Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 199 | 304 | 217 | 238 | 0 | 251 | 512 |
N.S. |
1 | 1.00 | 0.99 | 1.50 | 1.07 | 1.18 | 0.00 | 1.24 | 2.53 |
time (sec) |
N/A | 0.232 | 0.723 | 1.101 | 0.194 | 0.304 | 0.000 | 0.432 | 12.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 177 | 174 | 284 | 190 | 208 | 0 | 221 | 449 |
N.S. |
1 | 1.00 | 0.98 | 1.60 | 1.07 | 1.18 | 0.00 | 1.25 | 2.54 |
time (sec) |
N/A | 0.248 | 0.406 | 0.976 | 0.216 | 0.303 | 0.000 | 0.394 | 12.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 147 | 225 | 173 | 176 | 0 | 188 | 356 |
N.S. |
1 | 1.00 | 1.04 | 1.58 | 1.22 | 1.24 | 0.00 | 1.32 | 2.51 |
time (sec) |
N/A | 0.200 | 0.321 | 0.843 | 0.208 | 0.297 | 0.000 | 0.373 | 11.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 140 | 204 | 151 | 156 | 0 | 168 | 299 |
N.S. |
1 | 1.00 | 0.97 | 1.42 | 1.05 | 1.08 | 0.00 | 1.17 | 2.08 |
time (sec) |
N/A | 0.167 | 0.279 | 0.681 | 0.212 | 0.290 | 0.000 | 0.347 | 11.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 370 | 183 | 140 | 143 | 0 | 142 | 228 |
N.S. |
1 | 1.00 | 4.11 | 2.03 | 1.56 | 1.59 | 0.00 | 1.58 | 2.53 |
time (sec) |
N/A | 0.078 | 1.035 | 0.679 | 0.205 | 0.305 | 0.000 | 0.477 | 16.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 157 | 167 | 160 | 173 | 0 | 175 | 169 |
N.S. |
1 | 1.00 | 0.95 | 1.01 | 0.97 | 1.05 | 0.00 | 1.06 | 1.02 |
time (sec) |
N/A | 0.170 | 0.396 | 1.100 | 0.210 | 0.286 | 0.000 | 0.451 | 11.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 161 | 170 | 188 | 226 | 0 | 210 | 182 |
N.S. |
1 | 1.00 | 0.94 | 0.99 | 1.10 | 1.32 | 0.00 | 1.23 | 1.06 |
time (sec) |
N/A | 0.267 | 0.988 | 1.164 | 0.202 | 0.300 | 0.000 | 0.425 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 221 | 190 | 217 | 217 | 337 | 0 | 240 | 221 |
N.S. |
1 | 1.00 | 0.86 | 0.98 | 0.98 | 1.52 | 0.00 | 1.09 | 1.00 |
time (sec) |
N/A | 0.286 | 2.122 | 1.331 | 0.199 | 0.287 | 0.000 | 0.422 | 11.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 295 | 295 | 164 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.346 | 0.154 | 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 | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 158 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.203 | 0.120 | 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 | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 158 | 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 | 0.171 | 0.160 | 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 | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 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 | 0.080 | 0.080 | 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 | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 360 | 360 | 241 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.395 | 0.315 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 487 | 487 | 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 | 0.408 | 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 | F | C | B | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 502 | 0 | 1600 | 4486 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 3.19 | 8.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 23.519 | 5.269 | 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 | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 458 | 458 | 573 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.843 | 7.601 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 341 | 341 | 398 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.459 | 4.279 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 301 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.084 | 1.559 | 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 | F(-2) | F(-1) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 37 | 33 | 0 | 0 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.133 | 71.199 | 0.513 | 0.000 | 0.000 | 0.000 | 0.980 | 12.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-1) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 37 | 33 | 35 | 0 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 0.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.129 | 64.224 | 1.321 | 14.673 | 0.000 | 0.000 | 1.053 | 12.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 33 | 35 | 35 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.078 | 5.167 | 0.745 | 7.393 | 1.363 | 0.000 | 137.945 | 54.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 37 | 33 | 35 | 54 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.54 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.119 | 12.215 | 0.480 | 3.010 | 0.639 | 0.000 | 0.851 | 27.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 552 | 552 | 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 | 1.004 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 375 | 373 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.446 | 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 | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 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 | 0.064 | 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 | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 33 | 35 | 35 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.082 | 6.975 | 0.600 | 4.654 | 0.261 | 0.000 | 0.430 | 12.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 33 | 35 | 59 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.79 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.079 | 51.979 | 1.525 | 30.493 | 0.379 | 0.000 | 0.464 | 20.030 |
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 | 188 | 188 | 151 | 159 | 151 | 106 | 228 | 182 | 156 |
N.S. |
1 | 1.00 | 0.80 | 0.85 | 0.80 | 0.56 | 1.21 | 0.97 | 0.83 |
time (sec) |
N/A | 0.166 | 0.581 | 1.138 | 0.204 | 0.276 | 0.961 | 0.401 | 0.135 |
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 | 143 | 143 | 116 | 116 | 116 | 88 | 178 | 145 | 118 |
N.S. |
1 | 1.00 | 0.81 | 0.81 | 0.81 | 0.62 | 1.24 | 1.01 | 0.83 |
time (sec) |
N/A | 0.111 | 0.216 | 0.841 | 0.214 | 0.263 | 0.461 | 0.386 | 12.501 |
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 | 97 | 97 | 80 | 83 | 80 | 70 | 128 | 100 | 83 |
N.S. |
1 | 1.00 | 0.82 | 0.86 | 0.82 | 0.72 | 1.32 | 1.03 | 0.86 |
time (sec) |
N/A | 0.078 | 0.189 | 0.530 | 0.203 | 0.251 | 0.234 | 0.342 | 12.346 |
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 | 52 | 52 | 45 | 44 | 45 | 51 | 75 | 52 | 44 |
N.S. |
1 | 1.00 | 0.87 | 0.85 | 0.87 | 0.98 | 1.44 | 1.00 | 0.85 |
time (sec) |
N/A | 0.035 | 0.061 | 0.307 | 0.209 | 0.258 | 0.119 | 0.304 | 12.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 68 | 71 | 64 | 66 | 0 | 67 | 53 |
N.S. |
1 | 1.00 | 1.06 | 1.11 | 1.00 | 1.03 | 0.00 | 1.05 | 0.83 |
time (sec) |
N/A | 0.068 | 0.036 | 0.453 | 0.309 | 0.274 | 0.000 | 0.307 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 54 | 110 | 78 | 92 | 0 | 84 | 63 |
N.S. |
1 | 1.00 | 0.92 | 1.86 | 1.32 | 1.56 | 0.00 | 1.42 | 1.07 |
time (sec) |
N/A | 0.051 | 0.176 | 0.786 | 0.218 | 0.283 | 0.000 | 0.351 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 82 | 141 | 112 | 114 | 0 | 114 | 91 |
N.S. |
1 | 1.00 | 0.93 | 1.60 | 1.27 | 1.30 | 0.00 | 1.30 | 1.03 |
time (sec) |
N/A | 0.060 | 0.423 | 0.875 | 0.213 | 0.275 | 0.000 | 0.340 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 104 | 169 | 143 | 135 | 0 | 139 | 120 |
N.S. |
1 | 1.00 | 0.88 | 1.43 | 1.21 | 1.14 | 0.00 | 1.18 | 1.02 |
time (sec) |
N/A | 0.073 | 0.672 | 1.147 | 0.212 | 0.295 | 0.000 | 0.358 | 12.113 |
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 | 349 | 349 | 295 | 246 | 238 | 174 | 389 | 279 | 236 |
N.S. |
1 | 1.00 | 0.85 | 0.70 | 0.68 | 0.50 | 1.11 | 0.80 | 0.68 |
time (sec) |
N/A | 0.276 | 0.878 | 1.938 | 0.206 | 0.302 | 1.305 | 0.503 | 0.185 |
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 | 231 | 231 | 227 | 181 | 184 | 147 | 309 | 231 | 180 |
N.S. |
1 | 1.00 | 0.98 | 0.78 | 0.80 | 0.64 | 1.34 | 1.00 | 0.78 |
time (sec) |
N/A | 0.190 | 0.343 | 1.315 | 0.221 | 0.276 | 0.673 | 0.571 | 0.117 |
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 | 132 | 132 | 111 | 130 | 128 | 120 | 228 | 168 | 127 |
N.S. |
1 | 1.00 | 0.84 | 0.98 | 0.97 | 0.91 | 1.73 | 1.27 | 0.96 |
time (sec) |
N/A | 0.130 | 0.169 | 0.836 | 0.219 | 0.287 | 0.352 | 0.525 | 12.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 41 | 73 | 74 | 92 | 117 | 86 | 71 |
N.S. |
1 | 1.00 | 0.76 | 1.35 | 1.37 | 1.70 | 2.17 | 1.59 | 1.31 |
time (sec) |
N/A | 0.060 | 0.049 | 0.484 | 0.271 | 0.284 | 0.166 | 0.426 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 81 | 125 | 109 | 111 | 0 | 129 | 80 |
N.S. |
1 | 1.00 | 0.86 | 1.33 | 1.16 | 1.18 | 0.00 | 1.37 | 0.85 |
time (sec) |
N/A | 0.116 | 0.139 | 0.763 | 0.201 | 0.305 | 0.000 | 0.402 | 12.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 174 | 187 | 122 | 136 | 0 | 146 | 118 |
N.S. |
1 | 1.00 | 1.55 | 1.67 | 1.09 | 1.21 | 0.00 | 1.30 | 1.05 |
time (sec) |
N/A | 0.124 | 1.019 | 0.867 | 0.218 | 0.307 | 0.000 | 0.441 | 12.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 186 | 236 | 171 | 173 | 0 | 187 | 181 |
N.S. |
1 | 1.00 | 1.52 | 1.93 | 1.40 | 1.42 | 0.00 | 1.53 | 1.48 |
time (sec) |
N/A | 0.109 | 1.219 | 0.951 | 0.210 | 0.289 | 0.000 | 0.469 | 12.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 242 | 302 | 211 | 203 | 0 | 229 | 220 |
N.S. |
1 | 1.00 | 1.51 | 1.89 | 1.32 | 1.27 | 0.00 | 1.43 | 1.38 |
time (sec) |
N/A | 0.145 | 0.970 | 1.187 | 0.217 | 0.305 | 0.000 | 0.643 | 12.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 315 | 315 | 218 | 374 | 366 | 366 | 0 | 511 | 435 |
N.S. |
1 | 1.00 | 0.69 | 1.19 | 1.16 | 1.16 | 0.00 | 1.62 | 1.38 |
time (sec) |
N/A | 0.255 | 0.623 | 1.177 | 0.205 | 0.335 | 0.000 | 0.365 | 11.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 148 | 254 | 220 | 222 | 0 | 286 | 253 |
N.S. |
1 | 1.00 | 0.73 | 1.26 | 1.09 | 1.10 | 0.00 | 1.42 | 1.25 |
time (sec) |
N/A | 0.175 | 0.305 | 0.797 | 0.213 | 0.300 | 0.000 | 0.355 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 89 | 127 | 112 | 112 | 0 | 129 | 122 |
N.S. |
1 | 1.00 | 0.80 | 1.14 | 1.01 | 1.01 | 0.00 | 1.16 | 1.10 |
time (sec) |
N/A | 0.122 | 0.264 | 0.637 | 0.216 | 0.276 | 0.000 | 0.321 | 12.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 39 | 40 | 40 | 38 | 104 | 41 | 41 |
N.S. |
1 | 1.00 | 0.95 | 0.98 | 0.98 | 0.93 | 2.54 | 1.00 | 1.00 |
time (sec) |
N/A | 0.048 | 0.036 | 0.360 | 0.206 | 0.295 | 0.346 | 0.317 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 80 | 89 | 79 | 88 | 0 | 87 | 89 |
N.S. |
1 | 1.00 | 0.89 | 0.99 | 0.88 | 0.98 | 0.00 | 0.97 | 0.99 |
time (sec) |
N/A | 0.099 | 0.096 | 0.636 | 0.211 | 0.325 | 0.000 | 0.342 | 0.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 154 | 149 | 175 | 234 | 0 | 260 | 197 |
