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 | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 196 | 175 | 463 | 0 | 551 | 0 | 0 | 147 | 0 |
| N.S. |
1 | 1.04 | 0.93 | 2.45 | 0.00 | 2.92 | 0.00 | 0.00 | 0.78 | 0.00 |
| time (sec) |
N/A | 0.876 | 3.047 | 2.673 | 0.000 | 0.110 | 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 | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 263 | 207 | 1221 | 0 | 947 | 0 | 0 | 195 | 0 |
| N.S. |
1 | 1.06 | 0.84 | 4.94 | 0.00 | 3.83 | 0.00 | 0.00 | 0.79 | 0.00 |
| time (sec) |
N/A | 1.245 | 4.055 | 3.111 | 0.000 | 0.125 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 320 | 334 | 283 | 1430 | 0 | 1539 | 0 | 0 | 243 | 0 |
| N.S. |
1 | 1.04 | 0.88 | 4.47 | 0.00 | 4.81 | 0.00 | 0.00 | 0.76 | 0.00 |
| time (sec) |
N/A | 1.632 | 4.117 | 4.459 | 0.000 | 0.156 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 467 | 485 | 377 | 1926 | 0 | 818 | 0 | 0 | 308 | 0 |
| N.S. |
1 | 1.04 | 0.81 | 4.12 | 0.00 | 1.75 | 0.00 | 0.00 | 0.66 | 0.00 |
| time (sec) |
N/A | 2.788 | 6.320 | 47.168 | 0.000 | 0.162 | 0.000 | 0.000 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 390 | 406 | 318 | 1613 | 0 | 711 | 0 | 0 | 188 | 0 |
| N.S. |
1 | 1.04 | 0.82 | 4.14 | 0.00 | 1.82 | 0.00 | 0.00 | 0.48 | 0.00 |
| time (sec) |
N/A | 2.250 | 6.629 | 7.545 | 0.000 | 0.142 | 0.000 | 0.000 | 0.221 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 318 | 332 | 266 | 1316 | 0 | 615 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 1.04 | 0.84 | 4.14 | 0.00 | 1.93 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 1.791 | 3.093 | 5.490 | 0.000 | 0.123 | 0.000 | 0.000 | 0.204 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 258 | 270 | 246 | 1035 | 0 | 534 | 0 | 0 | 135 | 0 |
| N.S. |
1 | 1.05 | 0.95 | 4.01 | 0.00 | 2.07 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 1.446 | 6.195 | 3.054 | 0.000 | 0.110 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 280 | 234 | 1031 | 0 | 756 | 0 | 0 | 199 | 0 |
| N.S. |
1 | 1.04 | 0.87 | 3.82 | 0.00 | 2.80 | 0.00 | 0.00 | 0.74 | 0.00 |
| time (sec) |
N/A | 1.522 | 5.997 | 4.456 | 0.000 | 0.138 | 0.000 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 305 | 232 | 1254 | 0 | 1109 | 0 | 0 | 263 | 0 |
| N.S. |
1 | 1.09 | 0.83 | 4.48 | 0.00 | 3.96 | 0.00 | 0.00 | 0.94 | 0.00 |
| time (sec) |
N/A | 1.647 | 6.057 | 5.596 | 0.000 | 0.148 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 386 | 298 | 1583 | 0 | 1530 | 0 | 0 | 327 | 0 |
| N.S. |
1 | 1.15 | 0.89 | 4.71 | 0.00 | 4.55 | 0.00 | 0.00 | 0.97 | 0.00 |
| time (sec) |
N/A | 2.124 | 6.728 | 6.782 | 0.000 | 0.155 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 419 | 473 | 351 | 2072 | 0 | 2375 | 0 | 0 | 391 | 0 |
| N.S. |
1 | 1.13 | 0.84 | 4.95 | 0.00 | 5.67 | 0.00 | 0.00 | 0.93 | 0.00 |
| time (sec) |
N/A | 2.617 | 7.782 | 9.119 | 0.000 | 0.218 | 0.000 | 0.000 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 246 | 255 | 298 | 1372 | 0 | 776 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.04 | 1.21 | 5.58 | 0.00 | 3.15 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 1.267 | 1.173 | 2.799 | 0.000 | 0.120 | 0.000 | 0.000 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 186 | 198 | 223 | 925 | 0 | 630 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 1.06 | 1.20 | 4.97 | 0.00 | 3.39 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.944 | 1.275 | 1.158 | 0.000 | 0.114 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 182 | 201 | 382 | 0 | 515 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 1.07 | 1.18 | 2.25 | 0.00 | 3.03 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 0.819 | 0.942 | 0.876 | 0.000 | 0.102 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 198 | 210 | 441 | 0 | 542 | 0 | 0 | 48 | 0 |
| N.S. |
1 | 1.09 | 1.16 | 2.44 | 0.00 | 2.99 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.882 | 0.946 | 0.568 | 0.000 | 0.107 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 262 | 264 | 925 | 0 | 1092 | 0 | 0 | 80 | 0 |
| N.S. |
1 | 1.07 | 1.08 | 3.79 | 0.00 | 4.48 | 0.00 | 0.00 | 0.33 | 0.00 |
| time (sec) |
N/A | 1.237 | 1.893 | 1.068 | 0.000 | 0.123 | 0.000 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 333 | 351 | 367 | 1285 | 0 | 2098 | 0 | 0 | 112 | 0 |
| N.S. |
1 | 1.05 | 1.10 | 3.86 | 0.00 | 6.30 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 1.706 | 3.583 | 1.598 | 0.000 | 0.157 | 0.000 | 0.000 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 260 | 310 | 1365 | 0 | 1066 | 0 | 0 | 133 | 0 |
| N.S. |
1 | 1.02 | 1.21 | 5.33 | 0.00 | 4.16 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 1.420 | 2.340 | 22.638 | 0.000 | 0.132 | 0.000 | 0.000 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 259 | 283 | 1044 | 0 | 860 | 0 | 0 | 83 | 0 |
| N.S. |
1 | 1.09 | 1.19 | 4.41 | 0.00 | 3.63 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 1.380 | 2.435 | 1.418 | 0.000 | 0.112 | 0.000 | 0.000 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 244 | 256 | 902 | 0 | 808 | 0 | 0 | 38 | 0 |
| N.S. |
1 | 1.05 | 1.10 | 3.87 | 0.00 | 3.47 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.269 | 1.984 | 1.250 | 0.000 | 0.113 | 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 | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 266 | 290 | 505 | 0 | 967 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 1.04 | 1.13 | 1.96 | 0.00 | 3.76 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 1.347 | 5.721 | 0.667 | 0.000 | 0.116 | 0.000 | 0.000 | 0.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 326 | 344 | 405 | 1293 | 0 | 1942 | 0 | 0 | 118 | 0 |
| N.S. |
1 | 1.06 | 1.24 | 3.97 | 0.00 | 5.96 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 1.827 | 7.783 | 1.610 | 0.000 | 0.151 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 405 | 434 | 674 | 1750 | 0 | 3145 | 0 | 0 | 166 | 0 |
| N.S. |
1 | 1.07 | 1.66 | 4.32 | 0.00 | 7.77 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 2.368 | 10.528 | 2.336 | 0.000 | 0.218 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 322 | 355 | 385 | 1608 | 0 | 1409 | 0 | 0 | 163 | 0 |
| N.S. |
1 | 1.10 | 1.20 | 4.99 | 0.00 | 4.38 | 0.00 | 0.00 | 0.51 | 0.00 |
| time (sec) |
N/A | 2.018 | 4.886 | 125.067 | 0.000 | 0.119 | 0.000 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 323 | 350 | 441 | 1456 | 0 | 1485 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.08 | 1.37 | 4.51 | 0.00 | 4.60 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 2.071 | 5.441 | 1.995 | 0.000 | 0.125 | 0.000 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 334 | 355 | 449 | 1052 | 0 | 1554 | 0 | 0 | 48 | 0 |
| N.S. |
1 | 1.06 | 1.34 | 3.15 | 0.00 | 4.65 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 1.948 | 4.971 | 1.612 | 0.000 | 0.125 | 0.000 | 0.000 | 0.197 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 344 | 371 | 445 | 591 | 0 | 1640 | 0 | 0 | 92 | 0 |
| N.S. |
1 | 1.08 | 1.29 | 1.72 | 0.00 | 4.77 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 1.999 | 11.100 | 0.832 | 0.000 | 0.134 | 0.000 | 0.000 | 0.241 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 423 | 460 | 745 | 1843 | 0 | 2937 | 0 | 0 | 156 | 0 |
| N.S. |
1 | 1.09 | 1.76 | 4.36 | 0.00 | 6.94 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 2.574 | 12.618 | 2.485 | 0.000 | 0.217 | 0.000 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 518 | 565 | 828 | 2301 | 0 | 4632 | 0 | 0 | 220 | 0 |
| N.S. |
1 | 1.09 | 1.60 | 4.44 | 0.00 | 8.94 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 3.169 | 12.821 | 3.138 | 0.000 | 0.367 | 0.000 | 0.000 | 0.256 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 171 | 146 | 141 | 0 | 240 | 0 | 252 | 93 | 0 |
| N.S. |
1 | 1.06 | 0.91 | 0.88 | 0.00 | 1.49 | 0.00 | 1.57 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.749 | 0.598 | 1.417 | 0.000 | 0.089 | 0.000 | 0.175 | 0.263 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 123 | 111 | 92 | 0 | 157 | 0 | 158 | 65 | 0 |
| N.S. |
1 | 1.10 | 0.99 | 0.82 | 0.00 | 1.40 | 0.00 | 1.41 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.539 | 0.367 | 0.990 | 0.000 | 0.077 | 0.000 | 0.151 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 82 | 58 | 0 | 85 | 0 | 85 | 37 | 0 |
| N.S. |
1 | 1.00 | 1.32 | 0.94 | 0.00 | 1.37 | 0.00 | 1.37 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.301 | 0.177 | 0.942 | 0.000 | 0.076 | 0.000 | 0.144 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | F | B | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 65 | 43 | 0 | 50 | 0 | 36 | 14 | 33 |
| N.S. |
1 | 1.00 | 2.50 | 1.65 | 0.00 | 1.92 | 0.00 | 1.38 | 0.54 | 1.27 |
| time (sec) |
N/A | 0.188 | 0.025 | 0.351 | 0.000 | 0.071 | 0.000 | 0.129 | 0.221 | 16.929 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 657 | 80 | 0 | 464 | 0 | 63 | 27 | 0 |
| N.S. |
1 | 1.00 | 10.77 | 1.31 | 0.00 | 7.61 | 0.00 | 1.03 | 0.44 | 0.00 |
| time (sec) |
N/A | 0.287 | 4.242 | 0.612 | 0.000 | 0.144 | 0.000 | 0.125 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 871 | 155 | 0 | 786 | 0 | 134 | 43 | 0 |
| N.S. |
1 | 1.00 | 8.30 | 1.48 | 0.00 | 7.49 | 0.00 | 1.28 | 0.41 | 0.00 |
| time (sec) |
N/A | 0.439 | 5.509 | 0.660 | 0.000 | 0.160 | 0.000 | 0.135 | 0.197 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 160 | 920 | 254 | 0 | 1250 | 0 | 213 | 59 | 0 |
| N.S. |
1 | 1.04 | 5.97 | 1.65 | 0.00 | 8.12 | 0.00 | 1.38 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.609 | 7.267 | 0.685 | 0.000 | 0.201 | 0.000 | 0.148 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 230 | 203 | 195 | 0 | 339 | 0 | 355 | 192 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.84 | 0.00 | 1.47 | 0.00 | 1.54 | 0.83 | 0.00 |
| time (sec) |
N/A | 1.037 | 2.837 | 1.543 | 0.000 | 0.089 | 0.000 | 0.188 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 136 | 130 | 0 | 229 | 0 | 237 | 136 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.00 | 1.46 | 0.00 | 1.51 | 0.87 | 0.00 |
| time (sec) |
N/A | 0.659 | 2.272 | 1.088 | 0.000 | 0.086 | 0.000 | 0.172 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 99 | 101 | 77 | 0 | 136 | 0 | 139 | 80 | 0 |
| N.S. |
1 | 0.98 | 1.00 | 0.76 | 0.00 | 1.35 | 0.00 | 1.38 | 0.79 | 0.00 |
| time (sec) |
N/A | 0.403 | 1.296 | 0.993 | 0.000 | 0.081 | 0.000 | 0.149 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 89 | 53 | 0 | 76 | 0 | 67 | 34 | 0 |
| N.S. |
1 | 1.00 | 1.51 | 0.90 | 0.00 | 1.29 | 0.00 | 1.14 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.265 | 0.327 | 0.313 | 0.000 | 0.076 | 0.000 | 0.140 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 98 | 741 | 137 | 0 | 651 | 0 | 125 | 59 | 0 |
| N.S. |
1 | 1.00 | 7.56 | 1.40 | 0.00 | 6.64 | 0.00 | 1.28 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.501 | 7.831 | 0.621 | 0.000 | 0.159 | 0.000 | 0.145 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 759 | 233 | 0 | 970 | 0 | 196 | 91 | 0 |
| N.S. |
1 | 1.00 | 6.38 | 1.96 | 0.00 | 8.15 | 0.00 | 1.65 | 0.76 | 0.00 |
| time (sec) |
N/A | 0.519 | 8.198 | 0.644 | 0.000 | 0.185 | 0.000 | 0.148 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 179 | 888 | 429 | 0 | 1558 | 0 | 311 | 123 | 0 |
| N.S. |
1 | 1.00 | 4.96 | 2.40 | 0.00 | 8.70 | 0.00 | 1.74 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.728 | 8.847 | 0.658 | 0.000 | 0.226 | 0.000 | 0.158 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 328 | 302 | 246 | 249 | 0 | 493 | 0 | 486 | 296 | 0 |
| N.S. |
1 | 0.92 | 0.75 | 0.76 | 0.00 | 1.50 | 0.00 | 1.48 | 0.90 | 0.00 |
| time (sec) |
N/A | 1.386 | 6.524 | 38.359 | 0.000 | 0.096 | 0.000 | 0.225 | 0.243 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 191 | 180 | 168 | 0 | 339 | 0 | 331 | 212 | 0 |
| N.S. |
1 | 0.95 | 0.89 | 0.83 | 0.00 | 1.68 | 0.00 | 1.64 | 1.05 | 0.00 |
| time (sec) |
N/A | 0.798 | 4.412 | 7.511 | 0.000 | 0.089 | 0.000 | 0.186 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 133 | 119 | 99 | 0 | 206 | 0 | 202 | 128 | 0 |
| N.S. |
1 | 0.96 | 0.86 | 0.72 | 0.00 | 1.49 | 0.00 | 1.46 | 0.93 | 0.00 |
| time (sec) |
N/A | 0.509 | 3.073 | 1.654 | 0.000 | 0.084 | 0.000 | 0.151 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 93 | 117 | 65 | 0 | 115 | 0 | 102 | 58 | 0 |
| N.S. |
1 | 1.04 | 1.31 | 0.73 | 0.00 | 1.29 | 0.00 | 1.15 | 0.65 | 0.00 |
| time (sec) |
N/A | 0.358 | 1.078 | 0.374 | 0.000 | 0.073 | 0.000 | 0.140 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 148 | 801 | 228 | 0 | 868 | 0 | 229 | 95 | 0 |
| N.S. |
1 | 1.04 | 5.64 | 1.61 | 0.00 | 6.11 | 0.00 | 1.61 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.760 | 7.883 | 1.499 | 0.000 | 0.253 | 0.000 | 0.153 | 0.225 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 176 | 892 | 393 | 0 | 1322 | 0 | 301 | 143 | 0 |
| N.S. |
1 | 1.06 | 5.37 | 2.37 | 0.00 | 7.96 | 0.00 | 1.81 | 0.86 | 0.00 |
| time (sec) |
N/A | 0.768 | 8.469 | 10.706 | 0.000 | 0.192 | 0.000 | 0.162 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 203 | 920 | 567 | 0 | 1994 | 0 | 429 | 191 | 0 |
| N.S. |
1 | 1.05 | 4.74 | 2.92 | 0.00 | 10.28 | 0.00 | 2.21 | 0.98 | 0.00 |
| time (sec) |
N/A | 0.827 | 9.425 | 89.658 | 0.000 | 0.304 | 0.000 | 0.171 | 0.220 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 192 | 155 | 285 | 0 | 387 | 0 | 0 | 137 | 0 |
| N.S. |
1 | 1.08 | 0.87 | 1.60 | 0.00 | 2.17 | 0.00 | 0.00 | 0.77 | 0.00 |
| time (sec) |
N/A | 1.038 | 1.251 | 4.427 | 0.000 | 0.091 | 0.000 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 130 | 125 | 185 | 0 | 286 | 0 | 0 | 99 | 0 |
| N.S. |
1 | 1.06 | 1.02 | 1.50 | 0.00 | 2.33 | 0.00 | 0.00 | 0.80 | 0.00 |
| time (sec) |
N/A | 0.529 | 1.319 | 1.881 | 0.000 | 0.104 | 0.000 | 0.000 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 106 | 128 | 0 | 214 | 0 | 0 | 61 | 151 |
| N.S. |
1 | 1.00 | 1.34 | 1.62 | 0.00 | 2.71 | 0.00 | 0.00 | 0.77 | 1.91 |
| time (sec) |
N/A | 0.322 | 0.344 | 2.671 | 0.000 | 0.084 | 0.000 | 0.000 | 0.179 | 17.827 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 73 | 75 | 0 | 193 | 0 | 61 | 28 | 49 |
| N.S. |
1 | 1.00 | 1.55 | 1.60 | 0.00 | 4.11 | 0.00 | 1.30 | 0.60 | 1.04 |
| time (sec) |
N/A | 0.215 | 0.091 | 0.785 | 0.000 | 0.085 | 0.000 | 0.145 | 0.187 | 16.950 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 123 | 588 | 131 | 0 | 685 | 0 | 197 | 48 | 0 |
| N.S. |
1 | 1.00 | 4.78 | 1.07 | 0.00 | 5.57 | 0.00 | 1.60 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.529 | 1.965 | 0.952 | 0.000 | 0.170 | 0.000 | 0.154 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 198 | 646 | 448 | 0 | 1494 | 0 | 363 | 80 | 0 |
| N.S. |
1 | 1.13 | 3.69 | 2.56 | 0.00 | 8.54 | 0.00 | 2.07 | 0.46 | 0.00 |
| time (sec) |
N/A | 0.886 | 3.872 | 1.030 | 0.000 | 0.316 | 0.000 | 0.184 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 286 | 776 | 1065 | 0 | 2903 | 0 | 559 | 112 | 0 |
| N.S. |
1 | 1.16 | 3.14 | 4.31 | 0.00 | 11.75 | 0.00 | 2.26 | 0.45 | 0.00 |
| time (sec) |
N/A | 1.396 | 4.912 | 1.117 | 0.000 | 0.582 | 0.000 | 0.203 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 201 | 328 | 490 | 0 | 494 | 0 | 0 | 177 | 0 |
| N.S. |
1 | 1.05 | 1.71 | 2.55 | 0.00 | 2.57 | 0.00 | 0.00 | 0.92 | 0.00 |
| time (sec) |
N/A | 1.085 | 1.719 | 4.611 | 0.000 | 0.104 | 0.000 | 0.000 | 0.269 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 140 | 239 | 316 | 0 | 380 | 0 | 0 | 129 | 0 |
| N.S. |
1 | 1.01 | 1.73 | 2.29 | 0.00 | 2.75 | 0.00 | 0.00 | 0.93 | 0.00 |
| time (sec) |
N/A | 0.570 | 1.053 | 2.006 | 0.000 | 0.093 | 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 | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 150 | 176 | 0 | 293 | 0 | 0 | 81 | 0 |
| N.S. |
1 | 1.00 | 1.72 | 2.02 | 0.00 | 3.37 | 0.00 | 0.00 | 0.93 | 0.00 |
| time (sec) |
N/A | 0.332 | 0.391 | 1.688 | 0.000 | 0.134 | 0.000 | 0.000 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | B | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 108 | 125 | 0 | 252 | 0 | 133 | 38 | 0 |
| N.S. |
1 | 1.00 | 1.40 | 1.62 | 0.00 | 3.27 | 0.00 | 1.73 | 0.49 | 0.00 |
| time (sec) |
N/A | 0.285 | 0.209 | 0.602 | 0.000 | 0.087 | 0.000 | 0.145 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 177 | 747 | 348 | 0 | 1299 | 0 | 0 | 70 | 0 |
| N.S. |
1 | 1.08 | 4.55 | 2.12 | 0.00 | 7.92 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 0.848 | 2.740 | 1.004 | 0.000 | 0.281 | 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) | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 270 | 853 | 978 | 0 | 2515 | 0 | 0 | 118 | 0 |
| N.S. |
1 | 1.11 | 3.51 | 4.02 | 0.00 | 10.35 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 1.350 | 5.818 | 1.142 | 0.000 | 0.539 | 0.000 | 0.000 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 318 | 361 | 932 | 2219 | 0 | 4133 | 0 | 0 | 166 | 0 |
| N.S. |
1 | 1.14 | 2.93 | 6.98 | 0.00 | 13.00 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 1.926 | 7.993 | 1.185 | 0.000 | 1.060 | 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 | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 204 | 400 | 688 | 0 | 608 | 0 | 0 | 217 | 0 |
| N.S. |
1 | 1.05 | 2.06 | 3.55 | 0.00 | 3.13 | 0.00 | 0.00 | 1.12 | 0.00 |
| time (sec) |
N/A | 1.102 | 2.129 | 4.669 | 0.000 | 0.097 | 0.000 | 0.000 | 0.184 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 153 | 252 | 379 | 0 | 492 | 0 | 0 | 159 | 0 |
| N.S. |
1 | 1.04 | 1.71 | 2.58 | 0.00 | 3.35 | 0.00 | 0.00 | 1.08 | 0.00 |
| time (sec) |
N/A | 0.588 | 1.592 | 2.032 | 0.000 | 0.107 | 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 | B | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 124 | 227 | 279 | 0 | 392 | 0 | 0 | 101 | 0 |
| N.S. |
1 | 0.98 | 1.80 | 2.21 | 0.00 | 3.11 | 0.00 | 0.00 | 0.80 | 0.00 |
| time (sec) |
N/A | 0.439 | 0.708 | 1.610 | 0.000 | 0.107 | 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 | B | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 112 | 196 | 199 | 0 | 320 | 0 | 153 | 48 | 0 |
| N.S. |
1 | 1.05 | 1.83 | 1.86 | 0.00 | 2.99 | 0.00 | 1.43 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.385 | 0.202 | 0.613 | 0.000 | 0.091 | 0.000 | 0.141 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 218 | 244 | 863 | 732 | 0 | 2015 | 0 | 0 | 92 | 0 |
| N.S. |
1 | 1.12 | 3.96 | 3.36 | 0.00 | 9.24 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 1.303 | 5.585 | 1.013 | 0.000 | 0.448 | 0.000 | 0.000 | 0.214 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 313 | 359 | 932 | 1972 | 0 | 3719 | 0 | 0 | 156 | 0 |
| N.S. |
1 | 1.15 | 2.98 | 6.30 | 0.00 | 11.88 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 1.948 | 7.788 | 1.130 | 0.000 | 0.973 | 0.000 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 400 | 456 | 1045 | 3535 | 0 | 5999 | 0 | 0 | 220 | 0 |
| N.S. |
1 | 1.14 | 2.61 | 8.84 | 0.00 | 15.00 | 0.00 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 2.590 | 12.696 | 1.232 | 0.000 | 1.790 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 205 | 392 | 0 | 0 | 1257 | 0 | 0 | 99 | 0 |
| N.S. |
1 | 1.01 | 1.93 | 0.00 | 0.00 | 6.19 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 0.851 | 2.003 | 180.000 | 0.000 | 0.441 | 0.000 | 0.000 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 155 | 360 | 0 | 0 | 1069 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 0.99 | 2.31 | 0.00 | 0.00 | 6.85 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.629 | 1.412 | 180.000 | 0.000 | 0.380 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 342 | 0 | 0 | 945 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 3.26 | 0.00 | 0.00 | 9.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.452 | 0.975 | 180.000 | 0.000 | 0.355 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 292 | 1482 | 0 | 777 | 0 | 0 | 38 | 0 |
| N.S. |
1 | 1.00 | 4.79 | 24.30 | 0.00 | 12.74 | 0.00 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 0.288 | 0.961 | 278.991 | 0.000 | 0.332 | 0.000 | 0.000 | 0.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 84 | 104 | 179 | 129 | 0 | 151 | 54 | 145 |
| N.S. |
1 | 1.00 | 1.87 | 2.31 | 3.98 | 2.87 | 0.00 | 3.36 | 1.20 | 3.22 |
| time (sec) |
N/A | 0.282 | 0.480 | 5.496 | 0.157 | 0.085 | 0.000 | 0.326 | 0.205 | 18.474 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 100 | 253 | 340 | 300 | 0 | 471 | 70 | 353 |
| N.S. |
1 | 1.00 | 1.05 | 2.66 | 3.58 | 3.16 | 0.00 | 4.96 | 0.74 | 3.72 |
| time (sec) |
N/A | 0.462 | 0.521 | 14.569 | 0.156 | 0.098 | 0.000 | 0.525 | 0.189 | 23.386 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 152 | 128 | 379 | 544 | 556 | 0 | 1050 | 86 | 501 |
| N.S. |
1 | 1.07 | 0.90 | 2.67 | 3.83 | 3.92 | 0.00 | 7.39 | 0.61 | 3.53 |
| time (sec) |
N/A | 0.666 | 0.726 | 23.960 | 0.181 | 0.125 | 0.000 | 0.925 | 0.197 | 26.135 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 266 | 318 | 0 | 0 | 1579 | 0 | 0 | 203 | 0 |
| N.S. |
1 | 0.93 | 1.12 | 0.00 | 0.00 | 5.54 | 0.00 | 0.00 | 0.71 | 0.00 |
| time (sec) |
N/A | 1.199 | 4.022 | 0.000 | 0.000 | 0.790 | 0.000 | 0.000 | 0.273 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 216 | 281 | 0 | 0 | 1337 | 0 | 0 | 125 | 0 |
| N.S. |
1 | 0.95 | 1.23 | 0.00 | 0.00 | 5.86 | 0.00 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 0.934 | 2.539 | 180.000 | 0.000 | 0.479 | 0.000 | 0.000 | 0.261 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 166 | 247 | 0 | 0 | 1127 | 0 | 0 | 57 | 0 |
| N.S. |
1 | 0.97 | 1.44 | 0.00 | 0.00 | 6.59 | 0.00 | 0.00 | 0.33 | 0.00 |
| time (sec) |
N/A | 0.722 | 1.518 | 180.000 | 0.000 | 0.425 | 0.000 | 0.000 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F(-1) | F | B | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 111 | 301 | 0 | 0 | 989 | 0 | 0 | 81 | 0 |
| N.S. |
1 | 1.00 | 2.71 | 0.00 | 0.00 | 8.91 | 0.00 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.532 | 1.789 | 180.000 | 0.000 | 0.395 | 0.000 | 0.000 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F(-1) | F | B | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 377 | 0 | 0 | 1297 | 0 | 0 | 113 | 0 |
| N.S. |
1 | 1.00 | 3.22 | 0.00 | 0.00 | 11.09 | 0.00 | 0.00 | 0.97 | 0.00 |
| time (sec) |
N/A | 0.545 | 5.956 | 180.000 | 0.000 | 0.374 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 104 | 307 | 307 | 323 | 0 | 0 | 145 | 387 |
| N.S. |
1 | 1.00 | 0.90 | 2.67 | 2.67 | 2.81 | 0.00 | 0.00 | 1.26 | 3.37 |
| time (sec) |
N/A | 0.536 | 1.801 | 14.342 | 0.197 | 0.110 | 0.000 | 0.000 | 0.225 | 23.296 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 171 | 140 | 459 | 505 | 598 | 0 | 0 | 177 | 541 |
| N.S. |
1 | 0.99 | 0.81 | 2.67 | 2.94 | 3.48 | 0.00 | 0.00 | 1.03 | 3.15 |
| time (sec) |
N/A | 0.778 | 2.051 | 22.689 | 0.210 | 0.136 | 0.000 | 0.000 | 0.240 | 27.641 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 228 | 193 | 637 | 750 | 937 | 0 | 0 | 209 | 807 |
| N.S. |
1 | 1.00 | 0.84 | 2.78 | 3.28 | 4.09 | 0.00 | 0.00 | 0.91 | 3.52 |
| time (sec) |
N/A | 1.016 | 2.712 | 32.246 | 0.238 | 0.162 | 0.000 | 0.000 | 0.235 | 29.550 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 377 | 338 | 395 | 0 | 0 | 2083 | 0 | 0 | 312 | 0 |
| N.S. |
1 | 0.90 | 1.05 | 0.00 | 0.00 | 5.53 | 0.00 | 0.00 | 0.83 | 0.00 |
| time (sec) |
N/A | 1.589 | 7.499 | 180.000 | 0.000 | 1.019 | 0.000 | 0.000 | 0.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 290 | 327 | 0 | 0 | 1751 | 0 | 0 | 195 | 0 |
| N.S. |
1 | 0.93 | 1.05 | 0.00 | 0.00 | 5.61 | 0.00 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 1.325 | 6.722 | 180.000 | 0.000 | 0.827 | 0.000 | 0.000 | 0.299 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 238 | 285 | 0 | 0 | 1455 | 0 | 0 | 92 | 0 |
| N.S. |
1 | 0.99 | 1.18 | 0.00 | 0.00 | 6.04 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 1.086 | 2.822 | 180.000 | 0.000 | 0.516 | 0.000 | 0.000 | 0.244 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 182 | 256 | 0 | 0 | 1219 | 0 | 0 | 128 | 0 |
| N.S. |
1 | 1.02 | 1.44 | 0.00 | 0.00 | 6.85 | 0.00 | 0.00 | 0.72 | 0.00 |
| time (sec) |
N/A | 0.854 | 3.584 | 180.000 | 0.000 | 0.449 | 0.000 | 0.000 | 0.228 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 190 | 263 | 0 | 0 | 1665 | 0 | 0 | 176 | 0 |
| N.S. |
1 | 1.06 | 1.46 | 0.00 | 0.00 | 9.25 | 0.00 | 0.00 | 0.98 | 0.00 |
| time (sec) |
N/A | 0.867 | 3.920 | 180.000 | 0.000 | 0.436 | 0.000 | 0.000 | 0.267 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F(-1) | F | B | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 198 | 261 | 0 | 0 | 2297 | 0 | 0 | 224 | 0 |
| N.S. |
1 | 1.08 | 1.43 | 0.00 | 0.00 | 12.55 | 0.00 | 0.00 | 1.22 | 0.00 |
| time (sec) |
N/A | 0.862 | 8.227 | 180.000 | 0.000 | 0.489 | 0.000 | 0.000 | 0.251 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 203 | 152 | 513 | 464 | 654 | 0 | 0 | 272 | 590 |
| N.S. |
1 | 1.07 | 0.80 | 2.71 | 2.46 | 3.46 | 0.00 | 0.00 | 1.44 | 3.12 |
| time (sec) |
N/A | 0.893 | 4.796 | 24.108 | 0.232 | 0.125 | 0.000 | 0.000 | 0.250 | 27.704 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 257 | 216 | 717 | 703 | 1033 | 0 | 0 | 320 | 862 |
| N.S. |
1 | 1.01 | 0.85 | 2.82 | 2.77 | 4.07 | 0.00 | 0.00 | 1.26 | 3.39 |
| time (sec) |
N/A | 1.159 | 6.481 | 33.078 | 0.232 | 0.178 | 0.000 | 0.000 | 0.256 | 28.328 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 314 | 304 | 947 | 984 | 1492 | 0 | 0 | 368 | 1155 |
| N.S. |
1 | 0.99 | 0.96 | 2.99 | 3.10 | 4.71 | 0.00 | 0.00 | 1.16 | 3.64 |
| time (sec) |
N/A | 1.449 | 9.444 | 42.206 | 0.332 | 0.215 | 0.000 | 0.000 | 0.268 | 29.656 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 262 | 1893 | 0 | 0 | 3021 | 0 | 0 | 132 | 0 |
| N.S. |
1 | 1.05 | 7.60 | 0.00 | 0.00 | 12.13 | 0.00 | 0.00 | 0.53 | 0.00 |
| time (sec) |
N/A | 1.532 | 15.602 | 0.000 | 0.000 | 0.549 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F(-1) | F | B | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 196 | 1639 | 0 | 0 | 2621 | 0 | 0 | 83 | 0 |
| N.S. |
1 | 1.04 | 8.72 | 0.00 | 0.00 | 13.94 | 0.00 | 0.00 | 0.44 | 0.00 |
| time (sec) |
N/A | 1.016 | 15.613 | 180.000 | 0.000 | 0.475 | 0.000 | 0.000 | 0.202 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | B | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 1251 | 3454 | 0 | 2040 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.00 | 8.87 | 24.50 | 0.00 | 14.47 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 0.628 | 14.377 | 10.016 | 0.000 | 0.391 | 0.000 | 0.000 | 0.221 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | A | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 283 | 313 | 0 | 475 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 1.00 | 3.58 | 3.96 | 0.00 | 6.01 | 0.00 | 0.00 | 0.75 | 0.00 |
| time (sec) |
N/A | 0.304 | 2.200 | 6.037 | 0.000 | 0.224 | 0.000 | 0.000 | 0.214 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 145 | 306 | 985 | 0 | 1016 | 0 | 0 | 91 | 0 |
| N.S. |
1 | 1.11 | 2.34 | 7.52 | 0.00 | 7.76 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.506 | 3.653 | 10.145 | 0.000 | 0.415 | 0.000 | 0.000 | 0.180 | 0.000 |