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 | 221 | 206 | 171 | 723 | 0 | 286 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.93 | 0.77 | 3.27 | 0.00 | 1.29 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.267 | 2.907 | 6.386 | 0.000 | 0.106 | 0.000 | 0.000 | 0.208 | 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 | 177 | 178 | 125 | 650 | 0 | 247 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.01 | 0.71 | 3.67 | 0.00 | 1.40 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 1.100 | 4.351 | 5.400 | 0.000 | 0.100 | 0.000 | 0.000 | 0.208 | 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 | 161 | 164 | 124 | 404 | 0 | 208 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.02 | 0.77 | 2.51 | 0.00 | 1.29 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.003 | 3.732 | 5.195 | 0.000 | 0.104 | 0.000 | 0.000 | 0.243 | 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 | 171 | 174 | 128 | 487 | 0 | 226 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.02 | 0.75 | 2.85 | 0.00 | 1.32 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.014 | 4.352 | 11.151 | 0.000 | 0.098 | 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 | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 202 | 161 | 548 | 0 | 254 | 0 | 0 | 93 | 0 |
N.S. |
1 | 0.95 | 0.76 | 2.57 | 0.00 | 1.19 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.181 | 4.527 | 18.325 | 0.000 | 0.110 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 230 | 189 | 610 | 0 | 282 | 0 | 0 | 93 | 0 |
N.S. |
1 | 0.91 | 0.74 | 2.40 | 0.00 | 1.11 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.388 | 4.782 | 27.253 | 0.000 | 0.111 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 305 | 381 | 1166 | 0 | 401 | 0 | 0 | 117 | 0 |
N.S. |
1 | 0.88 | 1.10 | 3.38 | 0.00 | 1.16 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.976 | 7.134 | 16.684 | 0.000 | 0.122 | 0.000 | 0.000 | 0.187 | 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 | 295 | 277 | 225 | 917 | 0 | 364 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.94 | 0.76 | 3.11 | 0.00 | 1.23 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.791 | 3.891 | 12.725 | 0.000 | 0.105 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 248 | 190 | 970 | 0 | 326 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.02 | 0.78 | 3.98 | 0.00 | 1.34 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.611 | 10.698 | 10.804 | 0.000 | 0.119 | 0.000 | 0.000 | 0.190 | 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 | 239 | 238 | 166 | 886 | 0 | 298 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.00 | 0.69 | 3.71 | 0.00 | 1.25 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.559 | 7.170 | 9.117 | 0.000 | 0.105 | 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 | 236 | 240 | 172 | 641 | 0 | 270 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.02 | 0.73 | 2.72 | 0.00 | 1.14 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 1.594 | 6.631 | 11.898 | 0.000 | 0.108 | 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 | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 253 | 180 | 664 | 0 | 295 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.03 | 0.73 | 2.71 | 0.00 | 1.20 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.571 | 7.212 | 16.921 | 0.000 | 0.108 | 0.000 | 0.000 | 0.188 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 281 | 219 | 745 | 0 | 332 | 0 | 0 | 119 | 0 |
N.S. |
1 | 0.95 | 0.74 | 2.53 | 0.00 | 1.13 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.818 | 7.660 | 26.774 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 309 | 256 | 825 | 0 | 369 | 0 | 0 | 119 | 0 |
N.S. |
1 | 0.90 | 0.74 | 2.39 | 0.00 | 1.07 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 2.124 | 9.769 | 41.402 | 0.000 | 0.125 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 295 | 664 | 758 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.06 | 2.40 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.379 | 41.415 | 32.772 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 210 | 225 | 225 | 439 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.07 | 1.07 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.738 | 9.314 | 11.809 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 123 | 298 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.944 | 2.096 | 2.725 | 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(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 76 | 217 | 0 | 0 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.678 | 0.927 | 1.888 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 127 | 220 | 295 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.85 | 1.48 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.881 | 20.040 | 3.937 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 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 | 196 | 202 | 278 | 822 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.03 | 1.42 | 4.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.375 | 4.840 | 6.025 | 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 | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 254 | 299 | 1074 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.05 | 1.24 | 4.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.912 | 5.691 | 4.824 | 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(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 389 | 733 | 997 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.96 | 1.81 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 2.909 | 6.932 | 41.941 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 305 | 680 | 850 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.97 | 2.16 | 2.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.209 | 6.763 | 34.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 257 | 249 | 444 | 715 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.97 | 1.73 | 2.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.582 | 6.015 | 4.168 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 252 | 470 | 803 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.96 | 1.79 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.612 | 6.559 | 4.435 | 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 | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 275 | 460 | 843 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.97 | 1.63 | 2.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.744 | 6.701 | 6.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 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 | 365 | 350 | 699 | 1059 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.96 | 1.92 | 2.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.386 | 6.841 | 10.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 583 | 575 | 897 | 2151 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.99 | 1.54 | 3.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 4.288 | 7.116 | 163.155 | 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 | 480 | 475 | 842 | 1997 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.99 | 1.75 | 4.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 3.360 | 6.966 | 156.508 | 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 | 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 | 402 | 401 | 795 | 1768 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.98 | 4.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.593 | 6.791 | 154.894 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 398 | 882 | 1873 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.99 | 2.19 | 4.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.553 | 7.110 | 6.596 | 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(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 400 | 885 | 1960 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 2.20 | 4.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.529 | 7.211 | 6.965 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 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 | 427 | 427 | 818 | 2000 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.92 | 4.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.866 | 7.049 | 8.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 518 | 863 | 2216 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.99 | 1.66 | 4.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 3.796 | 7.169 | 10.756 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 335 | 422 | 1472 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 1.26 | 4.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 3.387 | 15.354 | 25.223 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 260 | 377 | 742 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.03 | 1.49 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 2.600 | 13.974 | 15.441 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 209 | 122 | 800 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 0.59 | 3.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 2.039 | 27.785 | 9.391 | 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 | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 202 | 165 | 1054 | 0 | 452 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 0.82 | 5.24 | 0.00 | 2.25 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.458 | 1.028 | 9.986 | 0.000 | 0.108 | 0.000 | 0.000 | 0.164 | 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 | 267 | 276 | 200 | 1535 | 0 | 519 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.03 | 0.75 | 5.75 | 0.00 | 1.94 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 2.052 | 2.621 | 21.286 | 0.000 | 0.122 | 0.000 | 0.000 | 0.166 | 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 | 343 | 360 | 208 | 2107 | 0 | 588 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.05 | 0.61 | 6.14 | 0.00 | 1.71 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 2.821 | 1.644 | 27.956 | 0.000 | 0.136 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 429 | 673 | 2327 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.02 | 1.60 | 5.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 4.459 | 7.003 | 44.493 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 346 | 595 | 1674 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.02 | 1.76 | 4.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 3.540 | 6.912 | 28.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 280 | 429 | 1389 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.03 | 1.58 | 5.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 2.844 | 6.182 | 20.292 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 277 | 437 | 1394 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.00 | 1.58 | 5.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 2.774 | 4.416 | 19.819 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 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 | 266 | 269 | 201 | 1645 | 0 | 520 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.01 | 0.76 | 6.18 | 0.00 | 1.95 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 2.111 | 2.452 | 21.653 | 0.000 | 0.120 | 0.000 | 0.000 | 0.184 | 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 | 342 | 350 | 255 | 2107 | 0 | 589 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.02 | 0.75 | 6.16 | 0.00 | 1.72 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 2.805 | 4.617 | 28.339 | 0.000 | 0.139 | 0.000 | 0.000 | 0.185 | 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 | 427 | 435 | 313 | 2699 | 0 | 666 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.02 | 0.73 | 6.32 | 0.00 | 1.56 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 3.693 | 3.134 | 41.493 | 0.000 | 0.144 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 513 | 0 | 768 | 3085 | 0 | 0 | 0 | 0 | 135 | 0 |
N.S. |
1 | 0.00 | 1.50 | 6.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.000 | 7.112 | 61.482 | 0.000 | 0.000 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 434 | 678 | 2400 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.03 | 1.61 | 5.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 4.542 | 6.928 | 48.481 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 360 | 628 | 2074 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.00 | 1.75 | 5.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 3.660 | 7.686 | 36.088 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 354 | 599 | 1914 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.01 | 1.72 | 5.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 3.657 | 7.645 | 30.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 348 | 616 | 1982 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.02 | 1.80 | 5.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 3.584 | 8.021 | 29.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 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 | 340 | 348 | 257 | 2217 | 0 | 589 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.02 | 0.76 | 6.52 | 0.00 | 1.73 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 2.740 | 3.212 | 28.756 | 0.000 | 0.131 | 0.000 | 0.000 | 0.193 | 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 | 425 | 433 | 313 | 2699 | 0 | 666 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.02 | 0.74 | 6.35 | 0.00 | 1.57 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 3.570 | 5.470 | 41.737 | 0.000 | 0.145 | 0.000 | 0.000 | 0.193 | 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 | 519 | 532 | 380 | 3311 | 0 | 753 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.03 | 0.73 | 6.38 | 0.00 | 1.45 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 4.545 | 4.551 | 48.077 | 0.000 | 0.159 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 343 | 451 | 1606 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.31 | 4.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 3.468 | 3.171 | 36.317 | 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 | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 269 | 339 | 802 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.05 | 1.32 | 3.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.376 | 13.930 | 19.487 | 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 | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 91 | 251 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.66 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.171 | 0.727 | 11.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 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 | 150 | 150 | 103 | 547 | 0 | 371 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.69 | 3.65 | 0.00 | 2.47 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.087 | 3.770 | 14.268 | 0.000 | 0.097 | 0.000 | 0.000 | 0.154 | 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 | 212 | 216 | 161 | 955 | 0 | 452 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.02 | 0.76 | 4.50 | 0.00 | 2.13 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.537 | 1.825 | 21.839 | 0.000 | 0.111 | 0.000 | 0.000 | 0.156 | 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 | 292 | 198 | 1535 | 0 | 520 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.04 | 0.71 | 5.48 | 0.00 | 1.86 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.107 | 1.672 | 30.920 | 0.000 | 0.118 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 386 | 518 | 1546 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.04 | 1.40 | 4.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 3.908 | 4.274 | 28.802 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 229 | 464 | 902 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.04 | 2.11 | 4.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.832 | 3.346 | 11.227 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 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 | 215 | 226 | 161 | 551 | 0 | 606 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.05 | 0.75 | 2.56 | 0.00 | 2.82 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.659 | 0.825 | 9.980 | 0.000 | 0.114 | 0.000 | 0.000 | 0.158 | 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 | 235 | 249 | 178 | 840 | 0 | 679 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.06 | 0.76 | 3.57 | 0.00 | 2.89 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.721 | 1.262 | 21.353 | 0.000 | 0.127 | 0.000 | 0.000 | 0.187 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 333 | 252 | 1269 | 0 | 792 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.02 | 0.77 | 3.89 | 0.00 | 2.43 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 2.479 | 1.856 | 29.757 | 0.000 | 0.146 | 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(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 423 | 427 | 316 | 1756 | 0 | 916 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.01 | 0.75 | 4.15 | 0.00 | 2.17 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 3.297 | 2.431 | 41.967 | 0.000 | 0.177 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 418 | 726 | 2603 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.05 | 1.82 | 6.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 4.025 | 6.964 | 26.806 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 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 | 329 | 338 | 217 | 1701 | 0 | 951 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.03 | 0.66 | 5.17 | 0.00 | 2.89 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 2.432 | 1.560 | 20.056 | 0.000 | 0.160 | 0.000 | 0.000 | 0.157 | 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 | 346 | 359 | 245 | 2085 | 0 | 1071 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.04 | 0.71 | 6.03 | 0.00 | 3.10 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 2.502 | 2.053 | 22.768 | 0.000 | 0.172 | 0.000 | 0.000 | 0.167 | 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 | 368 | 384 | 297 | 2669 | 0 | 1186 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.04 | 0.81 | 7.25 | 0.00 | 3.22 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 2.703 | 2.363 | 32.358 | 0.000 | 0.179 | 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 | 472 | 481 | 353 | 3221 | 0 | 1343 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.02 | 0.75 | 6.82 | 0.00 | 2.85 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 3.653 | 2.874 | 42.116 | 0.000 | 0.220 | 0.000 | 0.000 | 0.161 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 588 | 594 | 392 | 3925 | 0 | 1531 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.01 | 0.67 | 6.68 | 0.00 | 2.60 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 4.813 | 3.549 | 46.533 | 0.000 | 0.277 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 0 | 24 | 25 | 40 | 29 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.96 | 1.00 | 1.60 | 1.16 |
time (sec) |
N/A | 0.478 | 117.111 | 0.146 | 1.097 | 0.000 | 4.158 | 0.690 | 0.182 | 14.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 0 | 24 | 25 | 40 | 29 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.96 | 1.00 | 1.60 | 1.16 |
time (sec) |
N/A | 0.464 | 118.675 | 0.139 | 1.074 | 0.000 | 1.611 | 0.615 | 0.182 | 13.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 0 | 24 | 25 | 40 | 29 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.96 | 1.00 | 1.60 | 1.16 |
time (sec) |
N/A | 0.463 | 23.618 | 0.135 | 1.083 | 0.000 | 1.150 | 0.726 | 0.176 | 13.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 0 | 24 | 25 | 40 | 29 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.96 | 1.00 | 1.60 | 1.16 |
time (sec) |
N/A | 0.479 | 24.638 | 0.139 | 1.085 | 0.000 | 1.268 | 0.903 | 0.165 | 13.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 33 | 35 | 35 | 32 | 35 | 61 | 41 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.97 | 1.06 | 1.85 | 1.24 |
time (sec) |
N/A | 0.274 | 19.022 | 0.368 | 7.497 | 0.124 | 47.922 | 0.737 | 0.239 | 16.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 544 | 539 | 365 | 0 | 0 | 0 | 0 | 0 | 140 | 0 |
N.S. |
1 | 0.99 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 3.472 | 3.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 366 | 372 | 307 | 0 | 0 | 0 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.02 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 2.083 | 1.498 | 0.000 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 264 | 239 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.01 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.332 | 0.637 | 0.000 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 185 | 168 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.05 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.639 | 0.266 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 130 | 872 | 383 | 0 | 179 | 0 | 0 | 103 | 166 |
N.S. |
1 | 0.98 | 6.61 | 2.90 | 0.00 | 1.36 | 0.00 | 0.00 | 0.78 | 1.26 |
time (sec) |
N/A | 0.738 | 6.964 | 11.490 | 0.000 | 0.102 | 0.000 | 0.000 | 0.282 | 0.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 103 | 363 | 355 | 0 | 161 | 0 | 0 | 103 | 128 |
N.S. |
1 | 1.02 | 3.59 | 3.51 | 0.00 | 1.59 | 0.00 | 0.00 | 1.02 | 1.27 |
time (sec) |
N/A | 0.698 | 5.105 | 9.787 | 0.000 | 0.098 | 0.000 | 0.000 | 0.255 | 0.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 73 | 309 | 321 | 0 | 142 | 0 | 0 | 95 | 85 |
N.S. |
1 | 1.04 | 4.41 | 4.59 | 0.00 | 2.03 | 0.00 | 0.00 | 1.36 | 1.21 |
time (sec) |
N/A | 0.618 | 4.584 | 2.829 | 0.000 | 0.097 | 0.000 | 0.000 | 0.232 | 11.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 252 | 240 | 0 | 173 | 0 | 0 | 70 | 96 |
N.S. |
1 | 1.00 | 3.82 | 3.64 | 0.00 | 2.62 | 0.00 | 0.00 | 1.06 | 1.45 |
time (sec) |
N/A | 0.614 | 4.413 | 2.124 | 0.000 | 0.092 | 0.000 | 0.000 | 0.199 | 12.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 97 | 293 | 399 | 0 | 196 | 0 | 0 | 103 | 150 |
N.S. |
1 | 1.02 | 3.08 | 4.20 | 0.00 | 2.06 | 0.00 | 0.00 | 1.08 | 1.58 |
time (sec) |
N/A | 0.713 | 6.476 | 3.092 | 0.000 | 0.093 | 0.000 | 0.000 | 0.199 | 12.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 126 | 865 | 634 | 0 | 219 | 0 | 0 | 103 | 177 |
N.S. |
1 | 0.95 | 6.55 | 4.80 | 0.00 | 1.66 | 0.00 | 0.00 | 0.78 | 1.34 |
time (sec) |
N/A | 0.739 | 6.766 | 4.664 | 0.000 | 0.095 | 0.000 | 0.000 | 0.209 | 13.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 190 | 1086 | 413 | 0 | 223 | 0 | 0 | 163 | 266 |
N.S. |
1 | 0.98 | 5.60 | 2.13 | 0.00 | 1.15 | 0.00 | 0.00 | 0.84 | 1.37 |
time (sec) |
N/A | 1.107 | 7.085 | 20.735 | 0.000 | 0.099 | 0.000 | 0.000 | 0.358 | 12.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 162 | 1040 | 385 | 0 | 203 | 0 | 0 | 163 | 231 |
N.S. |
1 | 1.01 | 6.46 | 2.39 | 0.00 | 1.26 | 0.00 | 0.00 | 1.01 | 1.43 |
time (sec) |
N/A | 1.070 | 6.894 | 18.806 | 0.000 | 0.093 | 0.000 | 0.000 | 0.326 | 12.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 132 | 994 | 357 | 0 | 179 | 0 | 0 | 163 | 153 |
N.S. |
1 | 1.05 | 7.89 | 2.83 | 0.00 | 1.42 | 0.00 | 0.00 | 1.29 | 1.21 |
time (sec) |
N/A | 0.948 | 7.530 | 17.042 | 0.000 | 0.094 | 0.000 | 0.000 | 0.334 | 12.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 119 | 735 | 245 | 0 | 198 | 0 | 0 | 151 | 134 |
N.S. |
1 | 1.03 | 6.34 | 2.11 | 0.00 | 1.71 | 0.00 | 0.00 | 1.30 | 1.16 |
time (sec) |
N/A | 0.889 | 7.520 | 3.310 | 0.000 | 0.090 | 0.000 | 0.000 | 0.326 | 12.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 124 | 333 | 513 | 0 | 210 | 0 | 0 | 114 | 196 |
N.S. |
1 | 1.03 | 2.78 | 4.28 | 0.00 | 1.75 | 0.00 | 0.00 | 0.95 | 1.63 |
time (sec) |
N/A | 0.937 | 6.502 | 3.748 | 0.000 | 0.096 | 0.000 | 0.000 | 0.222 | 13.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 156 | 1025 | 714 | 0 | 239 | 0 | 0 | 163 | 229 |
N.S. |
1 | 0.98 | 6.45 | 4.49 | 0.00 | 1.50 | 0.00 | 0.00 | 1.03 | 1.44 |
time (sec) |
N/A | 1.063 | 7.913 | 4.912 | 0.000 | 0.112 | 0.000 | 0.000 | 0.217 | 13.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 186 | 1067 | 824 | 0 | 263 | 0 | 0 | 163 | 235 |
N.S. |
1 | 0.96 | 5.50 | 4.25 | 0.00 | 1.36 | 0.00 | 0.00 | 0.84 | 1.21 |
time (sec) |
N/A | 1.094 | 8.206 | 6.780 | 0.000 | 0.107 | 0.000 | 0.000 | 0.219 | 13.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 149 | 1056 | 282 | 0 | 269 | 0 | 0 | 71 | 0 |
N.S. |
1 | 0.95 | 6.73 | 1.80 | 0.00 | 1.71 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.782 | 7.674 | 6.139 | 0.000 | 0.103 | 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 | 124 | 121 | 1003 | 262 | 0 | 250 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.98 | 8.09 | 2.11 | 0.00 | 2.02 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.716 | 7.255 | 4.330 | 0.000 | 0.099 | 0.000 | 0.000 | 0.194 | 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 | 88 | 93 | 972 | 244 | 0 | 241 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.06 | 11.05 | 2.77 | 0.00 | 2.74 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.612 | 6.996 | 3.094 | 0.000 | 0.089 | 0.000 | 0.000 | 0.209 | 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 | 83 | 88 | 968 | 243 | 0 | 237 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.06 | 11.66 | 2.93 | 0.00 | 2.86 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.606 | 7.131 | 1.699 | 0.000 | 0.087 | 0.000 | 0.000 | 0.169 | 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 | 113 | 113 | 1004 | 318 | 0 | 292 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.00 | 8.88 | 2.81 | 0.00 | 2.58 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.715 | 7.240 | 2.173 | 0.000 | 0.094 | 0.000 | 0.000 | 0.169 | 0.000 |