N.S. |
1 | 1.00 | 0.97 | 0.94 | 1.10 | 1.47 | 0.00 | 1.64 | 1.24 |
time (sec) |
N/A | 0.217 | 0.419 | 1.018 | 0.219 | 0.474 | 0.000 | 0.396 | 0.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 263 | 263 | 357 | 256 | 367 | 413 | 0 | 539 | 427 |
N.S. |
1 | 1.00 | 1.36 | 0.97 | 1.40 | 1.57 | 0.00 | 2.05 | 1.62 |
time (sec) |
N/A | 0.331 | 6.164 | 1.416 | 0.324 | 1.200 | 0.000 | 0.373 | 12.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 383 | 383 | 583 | 393 | 632 | 643 | 0 | 907 | 729 |
N.S. |
1 | 1.00 | 1.52 | 1.03 | 1.65 | 1.68 | 0.00 | 2.37 | 1.90 |
time (sec) |
N/A | 0.481 | 6.278 | 2.412 | 0.244 | 2.480 | 0.000 | 0.414 | 12.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 324 | 324 | 396 | 468 | 377 | 508 | 0 | 570 | 682 |
N.S. |
1 | 1.00 | 1.22 | 1.44 | 1.16 | 1.57 | 0.00 | 1.76 | 2.10 |
time (sec) |
N/A | 0.290 | 1.066 | 1.849 | 0.221 | 0.346 | 0.000 | 0.406 | 11.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 234 | 258 | 229 | 322 | 0 | 328 | 290 |
N.S. |
1 | 1.00 | 1.14 | 1.25 | 1.11 | 1.56 | 0.00 | 1.59 | 1.41 |
time (sec) |
N/A | 0.186 | 1.327 | 1.426 | 0.203 | 0.321 | 0.000 | 0.352 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 111 | 118 | 118 | 178 | 0 | 188 | 128 |
N.S. |
1 | 1.00 | 0.98 | 1.04 | 1.04 | 1.58 | 0.00 | 1.66 | 1.13 |
time (sec) |
N/A | 0.110 | 0.331 | 0.928 | 0.203 | 0.289 | 0.000 | 0.343 | 11.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 42 | 47 | 48 | 54 | 178 | 80 | 48 |
N.S. |
1 | 1.00 | 0.88 | 0.98 | 1.00 | 1.12 | 3.71 | 1.67 | 1.00 |
time (sec) |
N/A | 0.054 | 0.069 | 0.428 | 0.206 | 0.282 | 0.542 | 0.325 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 178 | 128 | 147 | 283 | 0 | 205 | 131 |
N.S. |
1 | 1.00 | 1.32 | 0.95 | 1.09 | 2.10 | 0.00 | 1.52 | 0.97 |
time (sec) |
N/A | 0.148 | 0.876 | 1.025 | 0.216 | 0.399 | 0.000 | 0.347 | 0.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 246 | 191 | 346 | 598 | 0 | 335 | 327 |
N.S. |
1 | 1.00 | 1.08 | 0.84 | 1.52 | 2.62 | 0.00 | 1.47 | 1.43 |
time (sec) |
N/A | 0.240 | 1.208 | 2.184 | 0.223 | 0.760 | 0.000 | 0.387 | 12.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 372 | 372 | 370 | 297 | 659 | 881 | 0 | 761 | 615 |
N.S. |
1 | 1.00 | 0.99 | 0.80 | 1.77 | 2.37 | 0.00 | 2.05 | 1.65 |
time (sec) |
N/A | 0.406 | 2.724 | 4.372 | 0.242 | 1.818 | 0.000 | 0.407 | 12.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 550 | 550 | 542 | 435 | 1083 | 1244 | 0 | 1185 | 1024 |
N.S. |
1 | 1.00 | 0.99 | 0.79 | 1.97 | 2.26 | 0.00 | 2.15 | 1.86 |
time (sec) |
N/A | 0.640 | 5.735 | 6.836 | 0.270 | 4.603 | 0.000 | 0.447 | 13.941 |
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 | 37 | 37 | 39 | 37 | 39 | 39 | 36 | 39 | 39 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 1.05 | 1.05 | 0.97 | 1.05 | 1.05 |
time (sec) |
N/A | 0.065 | 7.987 | 0.986 | 5.885 | 0.295 | 77.166 | 1.168 | 14.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 330 | 330 | 5085 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 15.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.271 | 33.668 | 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 | B | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 508 | 508 | 12622 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 24.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 52.064 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 308 | 308 | 5113 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 16.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.397 | 26.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |