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 | C | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 84 | 82 | 37 | 0 | 53 | 44 | 0 | 0 |
N.S. |
1 | 0.98 | 0.95 | 0.43 | 0.00 | 0.62 | 0.51 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.042 | 0.608 | 0.000 | 0.087 | 0.604 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 69 | 50 | 23 | 48 | 49 | 61 | 49 | 0 |
N.S. |
1 | 1.10 | 0.79 | 0.37 | 0.76 | 0.78 | 0.97 | 0.78 | 0.00 |
time (sec) |
N/A | 0.462 | 0.027 | 0.303 | 0.187 | 0.249 | 0.711 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 51 | 41 | 43 | 39 | 39 | 46 | 38 | 0 |
N.S. |
1 | 1.04 | 0.84 | 0.88 | 0.80 | 0.80 | 0.94 | 0.78 | 0.00 |
time (sec) |
N/A | 0.366 | 0.022 | 0.302 | 0.210 | 0.253 | 0.842 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 29 | 29 | 30 | 29 | 29 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.86 | 0.83 | 0.83 | 0.00 |
time (sec) |
N/A | 0.269 | 0.008 | 0.297 | 0.212 | 0.257 | 0.480 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 16 | 16 | 12 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.07 | 1.07 | 0.80 | 1.00 | 0.00 |
time (sec) |
N/A | 0.165 | 0.004 | 0.201 | 0.185 | 0.249 | 0.479 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 20 | 0 | 0 | 22 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.47 | 0.00 | 0.00 | 0.51 | 0.00 | 0.00 |
time (sec) |
N/A | 0.195 | 0.005 | 0.368 | 0.000 | 0.000 | 0.370 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 30 | 26 | 24 | 36 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.04 | 0.96 | 1.44 | 1.48 | 0.00 |
time (sec) |
N/A | 0.301 | 0.009 | 0.342 | 0.250 | 0.254 | 0.564 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 46 | 47 | 32 | 31 | 41 | 149 | 0 |
N.S. |
1 | 1.09 | 1.00 | 1.02 | 0.70 | 0.67 | 0.89 | 3.24 | 0.00 |
time (sec) |
N/A | 0.382 | 0.011 | 0.311 | 0.253 | 0.255 | 0.522 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.192 | 1.923 | 0.214 | 0.224 | 0.254 | 1.266 | 0.279 | 4.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 232 | 107 | 154 | 0 | 105 | 0 | 117 | 0 |
N.S. |
1 | 1.56 | 0.72 | 1.03 | 0.00 | 0.70 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 1.411 | 0.093 | 0.556 | 0.000 | 0.262 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 158 | 78 | 84 | 0 | 81 | 0 | 150 | 0 |
N.S. |
1 | 1.41 | 0.70 | 0.75 | 0.00 | 0.72 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.954 | 0.052 | 0.582 | 0.000 | 0.271 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 58 | 62 | 0 | 56 | 0 | 65 | 0 |
N.S. |
1 | 1.07 | 0.78 | 0.84 | 0.00 | 0.76 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.526 | 0.039 | 0.484 | 0.000 | 0.256 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 37 | 32 | 32 | 0 | 31 | 0 | 49 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.00 | 0.00 | 0.97 | 0.00 | 1.53 | 0.00 |
time (sec) |
N/A | 0.348 | 0.010 | 0.416 | 0.000 | 0.264 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.190 | 0.318 | 0.096 | 0.217 | 0.259 | 0.968 | 0.282 | 4.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.193 | 0.344 | 0.148 | 0.215 | 0.259 | 0.965 | 0.274 | 4.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | C | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 74 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 7.40 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.193 | 0.363 | 0.149 | 0.211 | 0.256 | 0.950 | 0.279 | 5.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.499 | 2.636 | 0.285 | 0.201 | 0.269 | 0.609 | 0.273 | 5.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 164 | 96 | 156 | 123 | 92 | 0 | 338 | 0 |
N.S. |
1 | 0.89 | 0.52 | 0.85 | 0.67 | 0.50 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.640 | 0.156 | 0.446 | 0.250 | 0.262 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 109 | 63 | 99 | 91 | 64 | 0 | 252 | 0 |
N.S. |
1 | 0.92 | 0.53 | 0.84 | 0.77 | 0.54 | 0.00 | 2.14 | 0.00 |
time (sec) |
N/A | 0.524 | 0.104 | 0.429 | 0.267 | 0.278 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 66 | 50 | 57 | 68 | 48 | 0 | 191 | 0 |
N.S. |
1 | 0.93 | 0.70 | 0.80 | 0.96 | 0.68 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.439 | 0.072 | 0.410 | 0.236 | 0.244 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 41 | 24 | 23 | 23 | 0 | 303 | 0 |
N.S. |
1 | 1.00 | 1.58 | 0.92 | 0.88 | 0.88 | 0.00 | 11.65 | 0.00 |
time (sec) |
N/A | 0.183 | 0.028 | 0.415 | 0.189 | 0.260 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.193 | 0.388 | 0.243 | 0.371 | 0.255 | 0.320 | 0.282 | 5.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 39 | 46 | 0 | 39 | 0 | 181 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.00 | 0.85 | 0.00 | 3.93 | 0.00 |
time (sec) |
N/A | 0.458 | 0.073 | 0.424 | 0.000 | 0.274 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 92 | 84 | 83 | 0 | 96 | 0 | 809 | 0 |
N.S. |
1 | 0.83 | 0.76 | 0.75 | 0.00 | 0.86 | 0.00 | 7.29 | 0.00 |
time (sec) |
N/A | 0.581 | 0.235 | 0.410 | 0.000 | 0.279 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.212 | 5.468 | 0.249 | 0.245 | 0.270 | 1.143 | 0.335 | 5.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 329 | 435 | 158 | 0 | 0 | 151 | 0 | 0 | 0 |
N.S. |
1 | 1.32 | 0.48 | 0.00 | 0.00 | 0.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.656 | 1.254 | 0.000 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 187 | 95 | 111 | 0 | 100 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.62 | 0.72 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.636 | 0.332 | 0.855 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 54 | 43 | 45 | 0 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.88 | 0.92 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.408 | 0.009 | 0.428 | 0.000 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.204 | 2.244 | 0.105 | 0.226 | 0.245 | 0.358 | 0.308 | 4.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.209 | 3.672 | 0.180 | 0.218 | 0.246 | 0.292 | 0.353 | 4.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.212 | 1.652 | 0.183 | 0.224 | 0.256 | 0.337 | 0.351 | 4.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 137 | 156 | 106 | 0 | 0 | 140 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.77 | 0.00 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.609 | 1.197 | 0.000 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 137 | 156 | 106 | 0 | 0 | 140 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.77 | 0.00 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.576 | 1.115 | 0.000 | 0.000 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 145 | 102 | 0 | 0 | 127 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.80 | 0.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.546 | 1.095 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 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 | 54 | 53 | 95 | 54 | 49 | 57 | 0 | 59 | 0 |
N.S. |
1 | 0.98 | 1.76 | 1.00 | 0.91 | 1.06 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.280 | 0.060 | 1.025 | 0.189 | 0.259 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 131 | 147 | 107 | 0 | 0 | 142 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.82 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.592 | 1.144 | 0.000 | 0.000 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 139 | 158 | 111 | 0 | 0 | 147 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.80 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.578 | 1.149 | 0.000 | 0.000 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 176 | 244 | 128 | 0 | 0 | 180 | 0 | 0 | 0 |
N.S. |
1 | 1.39 | 0.73 | 0.00 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.661 | 2.057 | 0.000 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 96 | 128 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
N.S. |
1 | 1.33 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.055 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.518 | 0.590 | 0.178 | 0.252 | 0.259 | 1.243 | 0.285 | 4.992 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.00 | 0.00 |
time (sec) |
N/A | 0.185 | 0.011 | 0.247 | 0.189 | 0.253 | 0.222 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 23 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.88 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.298 | 0.015 | 0.322 | 0.000 | 0.247 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 44 | 45 | 0 | 43 | 0 | 55 | 0 |
N.S. |
1 | 1.08 | 0.72 | 0.74 | 0.00 | 0.70 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.467 | 0.062 | 0.659 | 0.000 | 0.272 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 140 | 64 | 69 | 0 | 67 | 0 | 138 | 0 |
N.S. |
1 | 1.54 | 0.70 | 0.76 | 0.00 | 0.74 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.845 | 0.078 | 0.825 | 0.000 | 0.277 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 214 | 93 | 138 | 0 | 92 | 0 | 106 | 0 |
N.S. |
1 | 1.70 | 0.74 | 1.10 | 0.00 | 0.73 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 1.238 | 0.128 | 1.039 | 0.000 | 0.266 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 1.003 | 0.593 | 0.191 | 0.291 | 0.250 | 1.796 | 0.274 | 5.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 44 | 48 | 0 | 0 | 0 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.511 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.193 | 0.686 | 0.208 | 0.287 | 0.256 | 1.380 | 0.274 | 4.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 28 | 0 | 25 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.82 | 0.00 | 0.74 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.277 | 0.016 | 0.595 | 0.000 | 0.243 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 71 | 42 | 44 | 0 | 43 | 0 | 124 | 0 |
N.S. |
1 | 1.16 | 0.69 | 0.72 | 0.00 | 0.70 | 0.00 | 2.03 | 0.00 |
time (sec) |
N/A | 0.460 | 0.037 | 0.834 | 0.000 | 0.247 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 129 | 72 | 89 | 0 | 73 | 0 | 82 | 0 |
N.S. |
1 | 1.32 | 0.73 | 0.91 | 0.00 | 0.74 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.731 | 0.071 | 1.006 | 0.000 | 0.272 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 234 | 94 | 111 | 0 | 92 | 0 | 180 | 0 |
N.S. |
1 | 1.83 | 0.73 | 0.87 | 0.00 | 0.72 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 1.376 | 0.078 | 1.680 | 0.000 | 0.265 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 34 | 25 | 24 | 0 | 41 | 0 | 23 | 0 |
N.S. |
1 | 1.17 | 0.86 | 0.83 | 0.00 | 1.41 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.269 | 0.023 | 1.220 | 0.000 | 0.265 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 34 | 25 | 24 | 0 | 42 | 0 | 23 | 0 |
N.S. |
1 | 1.17 | 0.86 | 0.83 | 0.00 | 1.45 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.275 | 0.022 | 1.367 | 0.000 | 0.263 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 212 | 123 | 175 | 0 | 114 | 0 | 398 | 0 |
N.S. |
1 | 1.13 | 0.66 | 0.94 | 0.00 | 0.61 | 0.00 | 2.13 | 0.00 |
time (sec) |
N/A | 1.843 | 0.247 | 2.506 | 0.000 | 0.260 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 105 | 71 | 82 | 0 | 72 | 0 | 507 | 0 |
N.S. |
1 | 1.08 | 0.73 | 0.85 | 0.00 | 0.74 | 0.00 | 5.23 | 0.00 |
time (sec) |
N/A | 0.930 | 0.175 | 1.578 | 0.000 | 0.261 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 33 | 31 | 0 | 31 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.91 | 0.00 | 0.91 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.327 | 0.014 | 0.673 | 0.000 | 0.251 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.279 | 2.287 | 0.267 | 0.298 | 0.247 | 1.056 | 0.295 | 8.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 239 | 134 | 212 | 0 | 125 | 0 | 431 | 0 |
N.S. |
1 | 1.10 | 0.61 | 0.97 | 0.00 | 0.57 | 0.00 | 1.98 | 0.00 |
time (sec) |
N/A | 2.003 | 0.240 | 4.360 | 0.000 | 0.262 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 115 | 74 | 95 | 0 | 77 | 0 | 528 | 0 |
N.S. |
1 | 1.06 | 0.69 | 0.88 | 0.00 | 0.71 | 0.00 | 4.89 | 0.00 |
time (sec) |
N/A | 0.894 | 0.137 | 2.391 | 0.000 | 0.267 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 38 | 0 | 37 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.83 | 0.00 | 0.80 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.325 | 0.017 | 1.211 | 0.000 | 0.258 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.291 | 1.733 | 0.240 | 0.379 | 0.246 | 1.031 | 0.302 | 6.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 371 | 377 | 407 | 1246 | 0 | 432 | 0 | 200182 | 0 |
N.S. |
1 | 1.02 | 1.10 | 3.36 | 0.00 | 1.16 | 0.00 | 539.57 | 0.00 |
time (sec) |
N/A | 1.546 | 3.592 | 2.880 | 0.000 | 0.289 | 0.000 | 4.926 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 160 | 168 | 274 | 0 | 146 | 0 | 9541 | 0 |
N.S. |
1 | 1.04 | 1.09 | 1.78 | 0.00 | 0.95 | 0.00 | 61.95 | 0.00 |
time (sec) |
N/A | 0.497 | 1.013 | 1.811 | 0.000 | 0.262 | 0.000 | 0.586 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.289 | 13.372 | 0.352 | 0.382 | 0.248 | 0.746 | 0.301 | 6.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 370 | 378 | 389 | 1240 | 0 | 429 | 0 | 206132 | 0 |
N.S. |
1 | 1.02 | 1.05 | 3.35 | 0.00 | 1.16 | 0.00 | 557.11 | 0.00 |
time (sec) |
N/A | 1.737 | 3.278 | 4.055 | 0.000 | 0.277 | 0.000 | 5.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 160 | 164 | 272 | 0 | 147 | 0 | 9214 | 0 |
N.S. |
1 | 1.05 | 1.07 | 1.78 | 0.00 | 0.96 | 0.00 | 60.22 | 0.00 |
time (sec) |
N/A | 0.503 | 1.033 | 2.288 | 0.000 | 0.268 | 0.000 | 0.559 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.276 | 7.838 | 0.382 | 0.385 | 0.251 | 0.845 | 0.289 | 6.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 88 | 78 | 124 | 0 | 109 | 700 | 0 | 0 |
N.S. |
1 | 0.98 | 0.87 | 1.38 | 0.00 | 1.21 | 7.78 | 0.00 | 0.00 |
time (sec) |
N/A | 0.340 | 0.055 | 0.674 | 0.000 | 0.094 | 1.010 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 70 | 53 | 54 | 94 | 59 | 85 | 0 | 0 |
N.S. |
1 | 1.11 | 0.84 | 0.86 | 1.49 | 0.94 | 1.35 | 0.00 | 0.00 |
time (sec) |
N/A | 0.469 | 0.029 | 0.357 | 0.286 | 0.259 | 1.517 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 53 | 44 | 42 | 49 | 54 | 70 | 0 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.86 | 1.00 | 1.10 | 1.43 | 0.00 | 0.00 |
time (sec) |
N/A | 0.369 | 0.020 | 0.373 | 0.206 | 0.253 | 1.226 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 36 | 35 | 28 | 70 | 51 | 53 | 0 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.80 | 2.00 | 1.46 | 1.51 | 0.00 | 0.00 |
time (sec) |
N/A | 0.279 | 0.007 | 0.362 | 0.289 | 0.256 | 0.876 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 27 | 28 | 31 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.69 | 1.75 | 1.94 | 0.00 | 0.00 |
time (sec) |
N/A | 0.168 | 0.004 | 0.238 | 0.200 | 0.246 | 0.817 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 94 | 158 | 0 | 0 | 44 | 0 | 0 |
N.S. |
1 | 1.00 | 1.54 | 2.59 | 0.00 | 0.00 | 0.72 | 0.00 | 0.00 |
time (sec) |
N/A | 0.201 | 0.024 | 0.447 | 0.000 | 0.000 | 0.581 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 32 | 34 | 25 | 42 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.23 | 1.31 | 0.96 | 1.62 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.009 | 0.364 | 0.290 | 0.251 | 0.624 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 49 | 46 | 47 | 61 | 42 | 87 | 0 | 0 |
N.S. |
1 | 1.07 | 1.00 | 1.02 | 1.33 | 0.91 | 1.89 | 0.00 | 0.00 |
time (sec) |
N/A | 0.388 | 0.011 | 0.360 | 0.347 | 0.263 | 1.484 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.195 | 1.938 | 0.224 | 0.230 | 0.256 | 3.591 | 0.265 | 4.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 232 | 108 | 135 | 0 | 118 | 0 | 0 | 0 |
N.S. |
1 | 1.42 | 0.66 | 0.83 | 0.00 | 0.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.372 | 0.085 | 0.565 | 0.000 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 156 | 78 | 84 | 0 | 111 | 0 | 0 | 0 |
N.S. |
1 | 1.39 | 0.70 | 0.75 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.945 | 0.065 | 0.621 | 0.000 | 0.250 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 79 | 58 | 62 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.77 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.525 | 0.034 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 36 | 31 | 30 | 0 | 59 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.00 | 0.97 | 0.00 | 1.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.348 | 0.011 | 0.487 | 0.000 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.184 | 0.309 | 0.099 | 0.255 | 0.250 | 3.382 | 0.265 | 4.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.191 | 0.334 | 0.158 | 0.239 | 0.254 | 3.371 | 0.268 | 4.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.188 | 0.365 | 0.131 | 0.216 | 0.253 | 3.461 | 0.284 | 4.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.499 | 2.189 | 0.270 | 0.214 | 0.258 | 0.613 | 0.274 | 5.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 164 | 95 | 153 | 502 | 176 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.52 | 0.83 | 2.73 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.627 | 0.161 | 0.435 | 1.101 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 108 | 64 | 98 | 423 | 148 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.54 | 0.83 | 3.58 | 1.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.530 | 0.112 | 0.482 | 0.833 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 66 | 49 | 56 | 311 | 104 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.69 | 0.79 | 4.38 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.446 | 0.080 | 0.468 | 0.739 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 42 | 26 | 44 | 47 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.96 | 1.63 | 1.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.183 | 0.026 | 0.424 | 0.202 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.190 | 0.388 | 0.258 | 0.752 | 0.261 | 0.336 | 0.274 | 5.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 40 | 47 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.445 | 0.053 | 0.437 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 92 | 76 | 85 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.68 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.562 | 0.283 | 0.444 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.208 | 5.622 | 0.246 | 0.222 | 0.271 | 1.187 | 0.269 | 4.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 329 | 435 | 159 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.32 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.596 | 0.884 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 188 | 96 | 113 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.62 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.699 | 0.250 | 0.901 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 53 | 41 | 43 | 0 | 88 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.85 | 0.90 | 0.00 | 1.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.406 | 0.009 | 0.429 | 0.000 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.204 | 0.797 | 0.095 | 0.218 | 0.253 | 0.373 | 0.273 | 4.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.212 | 1.391 | 0.176 | 0.224 | 0.255 | 0.293 | 0.263 | 4.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.210 | 1.762 | 0.182 | 0.233 | 0.256 | 0.355 | 0.270 | 4.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 133 | 152 | 102 | 0 | 0 | 448 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.77 | 0.00 | 0.00 | 3.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.611 | 1.195 | 0.000 | 0.000 | 0.270 | 0.000 | 0.000 | 0.000 |