0.00 | 17.23 | 0.11 | 94.76 |
| time (sec) |
N/A | 0.536 | 0.064 | 0.138 | 0.000 | 3.579 | 0.000 | 1.388 | 200.019 | 27.554 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 433 | 366 | 88 | 67 | 0 | 12866 | 0 | 0 | 27 | 50213 |
| N.S. |
1 | 0.85 | 0.20 | 0.15 | 0.00 | 29.71 | 0.00 | 0.00 | 0.06 | 115.97 |
| time (sec) |
N/A | 0.704 | 0.069 | 0.063 | 0.000 | 6.242 | 0.000 | 0.000 | 200.028 | 28.468 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 375 | 330 | 59 | 51 | 0 | 15561 | 0 | 0 | 27 | 29445 |
| N.S. |
1 | 0.88 | 0.16 | 0.14 | 0.00 | 41.50 | 0.00 | 0.00 | 0.07 | 78.52 |
| time (sec) |
N/A | 0.521 | 0.049 | 0.052 | 0.000 | 42.815 | 0.000 | 0.000 | 200.498 | 28.428 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 375 | 328 | 61 | 47 | 0 | 9245 | 0 | 0 | 24 | 36707 |
| N.S. |
1 | 0.87 | 0.16 | 0.13 | 0.00 | 24.65 | 0.00 | 0.00 | 0.06 | 97.89 |
| time (sec) |
N/A | 0.512 | 0.046 | 0.048 | 0.000 | 2.250 | 0.000 | 0.000 | 200.016 | 27.401 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 392 | 345 | 85 | 73 | 0 | 21400 | 0 | 0 | 27 | 39028 |
| N.S. |
1 | 0.88 | 0.22 | 0.19 | 0.00 | 54.59 | 0.00 | 0.00 | 0.07 | 99.56 |
| time (sec) |
N/A | 0.610 | 0.063 | 0.083 | 0.000 | 120.721 | 0.000 | 0.000 | 200.013 | 29.399 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 394 | 345 | 86 | 68 | 0 | 20184 | 0 | 0 | 27 | 65350 |
| N.S. |
1 | 0.88 | 0.22 | 0.17 | 0.00 | 51.23 | 0.00 | 0.00 | 0.07 | 165.86 |
| time (sec) |
N/A | 0.583 | 0.067 | 0.088 | 0.000 | 46.406 | 0.000 | 0.000 | 200.023 | 30.279 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 106 | 85 | 38 | 0 | 67 | 75 | 69 | 341 | 58 |
| N.S. |
1 | 1.61 | 1.29 | 0.58 | 0.00 | 1.02 | 1.14 | 1.05 | 5.17 | 0.88 |
| time (sec) |
N/A | 0.327 | 0.173 | 0.066 | 0.000 | 0.062 | 0.095 | 0.132 | 0.178 | 0.113 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 40 | 39 | 33 | 32 | 32 | 37 | 32 | 328 | 34 |
| N.S. |
1 | 1.03 | 1.00 | 0.85 | 0.82 | 0.82 | 0.95 | 0.82 | 8.41 | 0.87 |
| time (sec) |
N/A | 0.217 | 0.018 | 0.046 | 0.119 | 0.061 | 0.060 | 0.110 | 0.165 | 0.052 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | A | A | F | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 54 | 44 | 39 | 0 | 41 | 42 | 31 | 72 | 20 |
| N.S. |
1 | 2.08 | 1.69 | 1.50 | 0.00 | 1.58 | 1.62 | 1.19 | 2.77 | 0.77 |
| time (sec) |
N/A | 0.221 | 0.020 | 0.052 | 0.000 | 0.058 | 0.054 | 0.138 | 0.159 | 21.131 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 44 | 44 | 33 | 38 | 34 | 41 | 38 | 330 | 36 |
| N.S. |
1 | 1.07 | 1.07 | 0.80 | 0.93 | 0.83 | 1.00 | 0.93 | 8.05 | 0.88 |
| time (sec) |
N/A | 0.225 | 0.018 | 0.056 | 0.109 | 0.059 | 0.073 | 0.141 | 0.172 | 21.249 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 95 | 49 | 40 | 0 | 79 | 76 | 81 | 376 | 56 |
| N.S. |
1 | 1.44 | 0.74 | 0.61 | 0.00 | 1.20 | 1.15 | 1.23 | 5.70 | 0.85 |
| time (sec) |
N/A | 0.336 | 0.021 | 0.074 | 0.000 | 0.068 | 0.101 | 0.117 | 0.165 | 0.061 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 414 | 48 | 46 | 0 | 378 | 32 | 258 | 412 | 291 |
| N.S. |
1 | 1.48 | 0.17 | 0.16 | 0.00 | 1.35 | 0.11 | 0.92 | 1.47 | 1.04 |
| time (sec) |
N/A | 0.602 | 0.022 | 0.056 | 0.000 | 0.072 | 1.253 | 0.154 | 0.163 | 0.155 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 414 | 46 | 34 | 0 | 132 | 170 | 208 | 318 | 56 |
| N.S. |
1 | 1.86 | 0.21 | 0.15 | 0.00 | 0.59 | 0.77 | 0.94 | 1.43 | 0.25 |
| time (sec) |
N/A | 0.640 | 0.021 | 0.048 | 0.000 | 0.070 | 0.096 | 0.137 | 0.181 | 20.829 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 360 | 55 | 46 | 0 | 373 | 27 | 253 | 300 | 248 |
| N.S. |
1 | 1.26 | 0.19 | 0.16 | 0.00 | 1.31 | 0.09 | 0.89 | 1.05 | 0.87 |
| time (sec) |
N/A | 0.671 | 0.020 | 0.063 | 0.000 | 0.070 | 1.254 | 0.127 | 0.163 | 20.822 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 347 | 57 | 44 | 0 | 337 | 26 | 253 | 300 | 208 |
| N.S. |
1 | 1.22 | 0.20 | 0.15 | 0.00 | 1.18 | 0.09 | 0.89 | 1.05 | 0.73 |
| time (sec) |
N/A | 0.641 | 0.017 | 0.047 | 0.000 | 0.070 | 1.183 | 0.148 | 0.169 | 0.083 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 224 | 418 | 47 | 38 | 0 | 140 | 168 | 210 | 331 | 58 |
| N.S. |
1 | 1.87 | 0.21 | 0.17 | 0.00 | 0.62 | 0.75 | 0.94 | 1.48 | 0.26 |
| time (sec) |
N/A | 0.625 | 0.022 | 0.063 | 0.000 | 0.075 | 0.098 | 0.141 | 0.182 | 20.852 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 370 | 47 | 38 | 0 | 335 | 32 | 258 | 460 | 479 |
| N.S. |
1 | 1.32 | 0.17 | 0.14 | 0.00 | 1.20 | 0.11 | 0.92 | 1.64 | 1.71 |
| time (sec) |
N/A | 0.582 | 0.020 | 0.073 | 0.000 | 0.070 | 1.242 | 0.142 | 0.177 | 20.513 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 131 | 114 | 111 | 0 | 0 | 0 | 131 | 29 | 0 |
| N.S. |
1 | 0.99 | 0.86 | 0.84 | 0.00 | 0.00 | 0.00 | 0.99 | 0.22 | 0.00 |
| time (sec) |
N/A | 0.355 | 0.078 | 0.342 | 0.000 | 0.000 | 0.000 | 1.019 | 200.027 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 116 | 112 | 112 | 0 | 0 | 0 | 133 | 29 | 0 |
| N.S. |
1 | 0.87 | 0.84 | 0.84 | 0.00 | 0.00 | 0.00 | 1.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 0.325 | 0.069 | 0.329 | 0.000 | 0.000 | 0.000 | 1.044 | 200.034 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 168 | 163 | 165 | 0 | 0 | 0 | 170 | 29 | 0 |
| N.S. |
1 | 1.01 | 0.98 | 0.99 | 0.00 | 0.00 | 0.00 | 1.02 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.457 | 0.101 | 1.053 | 0.000 | 0.000 | 0.000 | 1.002 | 200.037 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 204 | 224 | 214 | 0 | 0 | 0 | 232 | 29 | 0 |
| N.S. |
1 | 1.00 | 1.09 | 1.04 | 0.00 | 0.00 | 0.00 | 1.13 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.545 | 0.187 | 1.808 | 0.000 | 0.000 | 0.000 | 1.044 | 200.034 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 268 | 266 | 302 | 283 | 0 | 0 | 0 | 327 | 29 | 0 |
| N.S. |
1 | 0.99 | 1.13 | 1.06 | 0.00 | 0.00 | 0.00 | 1.22 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.676 | 0.264 | 3.237 | 0.000 | 0.000 | 0.000 | 1.058 | 200.035 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 293 | 290 | 334 | 271 | 0 | 15577 | 0 | 5569 | 29 | 122445 |
| N.S. |
1 | 0.99 | 1.14 | 0.92 | 0.00 | 53.16 | 0.00 | 19.01 | 0.10 | 417.90 |
| time (sec) |
N/A | 1.002 | 0.481 | 0.349 | 0.000 | 119.776 | 0.000 | 1.649 | 200.029 | 84.468 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 261 | 289 | 219 | 0 | 12293 | 0 | 4297 | 29 | 104563 |
| N.S. |
1 | 0.98 | 1.09 | 0.83 | 0.00 | 46.39 | 0.00 | 16.22 | 0.11 | 394.58 |
| time (sec) |
N/A | 0.606 | 0.687 | 0.286 | 0.000 | 67.197 | 0.000 | 1.560 | 200.032 | 75.337 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 267 | 264 | 284 | 220 | 0 | 0 | 0 | 7671 | 27 | 104763 |
| N.S. |
1 | 0.99 | 1.06 | 0.82 | 0.00 | 0.00 | 0.00 | 28.73 | 0.10 | 392.37 |
| time (sec) |
N/A | 0.659 | 0.392 | 0.316 | 0.000 | 0.000 | 0.000 | 2.317 | 200.024 | 82.698 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 308 | 226 | 282 | 0 | 0 | 0 | 7626 | 29 | 0 |
| N.S. |
1 | 0.99 | 0.72 | 0.90 | 0.00 | 0.00 | 0.00 | 24.44 | 0.09 | 0.00 |
| time (sec) |
N/A | 0.956 | 0.282 | 0.426 | 0.000 | 0.000 | 0.000 | 2.496 | 200.036 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 366 | 358 | 298 | 356 | 0 | 0 | 0 | 9619 | 29 | 0 |
| N.S. |
1 | 0.98 | 0.81 | 0.97 | 0.00 | 0.00 | 0.00 | 26.28 | 0.08 | 0.00 |
| time (sec) |
N/A | 1.324 | 0.313 | 0.636 | 0.000 | 0.000 | 0.000 | 2.635 | 200.031 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 630 | 699 | 215 | 186 | 0 | 47212 | 0 | 0 | 29 | 359899 |
| N.S. |
1 | 1.11 | 0.34 | 0.30 | 0.00 | 74.94 | 0.00 | 0.00 | 0.05 | 571.27 |
| time (sec) |
N/A | 1.314 | 0.236 | 0.290 | 0.000 | 153.049 | 0.000 | 0.000 | 200.028 | 51.637 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 634 | 703 | 229 | 195 | 0 | 0 | 0 | 0 | 29 | 325549 |
| N.S. |
1 | 1.11 | 0.36 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 513.48 |
| time (sec) |
N/A | 1.274 | 0.227 | 0.262 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 52.159 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 634 | 703 | 231 | 196 | 0 | 0 | 0 | 0 | 26 | 419203 |
| N.S. |
1 | 1.11 | 0.36 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 661.20 |
| time (sec) |
N/A | 1.196 | 0.272 | 0.274 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 53.441 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 709 | 778 | 334 | 228 | 0 | 0 | 0 | 0 | 29 | 276728 |
| N.S. |
1 | 1.10 | 0.47 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 390.31 |
| time (sec) |
N/A | 1.520 | 0.307 | 0.424 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 39.252 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 711 | 780 | 347 | 224 | 0 | 0 | 0 | 0 | 29 | 522994 |
| N.S. |
1 | 1.10 | 0.49 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 735.58 |
| time (sec) |
N/A | 1.412 | 0.363 | 0.457 | 0.000 | 0.000 | 0.000 | 0.000 | 200.037 | 62.918 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 171 | 160 | 210 | 0 | 844 | 0 | 194 | 27 | 12336 |
| N.S. |
1 | 1.16 | 1.08 | 1.42 | 0.00 | 5.70 | 0.00 | 1.31 | 0.18 | 83.35 |
| time (sec) |
N/A | 0.402 | 0.201 | 0.279 | 0.000 | 1.410 | 0.000 | 5.644 | 200.027 | 37.248 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 109 | 112 | 125 | 0 | 542 | 0 | 120 | 3021 | 1081 |
| N.S. |
1 | 0.99 | 1.02 | 1.14 | 0.00 | 4.93 | 0.00 | 1.09 | 27.46 | 9.83 |
| time (sec) |
N/A | 0.279 | 0.147 | 0.121 | 0.000 | 0.112 | 0.000 | 4.841 | 7.317 | 24.651 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 97 | 100 | 96 | 0 | 478 | 374 | 104 | 3019 | 1036 |
| N.S. |
1 | 0.98 | 1.01 | 0.97 | 0.00 | 4.83 | 3.78 | 1.05 | 30.49 | 10.46 |
| time (sec) |
N/A | 0.263 | 0.077 | 0.115 | 0.000 | 0.103 | 15.181 | 4.785 | 7.282 | 25.572 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 180 | 185 | 211 | 0 | 989 | 0 | 201 | 27 | 35718 |
| N.S. |
1 | 1.21 | 1.24 | 1.42 | 0.00 | 6.64 | 0.00 | 1.35 | 0.18 | 239.72 |
| time (sec) |
N/A | 0.468 | 0.164 | 0.276 | 0.000 | 9.126 | 0.000 | 4.753 | 200.016 | 85.155 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 225 | 246 | 294 | 303 | 0 | 1647 | 0 | 254 | 27 | 47178 |
| N.S. |
1 | 1.09 | 1.31 | 1.35 | 0.00 | 7.32 | 0.00 | 1.13 | 0.12 | 209.68 |
| time (sec) |
N/A | 0.604 | 0.262 | 0.294 | 0.000 | 19.233 | 0.000 | 4.804 | 200.022 | 108.625 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 404 | 406 | 463 | 455 | 0 | 6774 | 0 | 4984 | 27 | 45062 |
| N.S. |
1 | 1.00 | 1.15 | 1.13 | 0.00 | 16.77 | 0.00 | 12.34 | 0.07 | 111.54 |
| time (sec) |
N/A | 0.865 | 1.490 | 0.180 | 0.000 | 7.000 | 0.000 | 5.054 | 200.018 | 27.102 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 331 | 366 | 364 | 0 | 4420 | 0 | 3779 | 27 | 34824 |
| N.S. |
1 | 0.99 | 1.09 | 1.08 | 0.00 | 13.15 | 0.00 | 11.25 | 0.08 | 103.64 |
| time (sec) |
N/A | 0.650 | 0.929 | 0.162 | 0.000 | 1.878 | 0.000 | 5.078 | 200.021 | 29.172 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 281 | 303 | 296 | 0 | 3377 | 0 | 3053 | 27 | 26677 |
| N.S. |
1 | 0.98 | 1.06 | 1.03 | 0.00 | 11.81 | 0.00 | 10.67 | 0.09 | 93.28 |
| time (sec) |
N/A | 0.484 | 0.696 | 0.152 | 0.000 | 1.214 | 0.000 | 5.001 | 200.025 | 29.353 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 289 | 316 | 472 | 0 | 4583 | 0 | 4435 | 25 | 32336 |
| N.S. |
1 | 0.97 | 1.06 | 1.58 | 0.00 | 15.33 | 0.00 | 14.83 | 0.08 | 108.15 |
| time (sec) |
N/A | 0.556 | 0.775 | 0.197 | 0.000 | 2.708 | 0.000 | 5.616 | 200.017 | 29.822 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 376 | 360 | 246 | 387 | 0 | 6960 | 0 | 5103 | 27 | 55298 |
| N.S. |
1 | 0.96 | 0.65 | 1.03 | 0.00 | 18.51 | 0.00 | 13.57 | 0.07 | 147.07 |
| time (sec) |
N/A | 0.697 | 0.259 | 0.209 | 0.000 | 9.292 | 0.000 | 4.715 | 200.020 | 31.018 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | B | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 619 | 477 | 171 | 167 | 0 | 26466 | 0 | 0 | 27 | 113499 |
| N.S. |
1 | 0.77 | 0.28 | 0.27 | 0.00 | 42.76 | 0.00 | 0.00 | 0.04 | 183.36 |
| time (sec) |
N/A | 0.919 | 0.321 | 0.109 | 0.000 | 85.482 | 0.000 | 0.000 | 200.020 | 29.870 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 527 | 429 | 140 | 148 | 0 | 0 | 0 | 0 | 27 | 84889 |
| N.S. |
1 | 0.81 | 0.27 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 161.08 |
| time (sec) |
N/A | 0.692 | 0.236 | 0.106 | 0.000 | 0.000 | 0.000 | 0.000 | 200.022 | 28.437 |