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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 51 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.007 | 0.000 | 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 | 23 | 23 | 25 | 23 | 25 | 25 | 19 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.83 | 1.09 | 1.09 |
time (sec) |
N/A | 0.181 | 0.067 | 0.026 | 0.213 | 0.246 | 1.450 | 0.294 | 0.465 |
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 | 23 | 23 | 25 | 23 | 25 | 42 | 20 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.83 | 0.87 | 1.09 | 1.09 |
time (sec) |
N/A | 0.267 | 0.035 | 0.029 | 0.214 | 0.251 | 2.910 | 0.301 | 0.489 |
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 | 23 | 23 | 25 | 23 | 25 | 59 | 20 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.57 | 0.87 | 1.09 | 1.09 |
time (sec) |
N/A | 0.352 | 0.037 | 0.027 | 0.213 | 0.265 | 6.926 | 0.432 | 0.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 0 | 0 | 0 | 15 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 |
time (sec) |
N/A | 0.212 | 0.004 | 0.000 | 0.000 | 0.000 | 1.004 | 0.000 | 0.000 |
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 | 33 | 35 | 33 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 0.004 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.000 | 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 | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 280 | 196 | 269 | 0 | 247 | 250 | 0 | 0 |
N.S. |
1 | 1.29 | 0.90 | 1.24 | 0.00 | 1.14 | 1.15 | 0.00 | 0.00 |
time (sec) |
N/A | 0.574 | 0.397 | 30.191 | 0.000 | 0.277 | 72.227 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 240 | 168 | 228 | 0 | 207 | 206 | 0 | 0 |
N.S. |
1 | 1.30 | 0.91 | 1.23 | 0.00 | 1.12 | 1.11 | 0.00 | 0.00 |
time (sec) |
N/A | 0.510 | 0.252 | 12.649 | 0.000 | 0.287 | 22.171 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 129 | 113 | 169 | 0 | 137 | 136 | 0 | 0 |
N.S. |
1 | 1.22 | 1.07 | 1.59 | 0.00 | 1.29 | 1.28 | 0.00 | 0.00 |
time (sec) |
N/A | 0.432 | 0.071 | 4.876 | 0.000 | 0.271 | 6.034 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 0 | 0 | 0 | 26 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.005 | 0.000 | 0.000 | 0.000 | 6.946 | 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 | 142 | 166 | 115 | 204 | 0 | 134 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.81 | 1.44 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.135 | 4.753 | 0.000 | 0.253 | 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 | 202 | 245 | 163 | 268 | 0 | 190 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.81 | 1.33 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.535 | 0.151 | 4.711 | 0.000 | 0.265 | 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 | 253 | 402 | 0 | 0 | 0 | 296 | 0 | 0 | 0 |
N.S. |
1 | 1.59 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.076 | 0.000 | 0.000 | 0.000 | 0.295 | 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 | 221 | 352 | 0 | 0 | 0 | 257 | 0 | 0 | 0 |
N.S. |
1 | 1.59 | 0.00 | 0.00 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.950 | 0.000 | 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 | 131 | 189 | 0 | 0 | 0 | 172 | 0 | 0 | 0 |
N.S. |
1 | 1.44 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.728 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 0 | 0 | 0 | 26 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.006 | 0.000 | 0.000 | 0.000 | 3.781 | 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 | 174 | 237 | 0 | 0 | 0 | 156 | 0 | 0 | 0 |
N.S. |
1 | 1.36 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.765 | 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 | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 238 | 349 | 0 | 0 | 0 | 221 | 0 | 0 | 0 |
N.S. |
1 | 1.47 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.001 | 0.000 | 0.000 | 0.000 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 266 | 844 | 172 | 43 | 0 | 28 | 28 |
N.S. |
1 | 1.00 | 10.23 | 32.46 | 6.62 | 1.65 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.192 | 0.296 | 146.060 | 0.320 | 0.285 | 0.000 | 1.119 | 1.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | B | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 867 | 302 | 35 | 0 | 24 | 25 |
N.S. |
1 | 1.00 | 1.09 | 37.70 | 13.13 | 1.52 | 0.00 | 1.04 | 1.09 |
time (sec) |
N/A | 0.435 | 0.096 | 0.089 | 0.292 | 0.316 | 0.000 | 0.336 | 0.606 |
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 | 23 | 23 | 25 | 1065 | 427 | 31 | 22 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 46.30 | 18.57 | 1.35 | 0.96 | 1.09 | 1.09 |
time (sec) |
N/A | 0.966 | 0.059 | 2.004 | 0.323 | 0.355 | 11.254 | 0.317 | 0.590 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 23 | 32 | 22 | 32 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.85 | 1.19 | 0.81 | 1.19 | 0.85 |
time (sec) |
N/A | 0.215 | 0.003 | 0.317 | 0.182 | 0.264 | 0.324 | 0.314 | 0.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 23 | 32 | 22 | 32 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.85 | 1.19 | 0.81 | 1.19 | 0.85 |
time (sec) |
N/A | 0.196 | 0.002 | 0.086 | 0.184 | 0.279 | 0.202 | 0.355 | 0.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 21 | 15 | 21 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.17 | 0.83 | 1.17 | 0.94 |
time (sec) |
N/A | 0.183 | 0.002 | 0.066 | 0.186 | 0.294 | 0.121 | 0.355 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 20 | 19 | 37 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.86 | 1.68 | 0.91 | 0.91 |
time (sec) |
N/A | 0.204 | 0.002 | 0.112 | 0.176 | 0.273 | 0.553 | 0.322 | 0.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 23 | 20 | 17 | 25 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 1.00 | 0.87 | 0.74 | 1.09 | 0.83 |
time (sec) |
N/A | 0.206 | 0.002 | 0.094 | 0.175 | 0.296 | 0.202 | 0.407 | 0.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 22 | 23 | 24 | 24 | 28 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.85 | 0.89 | 0.89 | 1.04 | 0.85 |
time (sec) |
N/A | 0.205 | 0.002 | 0.155 | 0.181 | 0.274 | 0.395 | 0.300 | 0.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 22 | 23 | 24 | 24 | 28 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.85 | 0.89 | 0.89 | 1.04 | 0.85 |
time (sec) |
N/A | 0.203 | 0.002 | 0.298 | 0.189 | 0.285 | 0.642 | 0.300 | 0.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 53 | 52 | 47 | 46 | 113 | 49 | 115 | 46 |
N.S. |
1 | 1.02 | 1.00 | 0.90 | 0.88 | 2.17 | 0.94 | 2.21 | 0.88 |
time (sec) |
N/A | 0.270 | 0.004 | 0.290 | 0.175 | 0.296 | 0.575 | 0.294 | 0.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 43 | 47 | 46 | 113 | 46 | 112 | 46 |
N.S. |
1 | 0.98 | 0.83 | 0.90 | 0.88 | 2.17 | 0.88 | 2.15 | 0.88 |
time (sec) |
N/A | 0.249 | 0.005 | 0.157 | 0.177 | 0.293 | 0.334 | 0.324 | 0.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 37 | 37 | 40 | 39 | 90 | 39 | 92 | 39 |
N.S. |
1 | 0.95 | 0.95 | 1.03 | 1.00 | 2.31 | 1.00 | 2.36 | 1.00 |
time (sec) |
N/A | 0.224 | 0.003 | 0.090 | 0.183 | 0.292 | 0.189 | 0.301 | 0.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 20 | 54 | 41 | 59 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 2.45 | 1.86 | 2.68 | 0.91 |
time (sec) |
N/A | 0.217 | 0.002 | 0.106 | 0.182 | 0.285 | 0.528 | 0.290 | 0.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 45 | 40 | 41 | 46 | 81 | 41 | 90 | 40 |
N.S. |
1 | 0.98 | 0.87 | 0.89 | 1.00 | 1.76 | 0.89 | 1.96 | 0.87 |
time (sec) |
N/A | 0.264 | 0.004 | 0.095 | 0.188 | 0.283 | 0.201 | 0.313 | 0.546 |
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 | 52 | 50 | 43 | 42 | 46 | 87 | 48 | 94 | 46 |
N.S. |
1 | 0.96 | 0.83 | 0.81 | 0.88 | 1.67 | 0.92 | 1.81 | 0.88 |
time (sec) |
N/A | 0.261 | 0.005 | 0.158 | 0.187 | 0.287 | 0.394 | 0.308 | 0.539 |
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 | 52 | 53 | 52 | 43 | 46 | 88 | 51 | 95 | 46 |
N.S. |
1 | 1.02 | 1.00 | 0.83 | 0.88 | 1.69 | 0.98 | 1.83 | 0.88 |
time (sec) |
N/A | 0.257 | 0.003 | 0.300 | 0.207 | 0.277 | 0.614 | 0.303 | 0.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 137 | 91 | 677 | 282 | 1358 | 0 | 1857 | 0 |
N.S. |
1 | 1.01 | 0.67 | 5.01 | 2.09 | 10.06 | 0.00 | 13.76 | 0.00 |
time (sec) |
N/A | 0.489 | 0.039 | 19.105 | 0.217 | 0.305 | 0.000 | 0.441 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 94 | 90 | 282 | 149 | 391 | 0 | 576 | 0 |
N.S. |
1 | 1.01 | 0.97 | 3.03 | 1.60 | 4.20 | 0.00 | 6.19 | 0.00 |
time (sec) |
N/A | 0.353 | 0.027 | 2.997 | 0.209 | 0.285 | 0.000 | 0.504 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 37 | 82 | 62 | 72 | 109 | 114 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.61 | 1.22 | 1.41 | 2.14 | 2.24 | 0.00 |
time (sec) |
N/A | 0.233 | 0.010 | 0.460 | 0.193 | 0.289 | 1.480 | 0.328 | 0.000 |
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 | 86 | 86 | 85 | 0 | 0 | 105 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.415 | 0.135 | 0.000 | 0.000 | 0.289 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 112 | 0 | 0 | 202 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 1.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.524 | 0.238 | 0.000 | 0.000 | 0.286 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 133 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 0.181 | 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 | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.415 | 0.127 | 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 | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.115 | 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 | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 108 | 0 | 0 | 73 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.347 | 0.102 | 0.000 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 34 | 33 | 49 | 80 | 36 | 33 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.48 | 2.42 | 1.09 | 1.00 |
time (sec) |
N/A | 0.271 | 0.008 | 0.665 | 0.184 | 0.261 | 1.071 | 0.404 | 0.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.396 | 0.114 | 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 | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.410 | 0.121 | 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 | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 101 | 113 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.429 | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |