Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 140 | 122 | 140 | 0 | 889 | 0 | 154 | 2763 | 488 |
N.S. |
1 | 1.09 | 0.95 | 1.09 | 0.00 | 6.89 | 0.00 | 1.19 | 21.42 | 3.78 |
time (sec) |
N/A | 0.287 | 0.331 | 0.773 | 0.000 | 0.275 | 0.000 | 0.128 | 0.309 | 1.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 136 | 122 | 97 | 0 | 351 | 0 | 412 | 939 | 0 |
N.S. |
1 | 1.06 | 0.95 | 0.76 | 0.00 | 2.74 | 0.00 | 3.22 | 7.34 | 0.00 |
time (sec) |
N/A | 0.295 | 0.420 | 0.800 | 0.000 | 0.115 | 0.000 | 0.352 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 197 | 154 | 170 | 0 | 1040 | 0 | 216 | 2988 | 441 |
N.S. |
1 | 1.16 | 0.91 | 1.00 | 0.00 | 6.12 | 0.00 | 1.27 | 17.58 | 2.59 |
time (sec) |
N/A | 0.369 | 0.568 | 0.834 | 0.000 | 0.267 | 0.000 | 0.136 | 0.685 | 2.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 179 | 1668 | 132 | 0 | 443 | 0 | 442 | 1460 | 0 |
N.S. |
1 | 1.08 | 10.05 | 0.80 | 0.00 | 2.67 | 0.00 | 2.66 | 8.80 | 0.00 |
time (sec) |
N/A | 0.383 | 7.453 | 0.905 | 0.000 | 0.150 | 0.000 | 0.415 | 0.624 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 283 | 219 | 218 | 0 | 1697 | 0 | 516 | 24 | 0 |
N.S. |
1 | 1.10 | 0.85 | 0.84 | 0.00 | 6.58 | 0.00 | 2.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.594 | 10.210 | 0.890 | 0.000 | 1.490 | 0.000 | 0.164 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 194 | 183 | 176 | 0 | 573 | 0 | 264 | 687 | 276 |
N.S. |
1 | 1.11 | 1.05 | 1.01 | 0.00 | 3.29 | 0.00 | 1.52 | 3.95 | 1.59 |
time (sec) |
N/A | 0.292 | 0.362 | 0.849 | 0.000 | 0.132 | 0.000 | 0.123 | 0.189 | 1.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 214 | 173 | 169 | 0 | 1379 | 0 | 446 | 1479 | 0 |
N.S. |
1 | 1.10 | 0.89 | 0.87 | 0.00 | 7.07 | 0.00 | 2.29 | 7.58 | 0.00 |
time (sec) |
N/A | 0.414 | 10.148 | 0.856 | 0.000 | 0.723 | 0.000 | 0.162 | 2.900 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 135 | 128 | 139 | 0 | 453 | 0 | 197 | 451 | 172 |
N.S. |
1 | 1.07 | 1.02 | 1.10 | 0.00 | 3.60 | 0.00 | 1.56 | 3.58 | 1.37 |
time (sec) |
N/A | 0.244 | 0.305 | 0.835 | 0.000 | 0.145 | 0.000 | 0.130 | 0.212 | 1.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 180 | 191 | 142 | 0 | 1228 | 0 | 407 | 1373 | 0 |
N.S. |
1 | 1.03 | 1.10 | 0.82 | 0.00 | 7.06 | 0.00 | 2.34 | 7.89 | 0.00 |
time (sec) |
N/A | 0.381 | 0.577 | 0.797 | 0.000 | 0.516 | 0.000 | 0.161 | 0.501 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 173 | 146 | 165 | 0 | 1138 | 0 | 206 | 3938 | 1321 |
N.S. |
1 | 1.08 | 0.91 | 1.03 | 0.00 | 7.11 | 0.00 | 1.29 | 24.61 | 8.26 |
time (sec) |
N/A | 0.345 | 0.336 | 0.807 | 0.000 | 0.866 | 0.000 | 0.123 | 0.318 | 1.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 181 | 192 | 181 | 0 | 1184 | 0 | 0 | 1975 | 0 |
N.S. |
1 | 1.08 | 1.14 | 1.08 | 0.00 | 7.05 | 0.00 | 0.00 | 11.76 | 0.00 |
time (sec) |
N/A | 0.378 | 0.542 | 0.868 | 0.000 | 0.359 | 0.000 | 0.000 | 0.379 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 192 | 160 | 194 | 0 | 1272 | 0 | 283 | 4167 | 1152 |
N.S. |
1 | 1.07 | 0.89 | 1.08 | 0.00 | 7.07 | 0.00 | 1.57 | 23.15 | 6.40 |
time (sec) |
N/A | 0.386 | 0.459 | 0.892 | 0.000 | 0.910 | 0.000 | 0.132 | 0.601 | 2.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 182 | 157 | 128 | 0 | 483 | 0 | 496 | 1511 | 0 |
N.S. |
1 | 1.03 | 0.89 | 0.73 | 0.00 | 2.74 | 0.00 | 2.82 | 8.59 | 0.00 |
time (sec) |
N/A | 0.396 | 0.624 | 0.932 | 0.000 | 0.147 | 0.000 | 0.393 | 0.637 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 156 | 148 | 115 | 0 | 1053 | 0 | 284 | 1041 | 0 |
N.S. |
1 | 1.18 | 1.12 | 0.87 | 0.00 | 7.98 | 0.00 | 2.15 | 7.89 | 0.00 |
time (sec) |
N/A | 0.286 | 0.699 | 0.755 | 0.000 | 0.308 | 0.000 | 0.151 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 98 | 100 | 83 | 0 | 450 | 0 | 116 | 415 | 93 |
N.S. |
1 | 0.99 | 1.01 | 0.84 | 0.00 | 4.55 | 0.00 | 1.17 | 4.19 | 0.94 |
time (sec) |
N/A | 0.228 | 0.234 | 0.736 | 0.000 | 0.110 | 0.000 | 0.122 | 0.194 | 1.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 608 | 79 | 0 | 418 | 0 | 231 | 450 | 0 |
N.S. |
1 | 1.00 | 6.83 | 0.89 | 0.00 | 4.70 | 0.00 | 2.60 | 5.06 | 0.00 |
time (sec) |
N/A | 0.214 | 3.070 | 0.751 | 0.000 | 0.153 | 0.000 | 0.320 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 86 | 71 | 0 | 404 | 0 | 93 | 247 | 82 |
N.S. |
1 | 0.99 | 0.99 | 0.82 | 0.00 | 4.64 | 0.00 | 1.07 | 2.84 | 0.94 |
time (sec) |
N/A | 0.211 | 0.161 | 0.797 | 0.000 | 0.102 | 0.000 | 0.126 | 0.204 | 1.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 122 | 88 | 0 | 459 | 0 | 225 | 830 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.88 | 0.00 | 4.59 | 0.00 | 2.25 | 8.30 | 0.00 |
time (sec) |
N/A | 0.221 | 0.047 | 0.737 | 0.000 | 0.172 | 0.000 | 0.139 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 155 | 124 | 146 | 0 | 1043 | 0 | 138 | 3098 | 3023 |
N.S. |
1 | 1.19 | 0.95 | 1.12 | 0.00 | 8.02 | 0.00 | 1.06 | 23.83 | 23.25 |
time (sec) |
N/A | 0.277 | 0.337 | 0.782 | 0.000 | 0.389 | 0.000 | 0.118 | 0.309 | 2.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 151 | 156 | 109 | 0 | 600 | 0 | 396 | 1036 | 0 |
N.S. |
1 | 1.03 | 1.06 | 0.74 | 0.00 | 4.08 | 0.00 | 2.69 | 7.05 | 0.00 |
time (sec) |
N/A | 0.297 | 0.672 | 0.803 | 0.000 | 0.194 | 0.000 | 0.348 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 213 | 163 | 191 | 0 | 1413 | 0 | 257 | 3434 | 3837 |
N.S. |
1 | 1.15 | 0.88 | 1.03 | 0.00 | 7.64 | 0.00 | 1.39 | 18.56 | 20.74 |
time (sec) |
N/A | 0.361 | 0.688 | 0.894 | 0.000 | 0.687 | 0.000 | 0.120 | 0.770 | 3.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 199 | 131 | 0 | 758 | 0 | 375 | 1796 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.64 | 0.00 | 3.68 | 0.00 | 1.82 | 8.72 | 0.00 |
time (sec) |
N/A | 0.391 | 0.854 | 0.987 | 0.000 | 0.272 | 0.000 | 0.392 | 0.606 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 145 | 672 | 95 | 0 | 552 | 0 | 298 | 1881 | 0 |
N.S. |
1 | 1.12 | 5.17 | 0.73 | 0.00 | 4.25 | 0.00 | 2.29 | 14.47 | 0.00 |
time (sec) |
N/A | 0.270 | 10.505 | 0.730 | 0.000 | 0.255 | 0.000 | 0.413 | 0.392 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 138 | 110 | 125 | 0 | 732 | 0 | 181 | 819 | 142 |
N.S. |
1 | 1.17 | 0.93 | 1.06 | 0.00 | 6.20 | 0.00 | 1.53 | 6.94 | 1.20 |
time (sec) |
N/A | 0.252 | 0.318 | 0.750 | 0.000 | 0.141 | 0.000 | 0.122 | 0.184 | 1.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 133 | 1437 | 97 | 0 | 744 | 0 | 299 | 2459 | 0 |
N.S. |
1 | 1.08 | 11.68 | 0.79 | 0.00 | 6.05 | 0.00 | 2.43 | 19.99 | 0.00 |
time (sec) |
N/A | 0.260 | 9.741 | 0.776 | 0.000 | 0.297 | 0.000 | 0.420 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 125 | 102 | 88 | 0 | 537 | 0 | 153 | 556 | 130 |
N.S. |
1 | 1.11 | 0.90 | 0.78 | 0.00 | 4.75 | 0.00 | 1.35 | 4.92 | 1.15 |
time (sec) |
N/A | 0.237 | 0.345 | 0.771 | 0.000 | 0.119 | 0.000 | 0.110 | 0.236 | 1.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 151 | 154 | 109 | 0 | 854 | 0 | 318 | 1811 | 0 |
N.S. |
1 | 1.06 | 1.08 | 0.77 | 0.00 | 6.01 | 0.00 | 2.24 | 12.75 | 0.00 |
time (sec) |
N/A | 0.276 | 0.545 | 0.802 | 0.000 | 0.349 | 0.000 | 0.408 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 208 | 157 | 199 | 0 | 1998 | 0 | 225 | 5685 | 5227 |
N.S. |
1 | 1.22 | 0.92 | 1.17 | 0.00 | 11.75 | 0.00 | 1.32 | 33.44 | 30.75 |
time (sec) |
N/A | 0.354 | 0.700 | 0.802 | 0.000 | 1.574 | 0.000 | 0.123 | 0.564 | 3.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 213 | 216 | 141 | 0 | 1018 | 0 | 554 | 1974 | 0 |
N.S. |
1 | 1.04 | 1.05 | 0.69 | 0.00 | 4.97 | 0.00 | 2.70 | 9.63 | 0.00 |
time (sec) |
N/A | 0.401 | 0.843 | 0.849 | 0.000 | 0.405 | 0.000 | 0.498 | 0.693 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 283 | 223 | 238 | 0 | 2560 | 0 | 367 | 6272 | 4286 |
N.S. |
1 | 1.17 | 0.93 | 0.99 | 0.00 | 10.62 | 0.00 | 1.52 | 26.02 | 17.78 |
time (sec) |
N/A | 0.443 | 0.913 | 0.957 | 0.000 | 2.993 | 0.000 | 0.127 | 2.506 | 5.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 288 | 265 | 158 | 0 | 1252 | 0 | 486 | 24 | 0 |
N.S. |
1 | 1.04 | 0.96 | 0.57 | 0.00 | 4.52 | 0.00 | 1.75 | 0.09 | 0.00 |
time (sec) |
N/A | 0.525 | 1.291 | 0.917 | 0.000 | 0.595 | 0.000 | 0.565 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 201 | 1715 | 146 | 0 | 1008 | 0 | 594 | 3695 | 0 |
N.S. |
1 | 1.16 | 9.86 | 0.84 | 0.00 | 5.79 | 0.00 | 3.41 | 21.24 | 0.00 |
time (sec) |
N/A | 0.352 | 15.471 | 0.833 | 0.000 | 0.533 | 0.000 | 0.406 | 0.840 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 177 | 154 | 162 | 0 | 993 | 0 | 260 | 1345 | 193 |
N.S. |
1 | 1.16 | 1.01 | 1.07 | 0.00 | 6.53 | 0.00 | 1.71 | 8.85 | 1.27 |
time (sec) |
N/A | 0.279 | 0.493 | 0.882 | 0.000 | 0.201 | 0.000 | 0.134 | 0.242 | 1.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 189 | 183 | 143 | 0 | 1292 | 0 | 595 | 2734 | 0 |
N.S. |
1 | 1.16 | 1.12 | 0.88 | 0.00 | 7.93 | 0.00 | 3.65 | 16.77 | 0.00 |
time (sec) |
N/A | 0.321 | 0.902 | 0.875 | 0.000 | 0.628 | 0.000 | 0.400 | 0.661 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 163 | 137 | 134 | 0 | 895 | 0 | 226 | 983 | 171 |
N.S. |
1 | 1.16 | 0.98 | 0.96 | 0.00 | 6.39 | 0.00 | 1.61 | 7.02 | 1.22 |
time (sec) |
N/A | 0.260 | 0.323 | 0.824 | 0.000 | 0.157 | 0.000 | 0.121 | 0.246 | 1.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 227 | 214 | 158 | 0 | 1434 | 0 | 619 | 3742 | 0 |
N.S. |
1 | 1.13 | 1.06 | 0.79 | 0.00 | 7.13 | 0.00 | 3.08 | 18.62 | 0.00 |
time (sec) |
N/A | 0.362 | 1.009 | 0.842 | 0.000 | 0.758 | 0.000 | 0.403 | 0.722 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 277 | 215 | 257 | 0 | 3409 | 0 | 298 | 8814 | 8467 |
N.S. |
1 | 1.23 | 0.96 | 1.14 | 0.00 | 15.15 | 0.00 | 1.32 | 39.17 | 37.63 |
time (sec) |
N/A | 0.434 | 0.841 | 1.177 | 0.000 | 4.137 | 0.000 | 0.127 | 2.123 | 5.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 310 | 287 | 176 | 0 | 1662 | 0 | 938 | 24 | 0 |
N.S. |
1 | 1.11 | 1.03 | 0.63 | 0.00 | 5.96 | 0.00 | 3.36 | 0.09 | 0.00 |
time (sec) |
N/A | 0.541 | 1.169 | 1.002 | 0.000 | 0.940 | 0.000 | 0.429 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 358 | 294 | 270 | 0 | 4121 | 0 | 505 | 9446 | 5800 |
N.S. |
1 | 1.18 | 0.97 | 0.89 | 0.00 | 13.56 | 0.00 | 1.66 | 31.07 | 19.08 |
time (sec) |
N/A | 0.535 | 1.316 | 1.055 | 0.000 | 7.773 | 0.000 | 0.128 | 39.566 | 6.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 391 | 348 | 367 | 0 | 1890 | 0 | 789 | 24 | 0 |
N.S. |
1 | 1.08 | 0.96 | 1.01 | 0.00 | 5.22 | 0.00 | 2.18 | 0.07 | 0.00 |
time (sec) |
N/A | 0.707 | 1.574 | 1.120 | 0.000 | 1.412 | 0.000 | 0.688 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 277 | 225 | 283 | 0 | 168 | 150 | 0 | 290 | 0 |
N.S. |
1 | 0.97 | 0.79 | 0.99 | 0.00 | 0.59 | 0.53 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.387 | 22.228 | 1.264 | 0.000 | 0.104 | 10.137 | 0.000 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 247 | 189 | 236 | 0 | 124 | 150 | 0 | 221 | 0 |
N.S. |
1 | 1.04 | 0.80 | 1.00 | 0.00 | 0.52 | 0.63 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.350 | 11.169 | 0.818 | 0.000 | 0.100 | 3.541 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 238 | 171 | 222 | 0 | 108 | 153 | 0 | 231 | 0 |
N.S. |
1 | 1.02 | 0.73 | 0.95 | 0.00 | 0.46 | 0.65 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.329 | 11.148 | 0.825 | 0.000 | 0.098 | 6.047 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 202 | 160 | 208 | 0 | 102 | 144 | 0 | 232 | 0 |
N.S. |
1 | 0.96 | 0.76 | 0.99 | 0.00 | 0.49 | 0.69 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.310 | 10.149 | 1.093 | 0.000 | 0.101 | 10.159 | 0.000 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 206 | 187 | 233 | 0 | 118 | 151 | 0 | 232 | 0 |
N.S. |
1 | 0.97 | 0.88 | 1.09 | 0.00 | 0.55 | 0.71 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.317 | 10.126 | 1.481 | 0.000 | 0.090 | 68.679 | 0.000 | 0.582 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 235 | 218 | 273 | 0 | 157 | 0 | 0 | 232 | 0 |
N.S. |
1 | 0.90 | 0.84 | 1.05 | 0.00 | 0.60 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.335 | 10.141 | 2.183 | 0.000 | 0.093 | 0.000 | 0.000 | 0.842 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 413 | 145 | 290 | 0 | 134 | 150 | 0 | 215 | 0 |
N.S. |
1 | 0.98 | 0.34 | 0.69 | 0.00 | 0.32 | 0.36 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.510 | 21.132 | 0.913 | 0.000 | 0.098 | 3.746 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 405 | 129 | 269 | 0 | 113 | 153 | 0 | 225 | 0 |
N.S. |
1 | 0.96 | 0.31 | 0.64 | 0.00 | 0.27 | 0.36 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.471 | 11.090 | 0.779 | 0.000 | 0.100 | 4.810 | 0.000 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 412 | 125 | 272 | 0 | 115 | 160 | 0 | 237 | 0 |
N.S. |
1 | 0.98 | 0.30 | 0.65 | 0.00 | 0.27 | 0.38 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.488 | 11.097 | 0.943 | 0.000 | 0.100 | 16.470 | 0.000 | 0.379 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 335 | 148 | 282 | 0 | 126 | 151 | 0 | 232 | 0 |
N.S. |
1 | 0.87 | 0.39 | 0.74 | 0.00 | 0.33 | 0.39 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.437 | 10.089 | 1.303 | 0.000 | 0.101 | 26.227 | 0.000 | 0.479 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 366 | 182 | 323 | 0 | 164 | 0 | 0 | 232 | 0 |
N.S. |
1 | 0.84 | 0.42 | 0.74 | 0.00 | 0.38 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.451 | 20.133 | 2.075 | 0.000 | 0.091 | 0.000 | 0.000 | 0.683 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 308 | 259 | 324 | 0 | 208 | 306 | 0 | 361 | 0 |
N.S. |
1 | 0.91 | 0.77 | 0.96 | 0.00 | 0.62 | 0.91 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.395 | 11.204 | 1.656 | 0.000 | 0.114 | 25.172 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 274 | 223 | 276 | 0 | 162 | 306 | 0 | 292 | 0 |
N.S. |
1 | 0.97 | 0.79 | 0.98 | 0.00 | 0.57 | 1.08 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.369 | 11.195 | 1.355 | 0.000 | 0.106 | 8.971 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 274 | 202 | 260 | 0 | 146 | 309 | 0 | 296 | 0 |
N.S. |
1 | 0.95 | 0.70 | 0.90 | 0.00 | 0.51 | 1.07 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.359 | 11.179 | 1.116 | 0.000 | 0.108 | 15.834 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 282 | 180 | 235 | 0 | 127 | 320 | 0 | 302 | 0 |
N.S. |
1 | 0.98 | 0.62 | 0.81 | 0.00 | 0.44 | 1.11 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.365 | 11.164 | 1.326 | 0.000 | 0.100 | 90.253 | 0.000 | 0.470 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 285 | 200 | 259 | 0 | 136 | 0 | 0 | 302 | 0 |
N.S. |
1 | 0.97 | 0.68 | 0.88 | 0.00 | 0.46 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.377 | 11.195 | 1.676 | 0.000 | 0.114 | 0.000 | 0.000 | 0.621 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 527 | 477 | 210 | 376 | 0 | 228 | 306 | 0 | 360 | 0 |
N.S. |
1 | 0.91 | 0.40 | 0.71 | 0.00 | 0.43 | 0.58 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.557 | 11.144 | 2.013 | 0.000 | 0.111 | 75.385 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 445 | 179 | 331 | 0 | 173 | 306 | 0 | 286 | 0 |
N.S. |
1 | 0.93 | 0.37 | 0.69 | 0.00 | 0.36 | 0.64 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.498 | 11.125 | 1.340 | 0.000 | 0.109 | 9.839 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 476 | 437 | 161 | 307 | 0 | 151 | 309 | 0 | 290 | 0 |
N.S. |
1 | 0.92 | 0.34 | 0.64 | 0.00 | 0.32 | 0.65 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.515 | 11.107 | 1.089 | 0.000 | 0.101 | 13.523 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 468 | 440 | 141 | 285 | 0 | 135 | 320 | 0 | 302 | 0 |
N.S. |
1 | 0.94 | 0.30 | 0.61 | 0.00 | 0.29 | 0.68 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.512 | 11.124 | 1.208 | 0.000 | 0.107 | 31.776 | 0.000 | 0.416 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 247 | 190 | 242 | 0 | 128 | 144 | 0 | 219 | 0 |
N.S. |
1 | 1.03 | 0.79 | 1.01 | 0.00 | 0.53 | 0.60 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.336 | 11.173 | 1.125 | 0.000 | 0.100 | 8.702 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 214 | 148 | 198 | 0 | 88 | 144 | 0 | 155 | 0 |
N.S. |
1 | 1.12 | 0.77 | 1.04 | 0.00 | 0.46 | 0.75 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.325 | 11.191 | 0.803 | 0.000 | 0.092 | 3.786 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 205 | 165 | 208 | 0 | 88 | 148 | 0 | 171 | 0 |
N.S. |
1 | 1.11 | 0.90 | 1.13 | 0.00 | 0.48 | 0.80 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.312 | 11.135 | 1.006 | 0.000 | 0.105 | 7.193 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 216 | 159 | 212 | 0 | 99 | 155 | 0 | 177 | 0 |
N.S. |
1 | 1.12 | 0.82 | 1.10 | 0.00 | 0.51 | 0.80 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.327 | 11.152 | 1.396 | 0.000 | 0.091 | 63.567 | 0.000 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 255 | 196 | 249 | 0 | 124 | 0 | 0 | 177 | 0 |
N.S. |
1 | 1.05 | 0.81 | 1.03 | 0.00 | 0.51 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.353 | 11.186 | 2.105 | 0.000 | 0.100 | 0.000 | 0.000 | 0.536 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 430 | 416 | 143 | 294 | 0 | 145 | 144 | 0 | 218 | 0 |
N.S. |
1 | 0.97 | 0.33 | 0.68 | 0.00 | 0.34 | 0.33 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.504 | 11.122 | 1.533 | 0.000 | 0.099 | 24.283 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 382 | 111 | 252 | 0 | 99 | 144 | 0 | 148 | 0 |
N.S. |
1 | 1.02 | 0.30 | 0.67 | 0.00 | 0.26 | 0.38 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.470 | 11.091 | 1.075 | 0.000 | 0.100 | 4.449 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 374 | 115 | 258 | 0 | 95 | 148 | 0 | 165 | 0 |
N.S. |
1 | 1.01 | 0.31 | 0.69 | 0.00 | 0.26 | 0.40 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.457 | 11.079 | 0.834 | 0.000 | 0.104 | 4.438 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 383 | 116 | 261 | 0 | 105 | 155 | 0 | 177 | 0 |
N.S. |
1 | 1.01 | 0.30 | 0.69 | 0.00 | 0.28 | 0.41 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.474 | 11.085 | 1.150 | 0.000 | 0.107 | 21.731 | 0.000 | 0.363 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 422 | 155 | 299 | 0 | 133 | 0 | 0 | 177 | 0 |
N.S. |
1 | 0.96 | 0.35 | 0.68 | 0.00 | 0.30 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.510 | 11.134 | 1.717 | 0.000 | 0.091 | 0.000 | 0.000 | 0.488 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 284 | 226 | 407 | 0 | 229 | 0 | 0 | 478 | 0 |
N.S. |
1 | 1.02 | 0.81 | 1.46 | 0.00 | 0.82 | 0.00 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.367 | 11.184 | 2.200 | 0.000 | 0.112 | 0.000 | 0.000 | 0.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 246 | 191 | 331 | 0 | 173 | 0 | 0 | 405 | 0 |
N.S. |
1 | 1.09 | 0.85 | 1.47 | 0.00 | 0.77 | 0.00 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.347 | 11.153 | 1.579 | 0.000 | 0.109 | 0.000 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 215 | 174 | 259 | 0 | 148 | 0 | 0 | 339 | 0 |
N.S. |
1 | 1.11 | 0.90 | 1.34 | 0.00 | 0.77 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.334 | 11.124 | 1.678 | 0.000 | 0.095 | 0.000 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 232 | 181 | 268 | 0 | 164 | 0 | 0 | 367 | 0 |
N.S. |
1 | 1.20 | 0.93 | 1.38 | 0.00 | 0.85 | 0.00 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.335 | 11.146 | 1.947 | 0.000 | 0.091 | 0.000 | 0.000 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 252 | 201 | 292 | 0 | 186 | 0 | 0 | 373 | 0 |
N.S. |
1 | 1.11 | 0.88 | 1.28 | 0.00 | 0.82 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.354 | 11.202 | 2.483 | 0.000 | 0.096 | 0.000 | 0.000 | 0.632 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 288 | 236 | 355 | 0 | 212 | 0 | 0 | 373 | 0 |
N.S. |
1 | 1.02 | 0.84 | 1.26 | 0.00 | 0.75 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.385 | 11.230 | 3.352 | 0.000 | 0.097 | 0.000 | 0.000 | 0.963 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 412 | 415 | 133 | 386 | 0 | 194 | 0 | 0 | 398 | 0 |
N.S. |
1 | 1.01 | 0.32 | 0.94 | 0.00 | 0.47 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.515 | 11.115 | 2.233 | 0.000 | 0.112 | 0.000 | 0.000 | 0.380 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 382 | 119 | 319 | 0 | 156 | 0 | 0 | 326 | 0 |
N.S. |
1 | 0.99 | 0.31 | 0.83 | 0.00 | 0.41 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.475 | 11.089 | 1.619 | 0.000 | 0.101 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 390 | 126 | 327 | 0 | 166 | 0 | 0 | 361 | 0 |
N.S. |
1 | 0.97 | 0.31 | 0.81 | 0.00 | 0.41 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.490 | 11.085 | 1.866 | 0.000 | 0.100 | 0.000 | 0.000 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 415 | 141 | 352 | 0 | 194 | 0 | 0 | 373 | 0 |
N.S. |
1 | 0.89 | 0.30 | 0.76 | 0.00 | 0.42 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.508 | 11.093 | 2.405 | 0.000 | 0.090 | 0.000 | 0.000 | 0.538 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 284 | 222 | 420 | 0 | 275 | 0 | 0 | 734 | 0 |
N.S. |
1 | 1.03 | 0.81 | 1.53 | 0.00 | 1.00 | 0.00 | 0.00 | 2.67 | 0.00 |
time (sec) |
N/A | 0.382 | 11.210 | 3.163 | 0.000 | 0.130 | 0.000 | 0.000 | 0.615 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 243 | 204 | 329 | 0 | 239 | 0 | 0 | 661 | 0 |
N.S. |
1 | 1.03 | 0.87 | 1.40 | 0.00 | 1.02 | 0.00 | 0.00 | 2.81 | 0.00 |
time (sec) |
N/A | 0.346 | 11.193 | 2.783 | 0.000 | 0.112 | 0.000 | 0.000 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 232 | 169 | 280 | 0 | 223 | 0 | 0 | 595 | 0 |
N.S. |
1 | 1.09 | 0.79 | 1.31 | 0.00 | 1.05 | 0.00 | 0.00 | 2.79 | 0.00 |
time (sec) |
N/A | 0.339 | 11.205 | 1.835 | 0.000 | 0.106 | 0.000 | 0.000 | 0.492 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 260 | 211 | 318 | 0 | 249 | 0 | 0 | 635 | 0 |
N.S. |
1 | 1.05 | 0.85 | 1.28 | 0.00 | 1.00 | 0.00 | 0.00 | 2.56 | 0.00 |
time (sec) |
N/A | 0.374 | 11.219 | 3.392 | 0.000 | 0.097 | 0.000 | 0.000 | 0.691 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 285 | 227 | 353 | 0 | 276 | 0 | 0 | 641 | 0 |
N.S. |
1 | 1.03 | 0.82 | 1.28 | 0.00 | 1.00 | 0.00 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.384 | 11.238 | 4.219 | 0.000 | 0.098 | 0.000 | 0.000 | 1.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 413 | 153 | 387 | 0 | 262 | 0 | 0 | 648 | 0 |
N.S. |
1 | 0.96 | 0.36 | 0.90 | 0.00 | 0.61 | 0.00 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.496 | 11.142 | 2.980 | 0.000 | 0.115 | 0.000 | 0.000 | 0.509 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 398 | 133 | 337 | 0 | 232 | 0 | 0 | 576 | 0 |
N.S. |
1 | 0.99 | 0.33 | 0.84 | 0.00 | 0.58 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.483 | 11.116 | 1.565 | 0.000 | 0.105 | 0.000 | 0.000 | 0.481 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 425 | 161 | 378 | 0 | 255 | 0 | 0 | 629 | 0 |
N.S. |
1 | 0.92 | 0.35 | 0.82 | 0.00 | 0.55 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.521 | 11.103 | 3.091 | 0.000 | 0.094 | 0.000 | 0.000 | 0.566 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 451 | 181 | 412 | 0 | 284 | 0 | 0 | 641 | 0 |
N.S. |
1 | 0.87 | 0.35 | 0.79 | 0.00 | 0.55 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.538 | 11.143 | 3.992 | 0.000 | 0.090 | 0.000 | 0.000 | 0.923 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 402 | 187 | 523 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.08 | 0.50 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.834 | 11.163 | 1.707 | 0.000 | 0.000 | 0.000 | 0.000 | 200.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 331 | 143 | 484 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 0.45 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.649 | 11.119 | 1.518 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 282 | 67 | 640 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.24 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.544 | 11.033 | 0.710 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 320 | 146 | 745 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.04 | 0.47 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.637 | 11.110 | 1.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.918 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 383 | 193 | 888 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.06 | 0.54 | 2.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.825 | 11.223 | 1.455 | 0.000 | 0.000 | 0.000 | 0.000 | 1.470 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 424 | 143 | 528 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.02 | 0.35 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.761 | 11.126 | 1.514 | 0.000 | 0.000 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 372 | 69 | 690 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.02 | 0.19 | 1.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.897 | 11.046 | 0.592 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 392 | 401 | 143 | 819 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.02 | 0.36 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.710 | 11.087 | 0.929 | 0.000 | 0.000 | 0.000 | 0.000 | 0.794 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 457 | 471 | 190 | 1030 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.03 | 0.42 | 2.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.860 | 11.182 | 1.188 | 0.000 | 0.000 | 0.000 | 0.000 | 1.696 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 403 | 182 | 527 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.08 | 0.49 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.866 | 11.173 | 1.540 | 0.000 | 0.000 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 338 | 153 | 488 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.03 | 0.47 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.701 | 11.133 | 1.618 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |