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 | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 107 | 0 | 236 | 0 | 93 | 260 |
N.S. |
1 | 1.00 | 1.00 | 1.49 | 0.00 | 3.28 | 0.00 | 1.29 | 3.61 |
time (sec) |
N/A | 0.172 | 0.035 | 1.627 | 0.000 | 0.240 | 0.000 | 0.292 | 4.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 392 | 133 | 0 | 711 | 0 | 0 | 4311 |
N.S. |
1 | 1.00 | 4.61 | 1.56 | 0.00 | 8.36 | 0.00 | 0.00 | 50.72 |
time (sec) |
N/A | 0.186 | 1.497 | 0.570 | 0.000 | 0.311 | 0.000 | 0.000 | 17.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 77 | 147 | 0 | 252 | 0 | 413 | 439 |
N.S. |
1 | 1.00 | 1.01 | 1.93 | 0.00 | 3.32 | 0.00 | 5.43 | 5.78 |
time (sec) |
N/A | 0.178 | 10.046 | 1.618 | 0.000 | 0.253 | 0.000 | 0.533 | 5.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 126 | 112 | 257 | 0 | 336 | 0 | 1048 | 901 |
N.S. |
1 | 0.96 | 0.85 | 1.96 | 0.00 | 2.56 | 0.00 | 8.00 | 6.88 |
time (sec) |
N/A | 0.212 | 10.078 | 0.572 | 0.000 | 0.306 | 0.000 | 0.668 | 20.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 206 | 160 | 408 | 0 | 440 | 0 | 2140 | 1574 |
N.S. |
1 | 1.08 | 0.84 | 2.14 | 0.00 | 2.30 | 0.00 | 11.20 | 8.24 |
time (sec) |
N/A | 0.301 | 10.106 | 1.634 | 0.000 | 0.413 | 0.000 | 2.184 | 92.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 224 | 192 | 574 | 0 | 546 | 0 | 501 | 0 |
N.S. |
1 | 0.88 | 0.76 | 2.26 | 0.00 | 2.15 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.292 | 0.569 | 0.577 | 0.000 | 0.250 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 160 | 136 | 395 | 0 | 412 | 0 | 346 | 0 |
N.S. |
1 | 0.94 | 0.80 | 2.31 | 0.00 | 2.41 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.234 | 0.317 | 1.642 | 0.000 | 0.248 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 94 | 140 | 0 | 306 | 0 | 233 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.24 | 0.00 | 2.71 | 0.00 | 2.06 | 0.00 |
time (sec) |
N/A | 0.197 | 0.021 | 0.573 | 0.000 | 0.241 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 126 | 116 | 219 | 0 | 844 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.00 | 1.89 | 0.00 | 7.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.352 | 1.640 | 0.000 | 0.556 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 129 | 119 | 223 | 0 | 858 | 0 | 484 | 0 |
N.S. |
1 | 1.08 | 1.00 | 1.87 | 0.00 | 7.21 | 0.00 | 4.07 | 0.00 |
time (sec) |
N/A | 0.231 | 0.327 | 0.573 | 0.000 | 0.474 | 0.000 | 0.421 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 120 | 98 | 255 | 0 | 334 | 0 | 1078 | 0 |
N.S. |
1 | 1.01 | 0.82 | 2.14 | 0.00 | 2.81 | 0.00 | 9.06 | 0.00 |
time (sec) |
N/A | 0.213 | 0.234 | 1.647 | 0.000 | 0.292 | 0.000 | 0.690 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 170 | 143 | 408 | 0 | 438 | 0 | 2219 | 0 |
N.S. |
1 | 0.94 | 0.79 | 2.27 | 0.00 | 2.43 | 0.00 | 12.33 | 0.00 |
time (sec) |
N/A | 0.242 | 0.307 | 0.575 | 0.000 | 0.397 | 0.000 | 2.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 266 | 283 | 202 | 593 | 0 | 574 | 0 | 3834 | 0 |
N.S. |
1 | 1.06 | 0.76 | 2.23 | 0.00 | 2.16 | 0.00 | 14.41 | 0.00 |
time (sec) |
N/A | 0.386 | 0.517 | 1.613 | 0.000 | 1.203 | 0.000 | 1.539 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 314 | 264 | 244 | 788 | 0 | 706 | 0 | 885 | 0 |
N.S. |
1 | 0.84 | 0.78 | 2.51 | 0.00 | 2.25 | 0.00 | 2.82 | 0.00 |
time (sec) |
N/A | 0.319 | 0.621 | 0.580 | 0.000 | 0.283 | 0.000 | 0.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 201 | 177 | 574 | 0 | 544 | 0 | 639 | 0 |
N.S. |
1 | 0.93 | 0.82 | 2.65 | 0.00 | 2.51 | 0.00 | 2.94 | 0.00 |
time (sec) |
N/A | 0.249 | 0.442 | 0.574 | 0.000 | 0.259 | 0.000 | 0.363 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 154 | 124 | 173 | 0 | 412 | 0 | 446 | 0 |
N.S. |
1 | 1.04 | 0.84 | 1.17 | 0.00 | 2.78 | 0.00 | 3.01 | 0.00 |
time (sec) |
N/A | 0.222 | 0.037 | 1.653 | 0.000 | 0.258 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 185 | 148 | 342 | 0 | 987 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.87 | 2.00 | 0.00 | 5.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.583 | 0.571 | 0.000 | 1.530 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 175 | 141 | 320 | 0 | 991 | 0 | 547 | 0 |
N.S. |
1 | 1.09 | 0.88 | 2.00 | 0.00 | 6.19 | 0.00 | 3.42 | 0.00 |
time (sec) |
N/A | 0.299 | 0.618 | 1.638 | 0.000 | 1.248 | 0.000 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 192 | 153 | 354 | 0 | 1031 | 0 | 1149 | 0 |
N.S. |
1 | 1.08 | 0.86 | 2.00 | 0.00 | 5.82 | 0.00 | 6.49 | 0.00 |
time (sec) |
N/A | 0.286 | 0.763 | 0.577 | 0.000 | 1.004 | 0.000 | 0.916 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 164 | 141 | 405 | 0 | 438 | 0 | 2153 | 0 |
N.S. |
1 | 1.04 | 0.90 | 2.58 | 0.00 | 2.79 | 0.00 | 13.71 | 0.00 |
time (sec) |
N/A | 0.236 | 0.355 | 1.603 | 0.000 | 0.398 | 0.000 | 2.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 214 | 200 | 593 | 0 | 574 | 0 | 3834 | 0 |
N.S. |
1 | 0.93 | 0.87 | 2.59 | 0.00 | 2.51 | 0.00 | 16.74 | 0.00 |
time (sec) |
N/A | 0.272 | 0.537 | 0.573 | 0.000 | 1.215 | 0.000 | 1.667 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 346 | 377 | 258 | 813 | 0 | 732 | 0 | 5928 | 0 |
N.S. |
1 | 1.09 | 0.75 | 2.35 | 0.00 | 2.12 | 0.00 | 17.13 | 0.00 |
time (sec) |
N/A | 0.507 | 0.712 | 1.653 | 0.000 | 2.734 | 0.000 | 15.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 127 | 73 | 92 | 84 | 62 | 0 | 59 | 0 |
N.S. |
1 | 1.08 | 0.62 | 0.78 | 0.71 | 0.53 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.210 | 0.190 | 0.576 | 0.280 | 0.228 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 119 | 68 | 87 | 70 | 57 | 0 | 52 | 0 |
N.S. |
1 | 1.08 | 0.62 | 0.79 | 0.64 | 0.52 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.198 | 0.142 | 1.647 | 0.289 | 0.231 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 63 | 80 | 56 | 52 | 0 | 46 | 0 |
N.S. |
1 | 1.05 | 0.72 | 0.91 | 0.64 | 0.59 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.182 | 0.130 | 0.569 | 0.308 | 0.226 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 54 | 66 | 40 | 45 | 0 | 37 | 0 |
N.S. |
1 | 1.08 | 0.89 | 1.08 | 0.66 | 0.74 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.163 | 0.104 | 1.319 | 0.287 | 0.231 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 41 | 39 | 57 | 28 | 40 | 134 | 31 | 0 |
N.S. |
1 | 0.87 | 0.83 | 1.21 | 0.60 | 0.85 | 2.85 | 0.66 | 0.00 |
time (sec) |
N/A | 0.150 | 0.024 | 0.548 | 0.275 | 0.229 | 2.379 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 54 | 51 | 41 | 57 | 0 | 158 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.19 | 0.95 | 1.33 | 0.00 | 3.67 | 0.00 |
time (sec) |
N/A | 0.165 | 0.126 | 1.804 | 0.279 | 0.230 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 59 | 55 | 42 | 65 | 0 | 236 | 0 |
N.S. |
1 | 1.00 | 1.34 | 1.25 | 0.95 | 1.48 | 0.00 | 5.36 | 0.00 |
time (sec) |
N/A | 0.167 | 0.135 | 1.651 | 0.285 | 0.237 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 70 | 54 | 64 | 54 | 50 | 0 | 234 | 0 |
N.S. |
1 | 1.01 | 0.78 | 0.93 | 0.78 | 0.72 | 0.00 | 3.39 | 0.00 |
time (sec) |
N/A | 0.170 | 0.194 | 0.571 | 0.302 | 0.233 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 98 | 59 | 78 | 68 | 55 | 0 | 278 | 0 |
N.S. |
1 | 1.11 | 0.67 | 0.89 | 0.77 | 0.62 | 0.00 | 3.16 | 0.00 |
time (sec) |
N/A | 0.183 | 0.165 | 1.365 | 0.281 | 0.235 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 126 | 66 | 93 | 82 | 60 | 0 | 326 | 0 |
N.S. |
1 | 1.10 | 0.57 | 0.81 | 0.71 | 0.52 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 0.216 | 0.268 | 0.574 | 0.278 | 0.219 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 180 | 155 | 395 | 0 | 410 | 0 | 215 | 900 |
N.S. |
1 | 1.07 | 0.92 | 2.34 | 0.00 | 2.43 | 0.00 | 1.27 | 5.33 |
time (sec) |
N/A | 0.271 | 0.559 | 1.666 | 0.000 | 0.296 | 0.000 | 0.311 | 41.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 133 | 110 | 251 | 0 | 308 | 0 | 150 | 508 |
N.S. |
1 | 1.05 | 0.87 | 1.98 | 0.00 | 2.43 | 0.00 | 1.18 | 4.00 |
time (sec) |
N/A | 0.245 | 0.351 | 0.576 | 0.000 | 0.254 | 0.000 | 0.300 | 16.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 75 | 148 | 0 | 232 | 0 | 95 | 259 |
N.S. |
1 | 1.00 | 1.00 | 1.97 | 0.00 | 3.09 | 0.00 | 1.27 | 3.45 |
time (sec) |
N/A | 0.184 | 0.208 | 1.658 | 0.000 | 0.242 | 0.000 | 0.293 | 4.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 76 | 0 | 178 | 0 | 50 | 45 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 0.00 | 4.24 | 0.00 | 1.19 | 1.07 |
time (sec) |
N/A | 0.155 | 0.007 | 0.580 | 0.000 | 0.235 | 0.000 | 0.301 | 1.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 73 | 0 | 187 | 0 | 85 | 121 |
N.S. |
1 | 1.00 | 1.00 | 1.74 | 0.00 | 4.45 | 0.00 | 2.02 | 2.88 |
time (sec) |
N/A | 0.156 | 0.106 | 1.379 | 0.000 | 0.243 | 0.000 | 0.306 | 2.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 78 | 149 | 0 | 250 | 0 | 388 | 443 |
N.S. |
1 | 1.00 | 1.00 | 1.91 | 0.00 | 3.21 | 0.00 | 4.97 | 5.68 |
time (sec) |
N/A | 0.185 | 0.193 | 0.587 | 0.000 | 0.277 | 0.000 | 0.311 | 6.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 114 | 258 | 0 | 332 | 0 | 951 | 900 |
N.S. |
1 | 1.04 | 0.83 | 1.88 | 0.00 | 2.42 | 0.00 | 6.94 | 6.57 |
time (sec) |
N/A | 0.239 | 0.321 | 1.655 | 0.000 | 0.338 | 0.000 | 0.587 | 20.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 210 | 162 | 408 | 0 | 436 | 0 | 1932 | 1518 |
N.S. |
1 | 1.06 | 0.82 | 2.06 | 0.00 | 2.20 | 0.00 | 9.76 | 7.67 |
time (sec) |
N/A | 0.302 | 0.488 | 0.580 | 0.000 | 0.507 | 0.000 | 2.177 | 87.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 188 | 194 | 673 | 0 | 630 | 0 | 305 | 0 |
N.S. |
1 | 1.07 | 1.11 | 3.85 | 0.00 | 3.60 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.287 | 0.427 | 1.669 | 0.000 | 0.333 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 115 | 134 | 439 | 0 | 468 | 0 | 193 | 0 |
N.S. |
1 | 1.03 | 1.20 | 3.92 | 0.00 | 4.18 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.221 | 0.261 | 0.581 | 0.000 | 0.275 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 77 | 251 | 0 | 335 | 0 | 108 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.26 | 0.00 | 4.35 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.180 | 0.162 | 1.673 | 0.000 | 0.265 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 47 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 1.57 | 0.87 |
time (sec) |
N/A | 0.141 | 0.006 | 0.584 | 0.000 | 0.237 | 0.000 | 0.289 | 1.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 77 | 243 | 0 | 346 | 0 | 140 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.16 | 0.00 | 4.49 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 0.183 | 0.158 | 2.344 | 0.000 | 0.313 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 133 | 126 | 441 | 0 | 492 | 0 | 476 | 0 |
N.S. |
1 | 1.07 | 1.02 | 3.56 | 0.00 | 3.97 | 0.00 | 3.84 | 0.00 |
time (sec) |
N/A | 0.244 | 0.294 | 1.680 | 0.000 | 0.414 | 0.000 | 0.676 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 207 | 186 | 683 | 0 | 664 | 0 | 1105 | 0 |
N.S. |
1 | 1.07 | 0.96 | 3.52 | 0.00 | 3.42 | 0.00 | 5.70 | 0.00 |
time (sec) |
N/A | 0.323 | 0.433 | 0.572 | 0.000 | 0.705 | 0.000 | 1.100 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 258 | 289 | 221 | 1287 | 0 | 1144 | 0 | 508 | 0 |
N.S. |
1 | 1.12 | 0.86 | 4.99 | 0.00 | 4.43 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.402 | 0.480 | 0.575 | 0.000 | 0.535 | 0.000 | 0.393 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 197 | 156 | 928 | 0 | 896 | 0 | 373 | 0 |
N.S. |
1 | 1.13 | 0.90 | 5.33 | 0.00 | 5.15 | 0.00 | 2.14 | 0.00 |
time (sec) |
N/A | 0.295 | 0.321 | 1.670 | 0.000 | 0.382 | 0.000 | 0.374 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 147 | 103 | 604 | 0 | 670 | 0 | 227 | 0 |
N.S. |
1 | 1.17 | 0.82 | 4.79 | 0.00 | 5.32 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.247 | 0.205 | 0.584 | 0.000 | 0.364 | 0.000 | 0.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 46 | 42 | 0 | 120 | 0 | 147 | 129 |
N.S. |
1 | 1.00 | 0.58 | 0.52 | 0.00 | 1.50 | 0.00 | 1.84 | 1.61 |
time (sec) |
N/A | 0.176 | 0.087 | 1.681 | 0.000 | 0.287 | 0.000 | 0.346 | 1.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 53 | 0 | 118 | 0 | 126 | 127 |
N.S. |
1 | 1.00 | 0.70 | 0.80 | 0.00 | 1.79 | 0.00 | 1.91 | 1.92 |
time (sec) |
N/A | 0.165 | 0.012 | 0.580 | 0.000 | 0.286 | 0.000 | 0.301 | 1.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 148 | 103 | 586 | 0 | 678 | 0 | 271 | 0 |
N.S. |
1 | 1.19 | 0.83 | 4.73 | 0.00 | 5.47 | 0.00 | 2.19 | 0.00 |
time (sec) |
N/A | 0.252 | 0.197 | 1.679 | 0.000 | 0.441 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 219 | 158 | 919 | 0 | 928 | 0 | 605 | 0 |
N.S. |
1 | 1.16 | 0.84 | 4.86 | 0.00 | 4.91 | 0.00 | 3.20 | 0.00 |
time (sec) |
N/A | 0.327 | 0.301 | 0.588 | 0.000 | 0.675 | 0.000 | 0.776 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 277 | 313 | 224 | 1288 | 0 | 1186 | 0 | 1234 | 0 |
N.S. |
1 | 1.13 | 0.81 | 4.65 | 0.00 | 4.28 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.435 | 0.474 | 0.586 | 0.000 | 1.571 | 0.000 | 1.084 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 18 | 24 | 23 | 24 | 35 | 17 |
N.S. |
1 | 1.00 | 1.10 | 0.86 | 1.14 | 1.10 | 1.14 | 1.67 | 0.81 |
time (sec) |
N/A | 0.136 | 0.012 | 1.672 | 0.192 | 0.221 | 0.587 | 0.290 | 1.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 76 | 79 | 47 | 110 | 83 | 55 | 92 |
N.S. |
1 | 1.00 | 1.81 | 1.88 | 1.12 | 2.62 | 1.98 | 1.31 | 2.19 |
time (sec) |
N/A | 0.160 | 0.116 | 0.597 | 0.198 | 0.235 | 12.782 | 0.303 | 2.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 88 | 114 | 0 | 180 | 0 | 0 | 260 |
N.S. |
1 | 1.00 | 1.63 | 2.11 | 0.00 | 3.33 | 0.00 | 0.00 | 4.81 |
time (sec) |
N/A | 0.179 | 0.373 | 1.732 | 0.000 | 0.237 | 0.000 | 0.000 | 3.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 251 | 260 | 961 | 0 | 788 | 0 | 411 | 0 |
N.S. |
1 | 0.93 | 0.96 | 3.55 | 0.00 | 2.91 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.333 | 10.482 | 1.668 | 0.000 | 0.408 | 0.000 | 0.473 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 228 | 194 | 692 | 0 | 600 | 0 | 325 | 0 |
N.S. |
1 | 0.93 | 0.79 | 2.81 | 0.00 | 2.44 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.300 | 10.327 | 0.622 | 0.000 | 0.328 | 0.000 | 0.447 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 170 | 142 | 455 | 0 | 434 | 0 | 250 | 0 |
N.S. |
1 | 0.99 | 0.83 | 2.66 | 0.00 | 2.54 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.241 | 0.712 | 0.587 | 0.000 | 0.293 | 0.000 | 0.388 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 86 | 0 | 0 | 311 | 0 | 204 | 0 |
N.S. |
1 | 1.04 | 0.88 | 0.00 | 0.00 | 3.17 | 0.00 | 2.08 | 0.00 |
time (sec) |
N/A | 0.192 | 0.036 | 0.000 | 0.000 | 0.280 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 129 | 431 | 306 | 0 | 956 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 3.62 | 2.57 | 0.00 | 8.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.230 | 3.673 | 0.619 | 0.000 | 0.497 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 91 | 298 | 0 | 341 | 0 | 904 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.76 | 0.00 | 3.16 | 0.00 | 8.37 | 0.00 |
time (sec) |
N/A | 0.200 | 10.066 | 0.586 | 0.000 | 0.302 | 0.000 | 0.867 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 159 | 130 | 464 | 0 | 474 | 0 | 1167 | 0 |
N.S. |
1 | 0.89 | 0.73 | 2.61 | 0.00 | 2.66 | 0.00 | 6.56 | 0.00 |
time (sec) |
N/A | 0.236 | 10.072 | 1.700 | 0.000 | 0.433 | 0.000 | 1.826 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 241 | 253 | 190 | 707 | 0 | 638 | 0 | 2310 | 0 |
N.S. |
1 | 1.05 | 0.79 | 2.93 | 0.00 | 2.65 | 0.00 | 9.59 | 0.00 |
time (sec) |
N/A | 0.359 | 10.115 | 0.585 | 0.000 | 1.015 | 0.000 | 4.912 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 346 | 292 | 307 | 1265 | 0 | 1008 | 0 | 533 | 0 |
N.S. |
1 | 0.84 | 0.89 | 3.66 | 0.00 | 2.91 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.357 | 0.895 | 0.588 | 0.000 | 0.508 | 0.000 | 0.587 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 306 | 269 | 228 | 961 | 0 | 790 | 0 | 431 | 0 |
N.S. |
1 | 0.88 | 0.75 | 3.14 | 0.00 | 2.58 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.338 | 0.652 | 1.693 | 0.000 | 0.411 | 0.000 | 0.521 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 214 | 211 | 160 | 689 | 0 | 594 | 0 | 340 | 0 |
N.S. |
1 | 0.99 | 0.75 | 3.22 | 0.00 | 2.78 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.268 | 0.474 | 0.583 | 0.000 | 0.329 | 0.000 | 0.472 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 138 | 143 | 124 | 0 | 0 | 439 | 0 | 287 | 0 |
N.S. |
1 | 1.04 | 0.90 | 0.00 | 0.00 | 3.18 | 0.00 | 2.08 | 0.00 |
time (sec) |
N/A | 0.217 | 0.034 | 0.000 | 0.000 | 0.293 | 0.000 | 0.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 181 | 146 | 492 | 0 | 1183 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.90 | 3.02 | 0.00 | 7.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 0.374 | 0.623 | 0.000 | 1.208 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 184 | 151 | 502 | 0 | 1234 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.93 | 3.08 | 0.00 | 7.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.358 | 0.589 | 0.000 | 1.009 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 152 | 130 | 507 | 0 | 481 | 0 | 1206 | 0 |
N.S. |
1 | 0.99 | 0.84 | 3.29 | 0.00 | 3.12 | 0.00 | 7.83 | 0.00 |
time (sec) |
N/A | 0.231 | 0.252 | 1.709 | 0.000 | 0.426 | 0.000 | 1.924 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 230 | 203 | 169 | 704 | 0 | 636 | 0 | 2324 | 0 |
N.S. |
1 | 0.88 | 0.73 | 3.06 | 0.00 | 2.77 | 0.00 | 10.10 | 0.00 |
time (sec) |
N/A | 0.267 | 0.484 | 0.592 | 0.000 | 1.017 | 0.000 | 5.065 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 318 | 346 | 241 | 982 | 0 | 836 | 0 | 3947 | 0 |
N.S. |
1 | 1.09 | 0.76 | 3.09 | 0.00 | 2.63 | 0.00 | 12.41 | 0.00 |
time (sec) |
N/A | 0.485 | 0.715 | 0.592 | 0.000 | 2.271 | 0.000 | 13.941 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 279 | 248 | 1369 | 0 | 1200 | 0 | 478 | 0 |
N.S. |
1 | 1.12 | 0.99 | 5.48 | 0.00 | 4.80 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.402 | 0.465 | 0.591 | 0.000 | 0.533 | 0.000 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 194 | 163 | 906 | 0 | 910 | 0 | 340 | 0 |
N.S. |
1 | 1.16 | 0.98 | 5.43 | 0.00 | 5.45 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.299 | 0.338 | 2.231 | 0.000 | 0.318 | 0.000 | 0.394 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 151 | 102 | 654 | 0 | 710 | 0 | 209 | 0 |
N.S. |
1 | 1.16 | 0.78 | 5.03 | 0.00 | 5.46 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.259 | 0.173 | 0.599 | 0.000 | 0.298 | 0.000 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 43 | 40 | 0 | 127 | 0 | 147 | 74 |
N.S. |
1 | 1.00 | 0.57 | 0.53 | 0.00 | 1.69 | 0.00 | 1.96 | 0.99 |
time (sec) |
N/A | 0.179 | 0.093 | 1.711 | 0.000 | 0.259 | 0.000 | 0.349 | 1.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 42 | 52 | 0 | 125 | 0 | 142 | 71 |
N.S. |
1 | 1.00 | 0.68 | 0.84 | 0.00 | 2.02 | 0.00 | 2.29 | 1.15 |
time (sec) |
N/A | 0.164 | 0.008 | 0.594 | 0.000 | 0.266 | 0.000 | 0.293 | 1.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 141 | 102 | 638 | 0 | 719 | 0 | 241 | 0 |
N.S. |
1 | 1.17 | 0.84 | 5.27 | 0.00 | 5.94 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 0.240 | 0.186 | 1.712 | 0.000 | 0.380 | 0.000 | 0.620 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 213 | 165 | 897 | 0 | 940 | 0 | 817 | 0 |
N.S. |
1 | 1.15 | 0.89 | 4.85 | 0.00 | 5.08 | 0.00 | 4.42 | 0.00 |
time (sec) |
N/A | 0.329 | 0.317 | 0.594 | 0.000 | 0.578 | 0.000 | 1.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 268 | 299 | 255 | 1372 | 0 | 1244 | 0 | 1204 | 0 |
N.S. |
1 | 1.12 | 0.95 | 5.12 | 0.00 | 4.64 | 0.00 | 4.49 | 0.00 |
time (sec) |
N/A | 0.436 | 0.464 | 0.601 | 0.000 | 1.582 | 0.000 | 3.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 392 | 320 | 2228 | 0 | 1960 | 0 | 982 | 0 |
N.S. |
1 | 1.12 | 0.91 | 6.35 | 0.00 | 5.58 | 0.00 | 2.80 | 0.00 |
time (sec) |
N/A | 0.548 | 0.574 | 1.718 | 0.000 | 1.083 | 0.000 | 0.521 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 289 | 234 | 1714 | 0 | 1628 | 0 | 756 | 0 |
N.S. |
1 | 1.15 | 0.93 | 6.83 | 0.00 | 6.49 | 0.00 | 3.01 | 0.00 |
time (sec) |
N/A | 0.412 | 0.387 | 0.594 | 0.000 | 0.582 | 0.000 | 0.498 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 186 | 150 | 1289 | 0 | 1326 | 0 | 490 | 0 |
N.S. |
1 | 1.13 | 0.91 | 7.81 | 0.00 | 8.04 | 0.00 | 2.97 | 0.00 |
time (sec) |
N/A | 0.293 | 0.261 | 1.719 | 0.000 | 0.583 | 0.000 | 0.438 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 162 | 71 | 83 | 0 | 275 | 0 | 395 | 139 |
N.S. |
1 | 1.07 | 0.47 | 0.55 | 0.00 | 1.82 | 0.00 | 2.62 | 0.92 |
time (sec) |
N/A | 0.279 | 0.131 | 0.595 | 0.000 | 0.480 | 0.000 | 0.383 | 1.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 83 | 87 | 0 | 281 | 0 | 393 | 143 |
N.S. |
1 | 1.04 | 0.70 | 0.74 | 0.00 | 2.38 | 0.00 | 3.33 | 1.21 |
time (sec) |
N/A | 0.201 | 0.107 | 1.729 | 0.000 | 0.467 | 0.000 | 0.386 | 1.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 110 | 78 | 95 | 0 | 273 | 0 | 373 | 132 |
N.S. |
1 | 1.12 | 0.80 | 0.97 | 0.00 | 2.79 | 0.00 | 3.81 | 1.35 |
time (sec) |
N/A | 0.188 | 0.013 | 0.579 | 0.000 | 0.430 | 0.000 | 0.341 | 1.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 215 | 150 | 1253 | 0 | 1336 | 0 | 520 | 0 |
N.S. |
1 | 1.19 | 0.83 | 6.96 | 0.00 | 7.42 | 0.00 | 2.89 | 0.00 |
time (sec) |
N/A | 0.323 | 0.254 | 1.723 | 0.000 | 0.834 | 0.000 | 0.697 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 264 | 308 | 235 | 1692 | 0 | 1658 | 0 | 1336 | 0 |
N.S. |
1 | 1.17 | 0.89 | 6.41 | 0.00 | 6.28 | 0.00 | 5.06 | 0.00 |
time (sec) |
N/A | 0.437 | 0.401 | 0.579 | 0.000 | 2.233 | 0.000 | 1.346 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 361 | 409 | 323 | 2216 | 0 | 2002 | 0 | 1482 | 0 |
N.S. |
1 | 1.13 | 0.89 | 6.14 | 0.00 | 5.55 | 0.00 | 4.11 | 0.00 |
time (sec) |
N/A | 0.555 | 0.539 | 1.725 | 0.000 | 4.881 | 0.000 | 4.986 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 497 | 409 | 391 | 1762 | 0 | 1338 | 0 | 1047 | 0 |
N.S. |
1 | 0.82 | 0.79 | 3.55 | 0.00 | 2.69 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.520 | 11.163 | 0.596 | 0.000 | 0.876 | 0.000 | 0.753 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 377 | 321 | 302 | 1366 | 0 | 1060 | 0 | 943 | 0 |
N.S. |
1 | 0.85 | 0.80 | 3.62 | 0.00 | 2.81 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.401 | 10.974 | 1.721 | 0.000 | 0.652 | 0.000 | 0.646 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 319 | 285 | 218 | 1002 | 0 | 804 | 0 | 848 | 0 |
N.S. |
1 | 0.89 | 0.68 | 3.14 | 0.00 | 2.52 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 0.385 | 10.515 | 0.595 | 0.000 | 0.493 | 0.000 | 0.571 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 206 | 122 | 750 | 0 | 619 | 0 | 840 | 0 |
N.S. |
1 | 0.93 | 0.55 | 3.38 | 0.00 | 2.79 | 0.00 | 3.78 | 0.00 |
time (sec) |
N/A | 0.267 | 10.093 | 1.697 | 0.000 | 0.407 | 0.000 | 0.518 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 136 | 119 | 0 | 0 | 475 | 0 | 650 | 0 |
N.S. |
1 | 1.06 | 0.93 | 0.00 | 0.00 | 3.71 | 0.00 | 5.08 | 0.00 |
time (sec) |
N/A | 0.211 | 0.004 | 0.000 | 0.000 | 0.344 | 0.000 | 0.480 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 181 | 456 | 566 | 0 | 1361 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 2.90 | 3.61 | 0.00 | 8.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.285 | 4.352 | 0.596 | 0.000 | 1.026 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 139 | 125 | 502 | 0 | 505 | 0 | 990 | 0 |
N.S. |
1 | 0.98 | 0.88 | 3.54 | 0.00 | 3.56 | 0.00 | 6.97 | 0.00 |
time (sec) |
N/A | 0.228 | 10.117 | 1.714 | 0.000 | 0.439 | 0.000 | 1.730 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 220 | 190 | 159 | 758 | 0 | 659 | 0 | 1694 | 0 |
N.S. |
1 | 0.86 | 0.72 | 3.45 | 0.00 | 3.00 | 0.00 | 7.70 | 0.00 |
time (sec) |
N/A | 0.261 | 10.204 | 0.602 | 0.000 | 0.946 | 0.000 | 1.511 | 0.000 |