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 | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 50 | 50 | 44 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.228 | 0.043 | 0.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 20 | 22 | 43 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.83 | 0.92 | 1.79 | 0.92 |
time (sec) |
N/A | 0.456 | 6.916 | 0.369 | 0.386 | 0.000 | 45.545 | 3.354 | 0.489 | 2.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 301 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 12.54 | 0.92 |
time (sec) |
N/A | 2.325 | 3.227 | 0.442 | 0.368 | 0.000 | 0.000 | 3.375 | 0.769 | 2.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 205 | 209 | 0 | 0 | 0 | 0 | 0 | 259 | 0 |
N.S. |
1 | 0.47 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.595 | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.516 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 148 | 153 | 0 | 0 | 0 | 0 | 0 | 172 | 0 |
N.S. |
1 | 0.50 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.460 | 0.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.109 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 104 | 114 | 0 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 0.59 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.392 | 0.139 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.517 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 46 | 46 | 41 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.229 | 0.031 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 27 | 22 | 55 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 1.12 | 0.92 | 2.29 | 0.92 |
time (sec) |
N/A | 0.222 | 5.038 | 0.246 | 0.330 | 0.000 | 14.538 | 1.861 | 0.322 | 2.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 70 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 2.92 | 0.92 |
time (sec) |
N/A | 0.226 | 5.307 | 0.332 | 0.334 | 0.000 | 0.000 | 1.886 | 0.336 | 2.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 433 | 241 | 411 | 0 | 0 | 0 | 0 | 0 | 306 | 0 |
N.S. |
1 | 0.56 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.854 | 0.908 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.562 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 183 | 239 | 0 | 0 | 0 | 0 | 0 | 204 | 0 |
N.S. |
1 | 0.64 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.737 | 0.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.983 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 148 | 127 | 0 | 0 | 0 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.87 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.659 | 0.273 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 46 | 46 | 41 | 0 | 59 | 0 | 0 | 50 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.84 | 0.00 | 1.20 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.311 | 0.030 | 0.072 | 0.000 | 0.178 | 0.000 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 61 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 2.54 | 0.92 |
time (sec) |
N/A | 0.865 | 4.420 | 0.256 | 0.335 | 0.000 | 0.000 | 0.180 | 0.494 | 2.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 84 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 3.50 | 0.92 |
time (sec) |
N/A | 0.878 | 5.121 | 0.322 | 0.328 | 0.000 | 0.000 | 0.191 | 0.577 | 2.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 251 | 317 | 0 | 0 | 0 | 0 | 0 | 216 | 0 |
N.S. |
1 | 0.76 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 2.582 | 0.448 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 182 | 141 | 0 | 0 | 0 | 0 | 0 | 111 | 0 |
N.S. |
1 | 0.91 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.621 | 0.256 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.484 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 48 | 48 | 41 | 0 | 59 | 0 | 0 | 50 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.80 | 0.00 | 1.16 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.228 | 0.029 | 0.098 | 0.000 | 0.103 | 0.000 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 61 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 2.54 | 0.92 |
time (sec) |
N/A | 0.560 | 4.384 | 0.242 | 0.333 | 0.000 | 0.000 | 0.187 | 0.512 | 2.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 84 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 3.50 | 0.92 |
time (sec) |
N/A | 0.590 | 4.041 | 0.311 | 0.337 | 0.000 | 0.000 | 0.196 | 0.562 | 2.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 343 | 265 | 302 | 415 | 333 | 0 | 0 | 481 | 0 |
N.S. |
1 | 1.02 | 0.79 | 0.90 | 1.23 | 0.99 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.944 | 0.221 | 0.151 | 0.035 | 0.118 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 322 | 216 | 246 | 385 | 250 | 0 | 316 | 398 | 0 |
N.S. |
1 | 1.03 | 0.69 | 0.79 | 1.23 | 0.80 | 0.00 | 1.01 | 1.28 | 0.00 |
time (sec) |
N/A | 1.392 | 0.136 | 0.144 | 0.038 | 0.116 | 0.000 | 0.131 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 236 | 154 | 168 | 257 | 179 | 0 | 214 | 268 | 0 |
N.S. |
1 | 1.07 | 0.70 | 0.76 | 1.16 | 0.81 | 0.00 | 0.97 | 1.21 | 0.00 |
time (sec) |
N/A | 1.124 | 0.099 | 0.142 | 0.048 | 0.100 | 0.000 | 0.127 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 167 | 103 | 106 | 154 | 121 | 0 | 134 | 162 | 0 |
N.S. |
1 | 1.14 | 0.70 | 0.72 | 1.05 | 0.82 | 0.00 | 0.91 | 1.10 | 0.00 |
time (sec) |
N/A | 0.471 | 0.083 | 0.138 | 0.039 | 0.097 | 0.000 | 0.125 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 90 | 60 | 56 | 74 | 71 | 0 | 70 | 80 | 0 |
N.S. |
1 | 1.07 | 0.71 | 0.67 | 0.88 | 0.85 | 0.00 | 0.83 | 0.95 | 0.00 |
time (sec) |
N/A | 0.275 | 0.041 | 0.074 | 0.027 | 0.087 | 0.000 | 0.119 | 0.184 | 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 | 481 | 481 | 375 | 222 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.200 | 0.235 | 10.978 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 774 | 774 | 687 | 790 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.581 | 1.410 | 9.651 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 609 | 609 | 453 | 632 | 684 | 586 | 0 | 0 | 442 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.04 | 1.12 | 0.96 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 2.904 | 0.392 | 0.522 | 0.063 | 0.102 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 359 | 299 | 402 | 429 | 380 | 0 | 0 | 283 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.12 | 1.19 | 1.06 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 1.715 | 0.281 | 0.323 | 0.048 | 0.095 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 174 | 203 | 218 | 209 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 1.04 | 1.21 | 1.30 | 1.24 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.894 | 0.160 | 0.273 | 0.042 | 0.095 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 55 | 84 | 78 | 72 | 96 | 0 | 111 | 50 | 0 |
N.S. |
1 | 1.08 | 1.65 | 1.53 | 1.41 | 1.88 | 0.00 | 2.18 | 0.98 | 0.00 |
time (sec) |
N/A | 0.389 | 0.041 | 0.123 | 0.027 | 0.089 | 0.000 | 0.214 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 763 | 763 | 623 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.848 | 0.425 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 388 | 388 | 254 | 380 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.044 | 0.393 | 0.662 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 180 | 125 | 178 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.29 | 0.90 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.564 | 0.168 | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 57 | 46 | 56 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.06 | 0.85 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.446 | 0.046 | 0.029 | 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 | 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 | 20 | 20 | 22 | 20 | 22 | 29 | 17 | 22 | 31 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.45 | 0.85 | 1.10 | 1.55 | 1.10 |
time (sec) |
N/A | 0.283 | 0.546 | 0.181 | 0.098 | 0.071 | 8.306 | 0.140 | 0.239 | 2.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 53 | 0 | 22 | 59 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.65 | 0.00 | 1.10 | 2.95 | 1.10 |
time (sec) |
N/A | 0.343 | 2.405 | 0.323 | 0.107 | 0.092 | 0.000 | 0.134 | 0.340 | 2.959 |
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 | 510 | 510 | 663 | 1102 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 1.30 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.654 | 2.342 | 0.572 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 338 | 465 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.984 | 0.917 | 0.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 86 | 80 | 125 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.96 | 0.89 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.748 | 0.268 | 0.047 | 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 | 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 | 20 | 20 | 22 | 20 | 816 | 57 | 19 | 22 | 64 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 40.80 | 2.85 | 0.95 | 1.10 | 3.20 | 1.10 |
time (sec) |
N/A | 0.209 | 16.586 | 0.197 | 1.110 | 0.097 | 81.031 | 0.138 | 0.240 | 2.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 1078 | 98 | 0 | 22 | 115 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 53.90 | 4.90 | 0.00 | 1.10 | 5.75 | 1.10 |
time (sec) |
N/A | 0.216 | 27.685 | 0.362 | 1.626 | 0.092 | 0.000 | 0.140 | 0.342 | 2.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.200 | 6.075 | 0.818 | 0.000 | 0.086 | 1.598 | 0.163 | 200.027 | 3.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.202 | 2.686 | 0.704 | 0.000 | 0.094 | 0.983 | 0.136 | 51.229 | 3.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 556 | 0 | 0 | 332 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 5.50 | 0.00 | 0.00 | 3.29 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.417 | 13.231 | 0.000 | 0.000 | 0.117 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 176 | 633 | 0 | 0 | 724 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.98 | 3.52 | 0.00 | 0.00 | 4.02 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.393 | 1.791 | 0.000 | 0.000 | 0.150 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 270 | 685 | 0 | 0 | 1360 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.02 | 2.59 | 0.00 | 0.00 | 5.15 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.169 | 2.825 | 0.000 | 0.000 | 0.215 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 22 | 22 | 24 | 20 | 0 | 34 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.355 | 14.129 | 0.372 | 0.000 | 0.095 | 1.638 | 0.250 | 200.026 | 3.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 22 | 22 | 24 | 20 | 0 | 34 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.367 | 7.650 | 0.288 | 0.000 | 0.093 | 1.069 | 0.181 | 54.741 | 3.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 22 | 22 | 24 | 20 | 0 | 54 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.45 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.348 | 12.948 | 0.776 | 0.000 | 0.090 | 7.239 | 0.173 | 200.029 | 3.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 107 | 65 | 0 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 4.86 | 2.95 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.286 | 26.175 | 0.565 | 0.576 | 0.099 | 0.000 | 0.183 | 200.031 | 3.418 |
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 | 22 | 22 | 24 | 20 | 22 | 22 | 19 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.287 | 0.878 | 0.589 | 0.113 | 0.094 | 0.479 | 0.141 | 126.835 | 3.006 |
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 | 22 | 22 | 24 | 20 | 22 | 39 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.77 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.293 | 0.758 | 0.524 | 0.096 | 0.082 | 0.746 | 0.150 | 65.950 | 3.209 |
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 | 22 | 22 | 24 | 20 | 22 | 63 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.86 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.338 | 1.277 | 0.711 | 0.118 | 0.081 | 3.126 | 0.150 | 197.558 | 3.183 |
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 | 22 | 22 | 24 | 20 | 22 | 87 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 3.95 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.328 | 2.592 | 0.707 | 0.126 | 0.075 | 35.462 | 0.155 | 200.027 | 3.099 |
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 | 22 | 22 | 24 | 20 | 596 | 36 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 27.09 | 1.64 | 0.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.218 | 10.051 | 0.615 | 0.602 | 0.099 | 0.873 | 0.144 | 192.204 | 3.359 |
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 | 22 | 22 | 24 | 20 | 580 | 67 | 22 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 26.36 | 3.05 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.241 | 10.483 | 0.500 | 1.041 | 0.082 | 2.106 | 0.151 | 73.057 | 3.338 |
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 | 22 | 22 | 24 | 20 | 857 | 108 | 22 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 38.95 | 4.91 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.230 | 15.472 | 0.681 | 2.075 | 0.106 | 15.209 | 0.166 | 200.032 | 3.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 1117 | 149 | 0 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 50.77 | 6.77 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.218 | 23.525 | 0.683 | 2.817 | 0.096 | 0.000 | 0.179 | 200.029 | 3.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 672 | 672 | 536 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.722 | 4.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.923 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 322 | 317 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.681 | 1.776 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.528 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 104 | 100 | 0 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.02 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.229 | 0.088 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 0 | 19 | 22 | 21 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 0.86 | 1.00 | 0.95 | 1.00 |
time (sec) |
N/A | 0.366 | 1.917 | 0.234 | 0.000 | 0.000 | 1.542 | 9.832 | 0.664 | 3.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 20 | 22 | 32 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.45 | 1.00 |
time (sec) |
N/A | 0.370 | 17.686 | 0.383 | 0.388 | 0.000 | 39.669 | 9.858 | 1.778 | 3.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 442 | 442 | 812 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.00 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 2.144 | 1.879 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.997 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 151 | 269 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.08 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.893 | 0.158 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.432 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 0 | 19 | 22 | 51 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 0.00 | 0.86 | 1.00 | 2.32 | 1.00 |
time (sec) |
N/A | 0.233 | 0.476 | 0.230 | 0.000 | 0.000 | 33.013 | 14.542 | 1.608 | 3.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 0 | 22 | 73 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.00 | 1.00 | 3.32 | 1.00 |
time (sec) |
N/A | 0.243 | 11.458 | 0.404 | 0.500 | 0.000 | 0.000 | 14.416 | 5.221 | 3.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 608 | 608 | 530 | 0 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.433 | 0.777 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.697 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 213 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.097 | 0.415 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 96 | 100 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.575 | 0.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 20 | 22 | 41 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.86 | 1.00 |
time (sec) |
N/A | 0.374 | 0.187 | 0.247 | 0.339 | 0.000 | 4.817 | 10.067 | 0.642 | 3.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 0 | 22 | 69 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.00 | 1.00 | 3.14 | 1.00 |
time (sec) |
N/A | 0.365 | 0.231 | 0.369 | 0.360 | 0.000 | 0.000 | 10.005 | 1.706 | 3.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 358 | 358 | 268 | 0 | 0 | 0 | 0 | 0 | 1233 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.44 | 0.00 |
time (sec) |
N/A | 1.231 | 1.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.479 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 0 | 842 | 0 |
N.S. |
1 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.02 | 0.00 |
time (sec) |
N/A | 0.799 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.747 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 20 | 22 | 74 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 3.36 | 1.00 |
time (sec) |
N/A | 0.238 | 0.195 | 0.240 | 0.386 | 0.000 | 36.155 | 0.210 | 0.642 | 4.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 0 | 22 | 14432 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.00 | 1.00 | 656.00 | 1.00 |
time (sec) |
N/A | 0.234 | 0.246 | 0.386 | 0.402 | 0.000 | 0.000 | 0.237 | 57.292 | 4.215 |