Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 218 | 756 | 936 | 1085 | 0 | 0 | 190 | 0 |
N.S. |
1 | 1.00 | 0.96 | 3.33 | 4.12 | 4.78 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.461 | 0.080 | 0.454 | 0.231 | 0.136 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 151 | 440 | 516 | 675 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.80 | 3.29 | 4.30 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.365 | 0.098 | 0.218 | 0.199 | 0.121 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 87 | 142 | 0 | 343 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.53 | 0.00 | 3.69 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.277 | 0.043 | 0.085 | 0.000 | 0.105 | 0.000 | 0.000 | 0.188 | 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 | 18 | 18 | 20 | 18 | 116 | 20 | 22 | 20 | 34 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 6.44 | 1.11 | 1.22 | 1.11 | 1.89 | 1.22 |
time (sec) |
N/A | 0.206 | 4.857 | 0.111 | 0.298 | 0.085 | 0.633 | 0.198 | 0.193 | 15.115 |
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 | 18 | 18 | 20 | 18 | 172 | 31 | 46 | 20 | 82 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 9.56 | 1.72 | 2.56 | 1.11 | 4.56 | 1.22 |
time (sec) |
N/A | 0.203 | 3.958 | 0.076 | 0.340 | 0.076 | 2.469 | 1.469 | 0.195 | 15.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 371 | 329 | 1517 | 3403 | 1887 | 0 | 0 | 222 | 0 |
N.S. |
1 | 1.00 | 0.89 | 4.09 | 9.17 | 5.09 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.730 | 1.328 | 0.426 | 0.447 | 0.162 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 262 | 232 | 679 | 1704 | 1096 | 0 | 0 | 173 | 0 |
N.S. |
1 | 1.00 | 0.89 | 2.59 | 6.50 | 4.18 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.569 | 1.752 | 0.277 | 0.393 | 0.137 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 123 | 191 | 0 | 525 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.43 | 0.00 | 3.92 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.343 | 0.732 | 0.092 | 0.000 | 0.109 | 0.000 | 0.000 | 0.192 | 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 | 507 | 37 | 41 | 22 | 70 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 25.35 | 1.85 | 2.05 | 1.10 | 3.50 | 1.20 |
time (sec) |
N/A | 0.222 | 20.926 | 0.101 | 0.727 | 0.081 | 1.172 | 1.055 | 0.195 | 15.005 |
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 | 624 | 48 | 76 | 22 | 157 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 31.20 | 2.40 | 3.80 | 1.10 | 7.85 | 1.20 |
time (sec) |
N/A | 0.222 | 16.825 | 0.100 | 1.026 | 0.081 | 2.447 | 36.676 | 0.194 | 14.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 216 | 417 | 1285 | 516 | 0 | 0 | 182 | 0 |
N.S. |
1 | 1.00 | 1.42 | 2.74 | 8.45 | 3.39 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.540 | 1.381 | 0.175 | 0.255 | 0.094 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 528 | 236 | 377 | 292 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.00 | 4.44 | 1.98 | 3.17 | 2.45 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.468 | 6.445 | 0.140 | 0.220 | 0.081 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 104 | 53 | 273 | 99 | 0 | 248 | 68 | 79 |
N.S. |
1 | 1.00 | 1.55 | 0.79 | 4.07 | 1.48 | 0.00 | 3.70 | 1.01 | 1.18 |
time (sec) |
N/A | 0.304 | 0.625 | 0.152 | 0.116 | 0.077 | 0.000 | 0.224 | 0.177 | 15.245 |
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 | 391 | 27 | 27 | 22 | 30 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 19.55 | 1.35 | 1.35 | 1.10 | 1.50 | 1.20 |
time (sec) |
N/A | 0.233 | 6.380 | 0.079 | 0.337 | 0.067 | 1.095 | 0.155 | 0.194 | 14.783 |
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 | 522 | 51 | 58 | 22 | 58 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 26.10 | 2.55 | 2.90 | 1.10 | 2.90 | 1.20 |
time (sec) |
N/A | 0.231 | 4.770 | 0.076 | 0.646 | 0.068 | 2.317 | 0.456 | 0.202 | 14.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 288 | 1447 | 810 | 4283 | 933 | 0 | 0 | 418 | 0 |
N.S. |
1 | 1.00 | 5.02 | 2.81 | 14.87 | 3.24 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.931 | 7.294 | 0.248 | 1.086 | 0.106 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 925 | 453 | 1035 | 493 | 0 | 0 | 246 | 0 |
N.S. |
1 | 1.00 | 4.04 | 1.98 | 4.52 | 2.15 | 0.00 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.725 | 6.760 | 0.193 | 0.540 | 0.091 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 172 | 86 | 1058 | 183 | 0 | 798 | 112 | 247 |
N.S. |
1 | 1.00 | 1.23 | 0.61 | 7.56 | 1.31 | 0.00 | 5.70 | 0.80 | 1.76 |
time (sec) |
N/A | 0.412 | 1.368 | 0.190 | 0.148 | 0.085 | 0.000 | 0.407 | 0.181 | 20.466 |
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 | 3956 | 57 | 54 | 22 | 53 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 197.80 | 2.85 | 2.70 | 1.10 | 2.65 | 1.20 |
time (sec) |
N/A | 0.228 | 9.967 | 0.102 | 9.213 | 0.080 | 2.373 | 0.235 | 0.189 | 14.894 |
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 | 4471 | 99 | 105 | 22 | 100 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 223.55 | 4.95 | 5.25 | 1.10 | 5.00 | 1.20 |
time (sec) |
N/A | 0.230 | 12.202 | 0.094 | 31.443 | 0.078 | 9.290 | 1.001 | 0.190 | 15.195 |
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 | 22 | 0 | 22 | 22 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.00 | 1.10 | 1.10 | 1.20 |
time (sec) |
N/A | 0.221 | 0.842 | 0.121 | 0.397 | 0.087 | 0.000 | 0.261 | 0.185 | 14.767 |
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 | 18 | 18 | 20 | 18 | 124 | 20 | 24 | 20 | 28 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 6.89 | 1.11 | 1.33 | 1.11 | 1.56 | 1.22 |
time (sec) |
N/A | 0.203 | 8.448 | 0.068 | 0.176 | 0.070 | 7.613 | 0.191 | 0.187 | 14.767 |
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 | 22 | 17 | 22 | 140 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 7.00 | 1.20 |
time (sec) |
N/A | 0.225 | 0.851 | 0.063 | 0.308 | 0.075 | 2.441 | 0.133 | 0.182 | 14.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 365 | 756 | 936 | 1085 | 0 | 0 | 229 | 0 |
N.S. |
1 | 1.00 | 1.61 | 3.33 | 4.12 | 4.78 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.440 | 0.334 | 0.258 | 0.235 | 0.137 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 203 | 440 | 516 | 675 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.00 | 1.29 | 2.80 | 3.29 | 4.30 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.363 | 0.173 | 0.181 | 0.181 | 0.123 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 104 | 142 | 0 | 343 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.53 | 0.00 | 3.69 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.283 | 0.010 | 0.080 | 0.000 | 0.106 | 0.000 | 0.000 | 0.171 | 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 | 18 | 18 | 20 | 18 | 116 | 20 | 15 | 20 | 59 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 6.44 | 1.11 | 0.83 | 1.11 | 3.28 | 1.22 |
time (sec) |
N/A | 0.205 | 0.666 | 0.069 | 0.283 | 0.077 | 0.795 | 0.238 | 0.185 | 15.086 |
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 | 18 | 18 | 20 | 18 | 172 | 31 | 17 | 20 | 85 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 9.56 | 1.72 | 0.94 | 1.11 | 4.72 | 1.22 |
time (sec) |
N/A | 0.204 | 1.062 | 0.059 | 0.323 | 0.071 | 2.936 | 1.699 | 0.185 | 15.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 364 | 364 | 646 | 1489 | 3267 | 1823 | 0 | 0 | 1395 | 0 |
N.S. |
1 | 1.00 | 1.77 | 4.09 | 8.98 | 5.01 | 0.00 | 0.00 | 3.83 | 0.00 |
time (sec) |
N/A | 0.754 | 1.670 | 0.412 | 0.479 | 0.169 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 356 | 662 | 1641 | 1056 | 0 | 0 | 742 | 0 |
N.S. |
1 | 1.00 | 1.39 | 2.58 | 6.39 | 4.11 | 0.00 | 0.00 | 2.89 | 0.00 |
time (sec) |
N/A | 0.572 | 1.011 | 0.317 | 0.266 | 0.147 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 151 | 190 | 0 | 505 | 0 | 0 | 343 | 0 |
N.S. |
1 | 1.00 | 1.15 | 1.45 | 0.00 | 3.85 | 0.00 | 0.00 | 2.62 | 0.00 |
time (sec) |
N/A | 0.344 | 0.376 | 0.103 | 0.000 | 0.113 | 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 | 501 | 36 | 17 | 22 | 124 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 25.05 | 1.80 | 0.85 | 1.10 | 6.20 | 1.20 |
time (sec) |
N/A | 0.229 | 39.276 | 0.148 | 1.089 | 0.086 | 1.205 | 1.834 | 0.207 | 14.711 |
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 | 618 | 47 | 19 | 22 | 172 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 30.90 | 2.35 | 0.95 | 1.10 | 8.60 | 1.20 |
time (sec) |
N/A | 0.224 | 22.007 | 0.104 | 1.114 | 0.080 | 2.504 | 56.267 | 0.188 | 15.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 526 | 526 | 449 | 0 | 0 | 2309 | 0 | 0 | 616 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 4.39 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 1.317 | 0.988 | 0.000 | 0.000 | 0.294 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 394 | 338 | 0 | 0 | 1625 | 0 | 0 | 431 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 4.12 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 1.093 | 0.751 | 0.000 | 0.000 | 0.241 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 214 | 516 | 0 | 1041 | 0 | 0 | 248 | 0 |
N.S. |
1 | 1.00 | 0.83 | 2.01 | 0.00 | 4.05 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.746 | 0.499 | 0.152 | 0.000 | 0.228 | 0.000 | 0.000 | 0.160 | 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 | 298 | 27 | 17 | 22 | 793 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 14.90 | 1.35 | 0.85 | 1.10 | 39.65 | 1.20 |
time (sec) |
N/A | 0.228 | 1.171 | 0.091 | 0.638 | 0.071 | 1.188 | 0.214 | 0.180 | 14.775 |
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 | 439 | 51 | 19 | 22 | 2871 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 21.95 | 2.55 | 0.95 | 1.10 | 143.55 | 1.20 |
time (sec) |
N/A | 0.228 | 8.863 | 0.087 | 1.006 | 0.073 | 2.409 | 0.571 | 0.210 | 14.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1523 | 1523 | 20116 | 0 | 0 | 7008 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 13.21 | 0.00 | 0.00 | 4.60 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.301 | 19.830 | 0.000 | 0.000 | 0.491 | 0.000 | 0.000 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1117 | 1117 | 3365 | 0 | 0 | 4274 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.01 | 0.00 | 0.00 | 3.83 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.505 | 16.570 | 0.000 | 0.000 | 0.354 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 582 | 582 | 1037 | 1289 | 0 | 2080 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.78 | 2.21 | 0.00 | 3.57 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.374 | 9.871 | 0.208 | 0.000 | 0.282 | 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 | 2279 | 55 | 19 | 22 | 5490 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 113.95 | 2.75 | 0.95 | 1.10 | 274.50 | 1.20 |
time (sec) |
N/A | 0.237 | 15.680 | 0.110 | 11.922 | 0.087 | 2.288 | 0.337 | 0.280 | 19.073 |
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 | 2918 | 96 | 20 | 22 | 19510 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 145.90 | 4.80 | 1.00 | 1.10 | 975.50 | 1.20 |
time (sec) |
N/A | 0.228 | 32.978 | 0.116 | 37.638 | 0.107 | 9.632 | 2.984 | 0.361 | 16.287 |
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 | 22 | 0 | 22 | 22 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.00 | 1.10 | 1.10 | 1.20 |
time (sec) |
N/A | 0.225 | 1.761 | 0.102 | 0.502 | 0.093 | 0.000 | 0.294 | 0.183 | 15.659 |
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 | 18 | 18 | 20 | 18 | 124 | 20 | 17 | 20 | 113 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 6.89 | 1.11 | 0.94 | 1.11 | 6.28 | 1.22 |
time (sec) |
N/A | 0.204 | 0.424 | 0.058 | 0.174 | 0.080 | 5.758 | 0.164 | 0.168 | 15.049 |
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 | 22 | 17 | 22 | 326 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 16.30 | 1.20 |
time (sec) |
N/A | 0.231 | 0.596 | 0.068 | 0.307 | 0.071 | 2.669 | 0.203 | 0.191 | 15.291 |