Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 143 | 1041 | 466 | 0 | 318 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 0.94 | 6.85 | 3.07 | 0.00 | 2.09 | 0.00 | 0.00 | 0.57 | 0.00 |
| time (sec) |
N/A | 0.757 | 7.550 | 3.402 | 0.000 | 0.095 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 200 | 1158 | 465 | 0 | 384 | 0 | 0 | 91 | 0 |
| N.S. |
1 | 0.98 | 5.68 | 2.28 | 0.00 | 1.88 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 1.105 | 8.072 | 8.825 | 0.000 | 0.111 | 0.000 | 0.000 | 0.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 173 | 1114 | 435 | 0 | 366 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.01 | 6.51 | 2.54 | 0.00 | 2.14 | 0.00 | 0.00 | 0.51 | 0.00 |
| time (sec) |
N/A | 1.024 | 7.808 | 5.075 | 0.000 | 0.106 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 144 | 1079 | 421 | 0 | 356 | 0 | 0 | 75 | 0 |
| N.S. |
1 | 1.05 | 7.88 | 3.07 | 0.00 | 2.60 | 0.00 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 0.912 | 7.491 | 4.458 | 0.000 | 0.103 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 131 | 800 | 350 | 0 | 314 | 0 | 0 | 111 | 0 |
| N.S. |
1 | 1.08 | 6.61 | 2.89 | 0.00 | 2.60 | 0.00 | 0.00 | 0.92 | 0.00 |
| time (sec) |
N/A | 0.852 | 7.245 | 3.405 | 0.000 | 0.089 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 130 | 801 | 350 | 0 | 318 | 0 | 0 | 123 | 0 |
| N.S. |
1 | 1.07 | 6.62 | 2.89 | 0.00 | 2.63 | 0.00 | 0.00 | 1.02 | 0.00 |
| time (sec) |
N/A | 0.841 | 7.643 | 2.913 | 0.000 | 0.090 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 166 | 1113 | 492 | 0 | 407 | 0 | 0 | 123 | 0 |
| N.S. |
1 | 1.01 | 6.79 | 3.00 | 0.00 | 2.48 | 0.00 | 0.00 | 0.75 | 0.00 |
| time (sec) |
N/A | 1.030 | 7.718 | 3.309 | 0.000 | 0.097 | 0.000 | 0.000 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 195 | 1154 | 723 | 0 | 436 | 0 | 0 | 123 | 0 |
| N.S. |
1 | 0.99 | 5.86 | 3.67 | 0.00 | 2.21 | 0.00 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 1.075 | 8.145 | 4.140 | 0.000 | 0.102 | 0.000 | 0.000 | 0.185 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 231 | 430 | 465 | 0 | 478 | 0 | 0 | 107 | 0 |
| N.S. |
1 | 1.05 | 1.95 | 2.10 | 0.00 | 2.16 | 0.00 | 0.00 | 0.48 | 0.00 |
| time (sec) |
N/A | 1.400 | 7.052 | 6.224 | 0.000 | 0.107 | 0.000 | 0.000 | 0.188 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 203 | 389 | 451 | 0 | 467 | 0 | 0 | 95 | 0 |
| N.S. |
1 | 1.08 | 2.07 | 2.40 | 0.00 | 2.48 | 0.00 | 0.00 | 0.51 | 0.00 |
| time (sec) |
N/A | 1.229 | 4.749 | 5.717 | 0.000 | 0.105 | 0.000 | 0.000 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 197 | 637 | 451 | 0 | 465 | 0 | 0 | 143 | 0 |
| N.S. |
1 | 1.08 | 3.50 | 2.48 | 0.00 | 2.55 | 0.00 | 0.00 | 0.79 | 0.00 |
| time (sec) |
N/A | 1.237 | 6.463 | 4.666 | 0.000 | 0.096 | 0.000 | 0.000 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 193 | 189 | 451 | 0 | 465 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.08 | 1.06 | 2.53 | 0.00 | 2.61 | 0.00 | 0.00 | 0.89 | 0.00 |
| time (sec) |
N/A | 1.188 | 2.354 | 4.982 | 0.000 | 0.104 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 195 | 1171 | 451 | 0 | 465 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.08 | 6.51 | 2.51 | 0.00 | 2.58 | 0.00 | 0.00 | 0.88 | 0.00 |
| time (sec) |
N/A | 1.195 | 7.791 | 4.425 | 0.000 | 0.095 | 0.000 | 0.000 | 0.197 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 227 | 1211 | 685 | 0 | 521 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.03 | 5.48 | 3.10 | 0.00 | 2.36 | 0.00 | 0.00 | 0.72 | 0.00 |
| time (sec) |
N/A | 1.395 | 7.911 | 4.324 | 0.000 | 0.103 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 220 | 235 | 119 | 117 | 547 | 116 | 0 | 244 | 68 | 0 |
| N.S. |
1 | 1.07 | 0.54 | 0.53 | 2.49 | 0.53 | 0.00 | 1.11 | 0.31 | 0.00 |
| time (sec) |
N/A | 1.267 | 0.321 | 1.233 | 0.271 | 0.082 | 0.000 | 0.254 | 0.245 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 192 | 96 | 97 | 418 | 99 | 0 | 199 | 68 | 0 |
| N.S. |
1 | 1.10 | 0.55 | 0.55 | 2.39 | 0.57 | 0.00 | 1.14 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.953 | 0.234 | 1.097 | 0.257 | 0.079 | 0.000 | 0.215 | 0.288 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 149 | 79 | 78 | 296 | 81 | 0 | 154 | 68 | 0 |
| N.S. |
1 | 1.15 | 0.61 | 0.60 | 2.28 | 0.62 | 0.00 | 1.18 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.766 | 0.110 | 1.065 | 0.251 | 0.080 | 0.000 | 0.208 | 0.245 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 103 | 56 | 59 | 141 | 64 | 0 | 108 | 64 | 0 |
| N.S. |
1 | 1.26 | 0.68 | 0.72 | 1.72 | 0.78 | 0.00 | 1.32 | 0.78 | 0.00 |
| time (sec) |
N/A | 0.596 | 0.125 | 1.067 | 0.226 | 0.078 | 0.000 | 0.165 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 97 | 94 | 145 | 262 | 298 | 0 | 163 | 52 | 0 |
| N.S. |
1 | 1.01 | 0.98 | 1.51 | 2.73 | 3.10 | 0.00 | 1.70 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.592 | 0.212 | 2.006 | 0.221 | 0.103 | 0.000 | 0.222 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 99 | 119 | 242 | 905 | 351 | 0 | 305 | 68 | 0 |
| N.S. |
1 | 1.01 | 1.21 | 2.47 | 9.23 | 3.58 | 0.00 | 3.11 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.602 | 0.278 | 2.181 | 0.289 | 0.123 | 0.000 | 0.630 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 144 | 141 | 294 | 1927 | 401 | 0 | 557 | 68 | 0 |
| N.S. |
1 | 0.95 | 0.93 | 1.95 | 12.76 | 2.66 | 0.00 | 3.69 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.772 | 0.477 | 2.204 | 0.295 | 0.134 | 0.000 | 0.481 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 196 | 187 | 176 | 313 | 3342 | 439 | 0 | 783 | 68 | 0 |
| N.S. |
1 | 0.95 | 0.90 | 1.60 | 17.05 | 2.24 | 0.00 | 3.99 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.974 | 0.584 | 1.976 | 0.383 | 0.135 | 0.000 | 0.538 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 288 | 135 | 138 | 703 | 142 | 0 | 285 | 141 | 0 |
| N.S. |
1 | 1.05 | 0.49 | 0.50 | 2.56 | 0.52 | 0.00 | 1.04 | 0.51 | 0.00 |
| time (sec) |
N/A | 1.587 | 7.233 | 1.623 | 0.280 | 0.092 | 0.000 | 0.333 | 0.353 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 245 | 113 | 118 | 558 | 124 | 0 | 238 | 141 | 0 |
| N.S. |
1 | 1.07 | 0.50 | 0.52 | 2.45 | 0.54 | 0.00 | 1.04 | 0.62 | 0.00 |
| time (sec) |
N/A | 1.323 | 6.527 | 1.638 | 0.252 | 0.086 | 0.000 | 0.317 | 0.377 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 202 | 91 | 98 | 451 | 105 | 0 | 195 | 141 | 0 |
| N.S. |
1 | 1.12 | 0.50 | 0.54 | 2.49 | 0.58 | 0.00 | 1.08 | 0.78 | 0.00 |
| time (sec) |
N/A | 1.138 | 6.364 | 1.628 | 0.247 | 0.079 | 0.000 | 0.278 | 0.378 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 150 | 75 | 79 | 276 | 86 | 0 | 150 | 141 | 0 |
| N.S. |
1 | 1.15 | 0.57 | 0.60 | 2.11 | 0.66 | 0.00 | 1.15 | 1.08 | 0.00 |
| time (sec) |
N/A | 0.799 | 6.256 | 1.621 | 0.258 | 0.077 | 0.000 | 0.233 | 0.375 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 149 | 101 | 189 | 583 | 343 | 0 | 231 | 133 | 0 |
| N.S. |
1 | 1.03 | 0.70 | 1.30 | 4.02 | 2.37 | 0.00 | 1.59 | 0.92 | 0.00 |
| time (sec) |
N/A | 0.888 | 0.281 | 2.572 | 0.266 | 0.104 | 0.000 | 0.281 | 0.312 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 152 | 133 | 353 | 1417 | 389 | 0 | 349 | 109 | 0 |
| N.S. |
1 | 1.06 | 0.92 | 2.45 | 9.84 | 2.70 | 0.00 | 2.42 | 0.76 | 0.00 |
| time (sec) |
N/A | 0.895 | 0.547 | 2.444 | 0.297 | 0.128 | 0.000 | 0.497 | 0.252 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 170 | 295 | 3389 | 409 | 0 | 557 | 141 | 0 |
| N.S. |
1 | 1.00 | 1.11 | 1.93 | 22.15 | 2.67 | 0.00 | 3.64 | 0.92 | 0.00 |
| time (sec) |
N/A | 0.901 | 0.484 | 2.475 | 0.359 | 0.122 | 0.000 | 0.602 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 197 | 177 | 314 | 4606 | 449 | 0 | 783 | 141 | 0 |
| N.S. |
1 | 0.98 | 0.88 | 1.57 | 23.03 | 2.24 | 0.00 | 3.92 | 0.70 | 0.00 |
| time (sec) |
N/A | 1.133 | 0.638 | 2.513 | 0.405 | 0.137 | 0.000 | 0.641 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 240 | 211 | 334 | 5879 | 485 | 0 | 942 | 141 | 0 |
| N.S. |
1 | 0.97 | 0.85 | 1.35 | 23.80 | 1.96 | 0.00 | 3.81 | 0.57 | 0.00 |
| time (sec) |
N/A | 1.344 | 1.044 | 2.580 | 0.588 | 0.158 | 0.000 | 0.717 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 299 | 137 | 140 | 754 | 154 | 0 | 286 | 219 | 0 |
| N.S. |
1 | 1.09 | 0.50 | 0.51 | 2.74 | 0.56 | 0.00 | 1.04 | 0.80 | 0.00 |
| time (sec) |
N/A | 1.806 | 0.650 | 1.199 | 0.274 | 0.089 | 0.000 | 0.562 | 0.464 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 256 | 116 | 120 | 596 | 133 | 0 | 241 | 219 | 0 |
| N.S. |
1 | 1.12 | 0.51 | 0.53 | 2.61 | 0.58 | 0.00 | 1.06 | 0.96 | 0.00 |
| time (sec) |
N/A | 1.489 | 0.384 | 0.994 | 0.271 | 0.083 | 0.000 | 0.458 | 0.491 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 194 | 99 | 100 | 482 | 112 | 0 | 196 | 219 | 0 |
| N.S. |
1 | 1.09 | 0.56 | 0.56 | 2.71 | 0.63 | 0.00 | 1.10 | 1.23 | 0.00 |
| time (sec) |
N/A | 0.994 | 0.259 | 0.969 | 0.268 | 0.079 | 0.000 | 0.427 | 0.476 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 201 | 118 | 210 | 352 | 399 | 0 | 276 | 219 | 0 |
| N.S. |
1 | 1.05 | 0.61 | 1.09 | 1.83 | 2.08 | 0.00 | 1.44 | 1.14 | 0.00 |
| time (sec) |
N/A | 1.226 | 0.424 | 1.189 | 0.247 | 0.102 | 0.000 | 0.382 | 0.465 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 205 | 117 | 366 | 2589 | 449 | 0 | 414 | 207 | 0 |
| N.S. |
1 | 1.04 | 0.59 | 1.86 | 13.14 | 2.28 | 0.00 | 2.10 | 1.05 | 0.00 |
| time (sec) |
N/A | 1.275 | 0.425 | 2.569 | 0.342 | 0.127 | 0.000 | 0.609 | 0.436 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 204 | 173 | 389 | 14322 | 453 | 0 | 599 | 171 | 0 |
| N.S. |
1 | 1.02 | 0.86 | 1.94 | 71.61 | 2.26 | 0.00 | 3.00 | 0.86 | 0.00 |
| time (sec) |
N/A | 1.255 | 0.826 | 2.562 | 3.154 | 0.129 | 0.000 | 0.662 | 0.317 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 206 | 152 | 316 | 6297 | 469 | 0 | 783 | 219 | 0 |
| N.S. |
1 | 1.03 | 0.76 | 1.58 | 31.48 | 2.34 | 0.00 | 3.92 | 1.10 | 0.00 |
| time (sec) |
N/A | 1.277 | 1.116 | 2.546 | 3.016 | 0.128 | 0.000 | 0.821 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 251 | 210 | 336 | 7331 | 509 | 0 | 942 | 219 | 0 |
| N.S. |
1 | 1.02 | 0.85 | 1.36 | 29.68 | 2.06 | 0.00 | 3.81 | 0.89 | 0.00 |
| time (sec) |
N/A | 1.502 | 0.744 | 2.420 | 0.626 | 0.154 | 0.000 | 0.872 | 0.227 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 294 | 607 | 356 | 9242 | 549 | 0 | 1191 | 219 | 0 |
| N.S. |
1 | 1.00 | 2.06 | 1.21 | 31.44 | 1.87 | 0.00 | 4.05 | 0.74 | 0.00 |
| time (sec) |
N/A | 1.768 | 6.411 | 2.426 | 1.062 | 0.168 | 0.000 | 1.046 | 0.250 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 281 | 170 | 228 | 749 | 409 | 0 | 227 | 91 | 0 |
| N.S. |
1 | 1.12 | 0.68 | 0.91 | 3.00 | 1.64 | 0.00 | 0.91 | 0.36 | 0.00 |
| time (sec) |
N/A | 1.690 | 0.750 | 1.155 | 0.269 | 0.107 | 0.000 | 169.876 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 226 | 154 | 208 | 581 | 377 | 0 | 203 | 91 | 0 |
| N.S. |
1 | 1.09 | 0.74 | 1.00 | 2.81 | 1.82 | 0.00 | 0.98 | 0.44 | 0.00 |
| time (sec) |
N/A | 1.246 | 0.492 | 1.116 | 0.258 | 0.113 | 0.000 | 171.589 | 0.184 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 171 | 124 | 189 | 478 | 345 | 0 | 140 | 87 | 0 |
| N.S. |
1 | 1.06 | 0.77 | 1.17 | 2.95 | 2.13 | 0.00 | 0.86 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.923 | 0.226 | 1.099 | 0.270 | 0.097 | 0.000 | 171.558 | 0.180 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 120 | 140 | 189 | 195 | 315 | 0 | 105 | 75 | 0 |
| N.S. |
1 | 1.01 | 1.18 | 1.59 | 1.64 | 2.65 | 0.00 | 0.88 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.646 | 0.226 | 1.082 | 0.226 | 0.096 | 0.000 | 167.054 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 121 | 115 | 204 | 699 | 366 | 0 | 195 | 99 | 0 |
| N.S. |
1 | 0.86 | 0.82 | 1.46 | 4.99 | 2.61 | 0.00 | 1.39 | 0.71 | 0.00 |
| time (sec) |
N/A | 0.757 | 0.141 | 2.020 | 0.267 | 0.112 | 0.000 | 169.395 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 171 | 193 | 340 | 1509 | 584 | 0 | 347 | 107 | 0 |
| N.S. |
1 | 0.94 | 1.07 | 1.88 | 8.34 | 3.23 | 0.00 | 1.92 | 0.59 | 0.00 |
| time (sec) |
N/A | 1.051 | 0.267 | 2.007 | 0.302 | 0.155 | 0.000 | 167.237 | 0.245 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 224 | 254 | 395 | 2704 | 630 | 0 | 559 | 107 | 0 |
| N.S. |
1 | 0.97 | 1.10 | 1.72 | 11.76 | 2.74 | 0.00 | 2.43 | 0.47 | 0.00 |
| time (sec) |
N/A | 1.405 | 0.543 | 2.119 | 0.352 | 0.161 | 0.000 | 166.883 | 0.201 | 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 | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 289 | 178 | 258 | 0 | 488 | 0 | 247 | 111 | 0 |
| N.S. |
1 | 1.07 | 0.66 | 0.96 | 0.00 | 1.81 | 0.00 | 0.91 | 0.41 | 0.00 |
| time (sec) |
N/A | 1.704 | 0.895 | 1.592 | 0.000 | 0.106 | 0.000 | 173.764 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 234 | 155 | 238 | 36231 | 450 | 0 | 219 | 107 | 0 |
| N.S. |
1 | 1.05 | 0.70 | 1.07 | 162.47 | 2.02 | 0.00 | 0.98 | 0.48 | 0.00 |
| time (sec) |
N/A | 1.347 | 0.822 | 1.561 | 0.695 | 0.100 | 0.000 | 172.689 | 0.204 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 179 | 194 | 244 | 8208 | 418 | 0 | 159 | 95 | 0 |
| N.S. |
1 | 1.02 | 1.10 | 1.39 | 46.64 | 2.38 | 0.00 | 0.90 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.975 | 1.231 | 1.599 | 0.315 | 0.104 | 0.000 | 166.948 | 0.197 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 128 | 325 | 196 | 2166 | 384 | 0 | 123 | 131 | 0 |
| N.S. |
1 | 1.01 | 2.56 | 1.54 | 17.06 | 3.02 | 0.00 | 0.97 | 1.03 | 0.00 |
| time (sec) |
N/A | 0.656 | 0.739 | 1.644 | 0.288 | 0.095 | 0.000 | 167.927 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 171 | 325 | 292 | 0 | 600 | 0 | 254 | 143 | 0 |
| N.S. |
1 | 0.92 | 1.76 | 1.58 | 0.00 | 3.24 | 0.00 | 1.37 | 0.77 | 0.00 |
| time (sec) |
N/A | 1.079 | 0.936 | 2.546 | 0.000 | 0.137 | 0.000 | 169.456 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 226 | 449 | 464 | 7057 | 724 | 0 | 411 | 143 | 0 |
| N.S. |
1 | 0.95 | 1.89 | 1.96 | 29.78 | 3.05 | 0.00 | 1.73 | 0.60 | 0.00 |
| time (sec) |
N/A | 1.480 | 1.639 | 2.523 | 0.553 | 0.202 | 0.000 | 169.644 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 287 | 280 | 517 | 496 | 13364 | 772 | 0 | 0 | 143 | 0 |
| N.S. |
1 | 0.98 | 1.80 | 1.73 | 46.56 | 2.69 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 1.890 | 3.179 | 2.585 | 1.182 | 0.175 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 344 | 161 | 308 | 244922 | 580 | 0 | 335 | 131 | 0 |
| N.S. |
1 | 1.09 | 0.51 | 0.97 | 772.62 | 1.83 | 0.00 | 1.06 | 0.41 | 0.00 |
| time (sec) |
N/A | 2.109 | 7.133 | 1.680 | 5.199 | 0.110 | 0.000 | 175.489 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 289 | 136 | 288 | 154245 | 550 | 0 | 249 | 127 | 0 |
| N.S. |
1 | 1.07 | 0.50 | 1.07 | 571.28 | 2.04 | 0.00 | 0.92 | 0.47 | 0.00 |
| time (sec) |
N/A | 1.720 | 7.024 | 1.693 | 3.200 | 0.104 | 0.000 | 174.360 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 234 | 228 | 303 | 261506 | 512 | 0 | 232 | 115 | 0 |
| N.S. |
1 | 1.05 | 1.02 | 1.36 | 1172.67 | 2.30 | 0.00 | 1.04 | 0.52 | 0.00 |
| time (sec) |
N/A | 1.347 | 1.600 | 1.700 | 3.021 | 0.103 | 0.000 | 170.283 | 0.252 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 234 | 481 | 255 | 5924 | 490 | 0 | 162 | 163 | 0 |
| N.S. |
1 | 1.05 | 2.16 | 1.14 | 26.57 | 2.20 | 0.00 | 0.73 | 0.73 | 0.00 |
| time (sec) |
N/A | 1.324 | 6.123 | 1.611 | 0.703 | 0.094 | 0.000 | 167.479 | 0.205 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 175 | 108 | 255 | 5356 | 486 | 0 | 161 | 179 | 0 |
| N.S. |
1 | 0.99 | 0.61 | 1.45 | 30.43 | 2.76 | 0.00 | 0.91 | 1.02 | 0.00 |
| time (sec) |
N/A | 0.891 | 3.801 | 1.599 | 0.601 | 0.097 | 0.000 | 166.984 | 0.215 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 226 | 146 | 374 | 0 | 728 | 0 | 295 | 179 | 0 |
| N.S. |
1 | 0.97 | 0.62 | 1.60 | 0.00 | 3.11 | 0.00 | 1.26 | 0.76 | 0.00 |
| time (sec) |
N/A | 1.445 | 4.221 | 2.513 | 0.000 | 0.129 | 0.000 | 169.276 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 283 | 164 | 554 | 14037 | 858 | 0 | 451 | 179 | 0 |
| N.S. |
1 | 0.99 | 0.57 | 1.94 | 49.08 | 3.00 | 0.00 | 1.58 | 0.63 | 0.00 |
| time (sec) |
N/A | 1.896 | 5.413 | 2.627 | 2.548 | 0.190 | 0.000 | 170.491 | 0.220 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 134 | 103 | 413 | 0 | 192 | 0 | 0 | 81 | 166 |
| N.S. |
1 | 0.96 | 0.74 | 2.95 | 0.00 | 1.37 | 0.00 | 0.00 | 0.58 | 1.19 |
| time (sec) |
N/A | 0.746 | 1.450 | 27.351 | 0.000 | 0.108 | 0.000 | 0.000 | 0.241 | 0.773 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 107 | 86 | 371 | 0 | 175 | 0 | 0 | 81 | 128 |
| N.S. |
1 | 0.99 | 0.80 | 3.44 | 0.00 | 1.62 | 0.00 | 0.00 | 0.75 | 1.19 |
| time (sec) |
N/A | 0.727 | 1.074 | 25.629 | 0.000 | 0.091 | 0.000 | 0.000 | 0.289 | 0.629 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 78 | 67 | 326 | 0 | 156 | 0 | 0 | 75 | 85 |
| N.S. |
1 | 1.04 | 0.89 | 4.35 | 0.00 | 2.08 | 0.00 | 0.00 | 1.00 | 1.13 |
| time (sec) |
N/A | 0.615 | 0.962 | 4.082 | 0.000 | 0.089 | 0.000 | 0.000 | 0.220 | 0.616 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 64 | 244 | 0 | 185 | 0 | 0 | 56 | 96 |
| N.S. |
1 | 1.00 | 0.90 | 3.44 | 0.00 | 2.61 | 0.00 | 0.00 | 0.79 | 1.35 |
| time (sec) |
N/A | 0.617 | 0.598 | 3.839 | 0.000 | 0.090 | 0.000 | 0.000 | 0.194 | 12.463 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 102 | 107 | 401 | 0 | 213 | 0 | 0 | 81 | 150 |
| N.S. |
1 | 0.99 | 1.04 | 3.89 | 0.00 | 2.07 | 0.00 | 0.00 | 0.79 | 1.46 |
| time (sec) |
N/A | 0.723 | 0.564 | 4.273 | 0.000 | 0.093 | 0.000 | 0.000 | 0.188 | 12.953 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 130 | 134 | 636 | 0 | 235 | 0 | 0 | 81 | 177 |
| N.S. |
1 | 0.93 | 0.96 | 4.54 | 0.00 | 1.68 | 0.00 | 0.00 | 0.58 | 1.26 |
| time (sec) |
N/A | 0.753 | 0.811 | 5.957 | 0.000 | 0.098 | 0.000 | 0.000 | 0.193 | 13.404 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 175 | 139 | 548 | 0 | 243 | 0 | 0 | 115 | 229 |
| N.S. |
1 | 0.96 | 0.76 | 3.01 | 0.00 | 1.34 | 0.00 | 0.00 | 0.63 | 1.26 |
| time (sec) |
N/A | 1.003 | 1.936 | 159.740 | 0.000 | 0.112 | 0.000 | 0.000 | 0.307 | 12.322 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 146 | 106 | 487 | 0 | 216 | 0 | 0 | 115 | 177 |
| N.S. |
1 | 1.04 | 0.76 | 3.48 | 0.00 | 1.54 | 0.00 | 0.00 | 0.82 | 1.26 |
| time (sec) |
N/A | 0.900 | 1.542 | 158.135 | 0.000 | 0.098 | 0.000 | 0.000 | 0.273 | 12.072 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 124 | 102 | 404 | 0 | 240 | 0 | 0 | 107 | 158 |
| N.S. |
1 | 1.02 | 0.84 | 3.34 | 0.00 | 1.98 | 0.00 | 0.00 | 0.88 | 1.31 |
| time (sec) |
N/A | 0.830 | 1.250 | 4.904 | 0.000 | 0.102 | 0.000 | 0.000 | 0.253 | 12.379 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 129 | 105 | 650 | 0 | 255 | 0 | 0 | 82 | 194 |
| N.S. |
1 | 1.02 | 0.83 | 5.16 | 0.00 | 2.02 | 0.00 | 0.00 | 0.65 | 1.54 |
| time (sec) |
N/A | 0.853 | 1.584 | 4.889 | 0.000 | 0.099 | 0.000 | 0.000 | 0.204 | 13.257 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 161 | 175 | 723 | 0 | 286 | 0 | 0 | 115 | 227 |
| N.S. |
1 | 0.94 | 1.02 | 4.20 | 0.00 | 1.66 | 0.00 | 0.00 | 0.67 | 1.32 |
| time (sec) |
N/A | 0.978 | 1.316 | 6.217 | 0.000 | 0.115 | 0.000 | 0.000 | 0.200 | 13.379 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 190 | 191 | 832 | 0 | 314 | 0 | 0 | 115 | 233 |
| N.S. |
1 | 0.89 | 0.89 | 3.89 | 0.00 | 1.47 | 0.00 | 0.00 | 0.54 | 1.09 |
| time (sec) |
N/A | 1.010 | 3.691 | 8.049 | 0.000 | 0.105 | 0.000 | 0.000 | 0.244 | 13.859 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 200 | 260 | 1074 | 0 | 0 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.10 | 1.43 | 5.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.651 | 11.906 | 7.190 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 147 | 207 | 822 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.08 | 1.52 | 6.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 1.159 | 1.073 | 6.140 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 87 | 128 | 295 | 0 | 0 | 0 | 0 | 9 | 0 |
| N.S. |
1 | 0.98 | 1.44 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 0.687 | 10.898 | 4.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 58 | 217 | 0 | 0 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.532 | 0.351 | 2.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 85 | 206 | 298 | 0 | 0 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 0.99 | 2.40 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.782 | 1.737 | 2.872 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 162 | 260 | 439 | 0 | 0 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.08 | 1.73 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 1.567 | 1.677 | 4.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 232 | 326 | 758 | 0 | 0 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.07 | 1.50 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 2.088 | 3.026 | 5.786 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 295 | 318 | 1059 | 0 | 0 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 0.97 | 1.04 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 2.044 | 2.351 | 8.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 220 | 281 | 843 | 0 | 0 | 0 | 0 | 22 | 0 |
| N.S. |
1 | 0.99 | 1.26 | 3.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.451 | 1.962 | 5.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.143 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 197 | 260 | 803 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 0.97 | 1.28 | 3.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 1.326 | 1.729 | 4.746 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 182 | 273 | 715 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 0.92 | 1.39 | 3.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 1.414 | 1.891 | 4.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 255 | 242 | 317 | 850 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 0.95 | 1.24 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 1.922 | 2.973 | 4.581 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 327 | 363 | 997 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 0.95 | 1.05 | 2.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 2.638 | 4.764 | 6.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 461 | 463 | 461 | 2216 | 0 | 0 | 0 | 0 | 44 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 4.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 3.083 | 4.139 | 10.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 367 | 372 | 390 | 2000 | 0 | 0 | 0 | 0 | 38 | 0 |
| N.S. |
1 | 1.01 | 1.06 | 5.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 2.327 | 3.613 | 8.357 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 352 | 361 | 1960 | 0 | 0 | 0 | 0 | 57 | 0 |
| N.S. |
1 | 1.02 | 1.04 | 5.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 2.265 | 3.062 | 6.867 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 338 | 336 | 364 | 1873 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.99 | 1.08 | 5.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 2.167 | 3.244 | 6.556 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 342 | 334 | 383 | 1768 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.98 | 1.12 | 5.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 2.260 | 3.410 | 5.692 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 420 | 413 | 458 | 1997 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.98 | 1.09 | 4.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 3.150 | 3.770 | 7.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 523 | 514 | 482 | 2151 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.98 | 0.92 | 4.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 4.031 | 6.767 | 8.351 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 381 | 418 | 2103 | 0 | 580 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 1.11 | 1.22 | 6.13 | 0.00 | 1.69 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 3.193 | 15.431 | 13.660 | 0.000 | 0.122 | 0.000 | 0.000 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 267 | 297 | 353 | 1533 | 0 | 511 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 1.11 | 1.32 | 5.74 | 0.00 | 1.91 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 2.276 | 11.537 | 10.297 | 0.000 | 0.107 | 0.000 | 0.000 | 0.292 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 223 | 305 | 1090 | 0 | 454 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 1.11 | 1.52 | 5.42 | 0.00 | 2.26 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 1.729 | 7.653 | 5.990 | 0.000 | 0.105 | 0.000 | 0.000 | 0.229 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 230 | 25347 | 760 | 0 | 0 | 0 | 0 | 53 | 0 |
| N.S. |
1 | 1.11 | 121.86 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 2.334 | 31.205 | 5.937 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 281 | 53253 | 744 | 0 | 0 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 1.11 | 210.49 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 2.919 | 33.557 | 8.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 356 | 78854 | 1473 | 0 | 0 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 1.06 | 234.68 | 4.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 3.594 | 34.249 | 12.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 456 | 540 | 2695 | 0 | 658 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 1.07 | 1.26 | 6.31 | 0.00 | 1.54 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 3.992 | 17.184 | 20.709 | 0.000 | 0.138 | 0.000 | 0.000 | 0.321 | 0.000 |