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 | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 200 | 204 | 124 | 0 | 1645 | 0 | 174 | 255 |
N.S. |
1 | 1.50 | 1.53 | 0.93 | 0.00 | 12.37 | 0.00 | 1.31 | 1.92 |
time (sec) |
N/A | 0.695 | 0.326 | 0.679 | 0.000 | 0.287 | 0.000 | 0.257 | 2.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 54 | 31 | 167 | 216 | 0 | 50 | 42 |
N.S. |
1 | 1.00 | 2.84 | 1.63 | 8.79 | 11.37 | 0.00 | 2.63 | 2.21 |
time (sec) |
N/A | 0.207 | 0.257 | 12.404 | 0.204 | 0.239 | 0.000 | 0.264 | 2.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 140 | 117 | 160 | 289 | 1268 | 3813 | 251 | 159 |
N.S. |
1 | 1.35 | 1.12 | 1.54 | 2.78 | 12.19 | 36.66 | 2.41 | 1.53 |
time (sec) |
N/A | 0.743 | 0.688 | 0.552 | 0.219 | 0.288 | 1.861 | 0.273 | 2.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 26 | 40 | 41 | 167 | 216 | 0 | 48 | 42 |
N.S. |
1 | 1.37 | 2.11 | 2.16 | 8.79 | 11.37 | 0.00 | 2.53 | 2.21 |
time (sec) |
N/A | 0.206 | 0.069 | 5.859 | 0.198 | 0.250 | 0.000 | 0.254 | 2.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 130 | 119 | 158 | 292 | 1269 | 3840 | 251 | 159 |
N.S. |
1 | 1.25 | 1.14 | 1.52 | 2.81 | 12.20 | 36.92 | 2.41 | 1.53 |
time (sec) |
N/A | 0.717 | 0.631 | 0.542 | 0.213 | 0.263 | 1.771 | 0.266 | 2.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 88 | 79 | 92 | 0 | 427 | 678 | 60 | 157 |
N.S. |
1 | 1.22 | 1.10 | 1.28 | 0.00 | 5.93 | 9.42 | 0.83 | 2.18 |
time (sec) |
N/A | 0.436 | 0.159 | 0.247 | 0.000 | 0.282 | 124.528 | 0.277 | 2.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 110 | 73 | 98 | 83 | 334 | 0 | 101 | 81 |
N.S. |
1 | 1.08 | 0.72 | 0.96 | 0.81 | 3.27 | 0.00 | 0.99 | 0.79 |
time (sec) |
N/A | 0.629 | 0.144 | 0.587 | 0.197 | 0.254 | 0.000 | 0.259 | 2.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 153 | 180 | 166 | 0 | 1861 | 0 | 163 | 261 |
N.S. |
1 | 1.12 | 1.31 | 1.21 | 0.00 | 13.58 | 0.00 | 1.19 | 1.91 |
time (sec) |
N/A | 0.747 | 0.781 | 3.858 | 0.000 | 0.291 | 0.000 | 0.250 | 2.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 113 | 73 | 99 | 84 | 334 | 0 | 102 | 81 |
N.S. |
1 | 1.11 | 0.72 | 0.97 | 0.82 | 3.27 | 0.00 | 1.00 | 0.79 |
time (sec) |
N/A | 0.620 | 0.372 | 0.617 | 0.194 | 0.259 | 0.000 | 0.257 | 2.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 142 | 179 | 168 | 0 | 1847 | 0 | 159 | 260 |
N.S. |
1 | 1.16 | 1.47 | 1.38 | 0.00 | 15.14 | 0.00 | 1.30 | 2.13 |
time (sec) |
N/A | 0.825 | 0.792 | 2.379 | 0.000 | 0.279 | 0.000 | 0.266 | 2.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 198 | 128 | 160 | 153 | 1158 | 0 | 199 | 127 |
N.S. |
1 | 1.02 | 0.66 | 0.82 | 0.79 | 5.97 | 0.00 | 1.03 | 0.65 |
time (sec) |
N/A | 1.236 | 0.433 | 10.944 | 0.205 | 0.267 | 0.000 | 0.255 | 2.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 156 | 167 | 174 | 0 | 1829 | 0 | 163 | 259 |
N.S. |
1 | 1.14 | 1.22 | 1.27 | 0.00 | 13.35 | 0.00 | 1.19 | 1.89 |
time (sec) |
N/A | 0.747 | 0.865 | 1.922 | 0.000 | 0.297 | 0.000 | 0.257 | 2.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 190 | 126 | 161 | 150 | 1162 | 0 | 202 | 129 |
N.S. |
1 | 0.98 | 0.65 | 0.83 | 0.77 | 5.99 | 0.00 | 1.04 | 0.66 |
time (sec) |
N/A | 1.224 | 0.379 | 7.100 | 0.200 | 0.281 | 0.000 | 0.281 | 2.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 0 | 325 | 266 | 0 | 4935 | 0 | 325 | 371 |
N.S. |
1 | 0.00 | 1.53 | 1.25 | 0.00 | 23.28 | 0.00 | 1.53 | 1.75 |
time (sec) |
N/A | 0.000 | 1.631 | 31.595 | 0.000 | 0.324 | 0.000 | 0.276 | 2.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 146 | 60 | 93 | 107 | 376 | 962 | 128 | 98 |
N.S. |
1 | 1.57 | 0.65 | 1.00 | 1.15 | 4.04 | 10.34 | 1.38 | 1.05 |
time (sec) |
N/A | 0.819 | 0.137 | 0.279 | 0.210 | 0.266 | 0.835 | 0.268 | 2.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 287 | 222 | 128 | 0 | 1819 | 0 | 179 | 397 |
N.S. |
1 | 1.74 | 1.35 | 0.78 | 0.00 | 11.02 | 0.00 | 1.08 | 2.41 |
time (sec) |
N/A | 1.538 | 0.798 | 0.675 | 0.000 | 0.288 | 0.000 | 0.260 | 2.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 0 | 176 | 177 | 241 | 1655 | 0 | 238 | 127 |
N.S. |
1 | 0.00 | 0.82 | 0.82 | 1.12 | 7.70 | 0.00 | 1.11 | 0.59 |
time (sec) |
N/A | 0.000 | 0.804 | 2.153 | 0.209 | 0.285 | 0.000 | 0.285 | 2.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 290 | 264 | 130 | 0 | 1805 | 0 | 179 | 397 |
N.S. |
1 | 1.78 | 1.62 | 0.80 | 0.00 | 11.07 | 0.00 | 1.10 | 2.44 |
time (sec) |
N/A | 1.530 | 0.662 | 0.687 | 0.000 | 0.289 | 0.000 | 0.256 | 2.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 0 | 174 | 190 | 244 | 1726 | 0 | 232 | 132 |
N.S. |
1 | 0.00 | 0.85 | 0.93 | 1.19 | 8.42 | 0.00 | 1.13 | 0.64 |
time (sec) |
N/A | 0.000 | 1.348 | 1.681 | 0.207 | 0.286 | 0.000 | 0.265 | 2.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 0 | 474 | 208 | 0 | 5061 | 0 | 310 | 592 |
N.S. |
1 | 0.00 | 1.82 | 0.80 | 0.00 | 19.39 | 0.00 | 1.19 | 2.27 |
time (sec) |
N/A | 0.000 | 2.783 | 6.113 | 0.000 | 0.332 | 0.000 | 0.269 | 2.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 0 | 183 | 178 | 240 | 1661 | 0 | 240 | 127 |
N.S. |
1 | 0.00 | 0.85 | 0.83 | 1.12 | 7.73 | 0.00 | 1.12 | 0.59 |
time (sec) |
N/A | 0.000 | 0.866 | 1.681 | 0.198 | 0.284 | 0.000 | 0.257 | 2.590 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 259 | 0 | 481 | 198 | 0 | 5031 | 0 | 310 | 590 |
N.S. |
1 | 0.00 | 1.86 | 0.76 | 0.00 | 19.42 | 0.00 | 1.20 | 2.28 |
time (sec) |
N/A | 0.000 | 1.465 | 4.435 | 0.000 | 0.361 | 0.000 | 0.278 | 2.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 314 | 0 | 366 | 276 | 384 | 4001 | 0 | 384 | 173 |
N.S. |
1 | 0.00 | 1.17 | 0.88 | 1.22 | 12.74 | 0.00 | 1.22 | 0.55 |
time (sec) |
N/A | 0.000 | 1.031 | 17.210 | 0.211 | 0.315 | 0.000 | 0.267 | 2.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 89 | 78 | 126 | 0 | 233 | 367 | 80 | 178 |
N.S. |
1 | 1.11 | 0.98 | 1.58 | 0.00 | 2.91 | 4.59 | 1.00 | 2.22 |
time (sec) |
N/A | 0.328 | 0.608 | 0.844 | 0.000 | 0.281 | 26.639 | 0.263 | 4.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 90 | 155 | 115 | 0 | 679 | 0 | 83 | 168 |
N.S. |
1 | 1.10 | 1.89 | 1.40 | 0.00 | 8.28 | 0.00 | 1.01 | 2.05 |
time (sec) |
N/A | 0.350 | 0.484 | 5.330 | 0.000 | 0.272 | 0.000 | 0.261 | 2.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 145 | 134 | 187 | 0 | 1855 | 0 | 152 | 217 |
N.S. |
1 | 1.18 | 1.09 | 1.52 | 0.00 | 15.08 | 0.00 | 1.24 | 1.76 |
time (sec) |
N/A | 0.526 | 1.026 | 31.777 | 0.000 | 0.313 | 0.000 | 0.267 | 2.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 89 | 78 | 126 | 0 | 234 | 697 | 80 | 177 |
N.S. |
1 | 1.11 | 0.98 | 1.58 | 0.00 | 2.92 | 8.71 | 1.00 | 2.21 |
time (sec) |
N/A | 0.331 | 0.150 | 0.611 | 0.000 | 0.267 | 30.011 | 0.260 | 3.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 87 | 151 | 116 | 0 | 680 | 0 | 83 | 168 |
N.S. |
1 | 1.12 | 1.94 | 1.49 | 0.00 | 8.72 | 0.00 | 1.06 | 2.15 |
time (sec) |
N/A | 0.340 | 0.221 | 2.604 | 0.000 | 0.274 | 0.000 | 0.256 | 2.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 143 | 134 | 211 | 0 | 1855 | 0 | 152 | 216 |
N.S. |
1 | 1.19 | 1.12 | 1.76 | 0.00 | 15.46 | 0.00 | 1.27 | 1.80 |
time (sec) |
N/A | 0.505 | 0.759 | 13.826 | 0.000 | 0.299 | 0.000 | 0.258 | 2.395 |
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 | 11 | 11 | 17 | 7 | 6 | 16 | 8 | 6 | 6 |
N.S. |
1 | 1.00 | 1.55 | 0.64 | 0.55 | 1.45 | 0.73 | 0.55 | 0.55 |
time (sec) |
N/A | 0.211 | 0.032 | 0.346 | 0.194 | 0.243 | 0.215 | 0.269 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 17 | 7 | 6 | 19 | 10 | 6 | 6 |
N.S. |
1 | 1.00 | 1.55 | 0.64 | 0.55 | 1.73 | 0.91 | 0.55 | 0.55 |
time (sec) |
N/A | 0.210 | 0.024 | 0.306 | 0.189 | 0.256 | 0.177 | 0.261 | 2.236 |
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 | 14 | 14 | 15 | 17 | 10 | 13 | 12 | 13 | 16 |
N.S. |
1 | 1.00 | 1.07 | 1.21 | 0.71 | 0.93 | 0.86 | 0.93 | 1.14 |
time (sec) |
N/A | 0.196 | 0.051 | 0.694 | 0.190 | 0.253 | 0.075 | 0.254 | 0.095 |
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 | 53 | 53 | 43 | 56 | 87 | 60 | 326 | 54 | 53 |
N.S. |
1 | 1.00 | 0.81 | 1.06 | 1.64 | 1.13 | 6.15 | 1.02 | 1.00 |
time (sec) |
N/A | 0.243 | 0.201 | 0.444 | 0.204 | 0.256 | 0.339 | 0.257 | 2.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 87 | 87 | 118 | 0 | 749 | 0 | 88 | 199 |
N.S. |
1 | 1.12 | 1.12 | 1.51 | 0.00 | 9.60 | 0.00 | 1.13 | 2.55 |
time (sec) |
N/A | 0.343 | 0.305 | 1.653 | 0.000 | 0.285 | 0.000 | 0.253 | 2.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 70 | 63 | 337 | 232 | 0 | 70 | 67 |
N.S. |
1 | 1.00 | 0.99 | 0.89 | 4.75 | 3.27 | 0.00 | 0.99 | 0.94 |
time (sec) |
N/A | 0.323 | 0.255 | 14.047 | 0.218 | 0.253 | 0.000 | 0.263 | 2.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 101 | 90 | 175 | 0 | 264 | 643 | 89 | 302 |
N.S. |
1 | 1.10 | 0.98 | 1.90 | 0.00 | 2.87 | 6.99 | 0.97 | 3.28 |
time (sec) |
N/A | 0.352 | 0.540 | 0.641 | 0.000 | 0.273 | 30.671 | 0.252 | 4.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 97 | 106 | 133 | 0 | 799 | 0 | 95 | 210 |
N.S. |
1 | 1.10 | 1.20 | 1.51 | 0.00 | 9.08 | 0.00 | 1.08 | 2.39 |
time (sec) |
N/A | 0.362 | 0.482 | 2.408 | 0.000 | 0.287 | 0.000 | 0.253 | 2.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 158 | 146 | 228 | 0 | 1931 | 0 | 183 | 224 |
N.S. |
1 | 1.17 | 1.08 | 1.69 | 0.00 | 14.30 | 0.00 | 1.36 | 1.66 |
time (sec) |
N/A | 0.551 | 0.920 | 12.656 | 0.000 | 0.298 | 0.000 | 0.258 | 2.497 |
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 | 119 | 128 | 116 | 97 | 137 | 160 | 196 | 219 | 131 |
N.S. |
1 | 1.08 | 0.97 | 0.82 | 1.15 | 1.34 | 1.65 | 1.84 | 1.10 |
time (sec) |
N/A | 0.412 | 0.131 | 4.824 | 0.192 | 0.258 | 0.145 | 0.250 | 0.164 |
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 | 59 | 57 | 54 | 54 | 63 | 59 | 100 | 83 | 55 |
N.S. |
1 | 0.97 | 0.92 | 0.92 | 1.07 | 1.00 | 1.69 | 1.41 | 0.93 |
time (sec) |
N/A | 0.242 | 0.067 | 1.001 | 0.188 | 0.245 | 0.095 | 0.247 | 2.353 |
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 | 12 | 12 | 12 | 13 | 12 | 12 | 12 | 26 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.00 | 2.17 | 1.00 |
time (sec) |
N/A | 0.147 | 0.038 | 0.233 | 0.196 | 0.245 | 0.067 | 0.266 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 56 | 54 | 53 | 0 | 248 | 0 | 46 | 78 |
N.S. |
1 | 1.10 | 1.06 | 1.04 | 0.00 | 4.86 | 0.00 | 0.90 | 1.53 |
time (sec) |
N/A | 0.235 | 0.060 | 0.572 | 0.000 | 0.273 | 0.000 | 0.258 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 95 | 105 | 191 | 0 | 1268 | 0 | 111 | 0 |
N.S. |
1 | 1.06 | 1.17 | 2.12 | 0.00 | 14.09 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.356 | 0.193 | 3.235 | 0.000 | 0.274 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 168 | 183 | 577 | 0 | 7379 | 0 | 304 | 0 |
N.S. |
1 | 1.15 | 1.25 | 3.95 | 0.00 | 50.54 | 0.00 | 2.08 | 0.00 |
time (sec) |
N/A | 0.551 | 0.356 | 21.914 | 0.000 | 0.332 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 220 | 261 | 488 | 1588 | 0 | 23093 | 0 | 717 | 0 |
N.S. |
1 | 1.19 | 2.22 | 7.22 | 0.00 | 104.97 | 0.00 | 3.26 | 0.00 |
time (sec) |
N/A | 0.902 | 0.628 | 118.960 | 0.000 | 0.494 | 0.000 | 0.297 | 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 | 105 | 115 | 112 | 96 | 137 | 144 | 189 | 186 | 131 |
N.S. |
1 | 1.10 | 1.07 | 0.91 | 1.30 | 1.37 | 1.80 | 1.77 | 1.25 |
time (sec) |
N/A | 0.404 | 0.127 | 4.421 | 0.187 | 0.255 | 0.122 | 0.258 | 0.161 |
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 | 57 | 55 | 55 | 55 | 63 | 57 | 100 | 81 | 51 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 1.11 | 1.00 | 1.75 | 1.42 | 0.89 |
time (sec) |
N/A | 0.242 | 0.051 | 0.971 | 0.193 | 0.251 | 0.082 | 0.249 | 2.308 |
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 | 12 | 12 | 12 | 13 | 12 | 12 | 12 | 26 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.00 | 2.17 | 1.00 |
time (sec) |
N/A | 0.153 | 0.003 | 0.223 | 0.182 | 0.245 | 0.053 | 0.263 | 2.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 35 | 14 | 36 | 32 | 17 | 39 | 46 |
N.S. |
1 | 1.00 | 2.33 | 0.93 | 2.40 | 2.13 | 1.13 | 2.60 | 3.07 |
time (sec) |
N/A | 0.190 | 0.030 | 0.521 | 0.192 | 0.250 | 0.255 | 0.259 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 87 | 49 | 86 | 236 | 0 | 84 | 0 |
N.S. |
1 | 1.00 | 2.02 | 1.14 | 2.00 | 5.49 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 0.287 | 0.232 | 2.254 | 0.200 | 0.261 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 92 | 148 | 103 | 248 | 1504 | 0 | 205 | 0 |
N.S. |
1 | 1.03 | 1.66 | 1.16 | 2.79 | 16.90 | 0.00 | 2.30 | 0.00 |
time (sec) |
N/A | 0.448 | 0.370 | 11.128 | 0.215 | 0.266 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 151 | 300 | 178 | 487 | 4015 | 0 | 377 | 0 |
N.S. |
1 | 1.08 | 2.14 | 1.27 | 3.48 | 28.68 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.692 | 0.413 | 44.907 | 0.228 | 0.303 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 187 | 208 | 321 | 277 | 1293 | 626 | 390 | 361 |
N.S. |
1 | 0.99 | 1.11 | 1.71 | 1.47 | 6.88 | 3.33 | 2.07 | 1.92 |
time (sec) |
N/A | 0.581 | 0.325 | 1.935 | 0.201 | 0.273 | 0.306 | 0.276 | 0.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 132 | 134 | 161 | 161 | 664 | 298 | 194 | 144 |
N.S. |
1 | 0.97 | 0.99 | 1.18 | 1.18 | 4.88 | 2.19 | 1.43 | 1.06 |
time (sec) |
N/A | 0.411 | 0.197 | 0.634 | 0.198 | 0.265 | 0.210 | 0.255 | 2.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 77 | 72 | 80 | 79 | 238 | 122 | 96 | 70 |
N.S. |
1 | 0.86 | 0.80 | 0.89 | 0.88 | 2.64 | 1.36 | 1.07 | 0.78 |
time (sec) |
N/A | 0.273 | 0.100 | 0.443 | 0.182 | 0.261 | 0.119 | 0.251 | 2.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 23 | 22 | 61 | 20 | 36 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.92 | 2.54 | 0.83 | 1.50 | 0.92 |
time (sec) |
N/A | 0.156 | 0.006 | 0.199 | 0.188 | 0.252 | 0.069 | 0.265 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 25 | 0 | 88 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.74 | 0.00 | 2.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.225 | 0.066 | 0.401 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 68 | 47 | 0 | 660 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.47 | 0.00 | 6.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.381 | 0.116 | 0.559 | 0.000 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 168 | 184 | 92 | 0 | 3035 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.26 | 0.63 | 0.00 | 20.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.541 | 0.285 | 0.684 | 0.000 | 0.451 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 236 | 425 | 184 | 0 | 6590 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 2.15 | 0.93 | 0.00 | 33.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.743 | 0.619 | 0.883 | 0.000 | 1.605 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 306 | 3775 | 899 | 0 | 928 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 12.84 | 3.06 | 0.00 | 3.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.491 | 6.275 | 1.742 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 250 | 2292 | 321 | 0 | 463 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 9.20 | 1.29 | 0.00 | 1.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.045 | 6.116 | 0.794 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 1401 | 317 | 0 | 314 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 13.74 | 3.11 | 0.00 | 3.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.379 | 6.090 | 1.824 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 237 | 251 | 0 | 108 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.32 | 2.46 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.379 | 0.407 | 0.742 | 0.000 | 0.075 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 806 | 888 | 0 | 798 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 5.17 | 5.69 | 0.00 | 5.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.523 | 6.019 | 1.023 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 322 | 335 | 2492 | 2160 | 0 | 3730 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 7.74 | 6.71 | 0.00 | 11.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.378 | 6.234 | 2.506 | 0.000 | 0.175 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 411 | 443 | 4093 | 57909 | 0 | 13897 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 9.96 | 140.90 | 0.00 | 33.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.015 | 6.424 | 8.225 | 0.000 | 0.742 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 149 | 4500 | 289 | 1783 | 784 | 0 | 315 | 0 |
N.S. |
1 | 1.06 | 32.14 | 2.06 | 12.74 | 5.60 | 0.00 | 2.25 | 0.00 |
time (sec) |
N/A | 0.523 | 56.315 | 0.604 | 2.151 | 0.323 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 4392 | 189 | 640 | 329 | 0 | 183 | 0 |
N.S. |
1 | 1.00 | 47.74 | 2.05 | 6.96 | 3.58 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 0.367 | 35.933 | 0.210 | 0.527 | 0.300 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 455 | 125 | 153 | 143 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 12.30 | 3.38 | 4.14 | 3.86 | 0.00 | 2.19 | 0.00 |
time (sec) |
N/A | 0.229 | 31.802 | 0.215 | 0.363 | 0.276 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 211 | 129 | 0 | 681 | 0 | 538 | 0 |
N.S. |
1 | 1.00 | 2.13 | 1.30 | 0.00 | 6.88 | 0.00 | 5.43 | 0.00 |
time (sec) |
N/A | 0.375 | 49.812 | 0.387 | 0.000 | 0.309 | 0.000 | 0.485 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | B | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 0 | 417 | 0 | 1801 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 2.69 | 0.00 | 11.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.534 | 0.000 | 0.238 | 0.000 | 0.434 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | B | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 225 | 0 | 817 | 0 | 5297 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.00 | 3.99 | 0.00 | 25.84 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.742 | 0.000 | 0.268 | 0.000 | 1.553 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 155 | 4368 | 275 | 1789 | 784 | 0 | 315 | 0 |
N.S. |
1 | 1.06 | 29.92 | 1.88 | 12.25 | 5.37 | 0.00 | 2.16 | 0.00 |
time (sec) |
N/A | 0.530 | 56.146 | 0.602 | 2.284 | 0.329 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 4260 | 189 | 644 | 329 | 0 | 184 | 0 |
N.S. |
1 | 1.00 | 44.38 | 1.97 | 6.71 | 3.43 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 0.373 | 31.280 | 0.221 | 0.470 | 0.291 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 4196 | 131 | 156 | 143 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 107.59 | 3.36 | 4.00 | 3.67 | 0.00 | 2.08 | 0.00 |
time (sec) |
N/A | 0.229 | 35.969 | 0.227 | 0.337 | 0.279 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 52609 | 129 | 0 | 680 | 0 | 546 | 0 |
N.S. |
1 | 1.00 | 515.77 | 1.26 | 0.00 | 6.67 | 0.00 | 5.35 | 0.00 |
time (sec) |
N/A | 0.371 | 54.832 | 0.405 | 0.000 | 0.324 | 0.000 | 0.524 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | B | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 0 | 415 | 0 | 2137 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 2.61 | 0.00 | 13.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.549 | 0.000 | 0.234 | 0.000 | 0.465 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | B | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 231 | 0 | 817 | 0 | 5675 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.00 | 3.87 | 0.00 | 26.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.764 | 0.000 | 0.287 | 0.000 | 1.632 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 113 | 86 | 177 | 0 | 429 | 0 | 106 | 472 |
N.S. |
1 | 1.06 | 0.80 | 1.65 | 0.00 | 4.01 | 0.00 | 0.99 | 4.41 |
time (sec) |
N/A | 0.412 | 0.211 | 0.431 | 0.000 | 0.265 | 0.000 | 0.265 | 7.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 120 | 86 | 178 | 0 | 438 | 0 | 106 | 324 |
N.S. |
1 | 1.06 | 0.76 | 1.58 | 0.00 | 3.88 | 0.00 | 0.94 | 2.87 |
time (sec) |
N/A | 0.431 | 0.423 | 0.280 | 0.000 | 0.284 | 0.000 | 0.270 | 0.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 120 | 86 | 181 | 0 | 455 | 0 | 106 | 325 |
N.S. |
1 | 1.15 | 0.83 | 1.74 | 0.00 | 4.38 | 0.00 | 1.02 | 3.12 |
time (sec) |
N/A | 0.371 | 0.386 | 0.296 | 0.000 | 0.275 | 0.000 | 0.259 | 2.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 28 | 18 | 11 | 10 | 19 | 34 | 10 | 10 |
N.S. |
1 | 1.56 | 1.00 | 0.61 | 0.56 | 1.06 | 1.89 | 0.56 | 0.56 |
time (sec) |
N/A | 0.193 | 0.114 | 0.108 | 0.206 | 0.247 | 0.319 | 0.267 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 60 | 54 | 53 | 0 | 234 | 0 | 46 | 78 |
N.S. |
1 | 1.11 | 1.00 | 0.98 | 0.00 | 4.33 | 0.00 | 0.85 | 1.44 |
time (sec) |
N/A | 0.292 | 0.059 | 0.265 | 0.000 | 0.273 | 0.000 | 0.259 | 0.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 144 | 96 | 167 | 0 | 486 | 0 | 126 | 1069 |
N.S. |
1 | 0.99 | 0.66 | 1.14 | 0.00 | 3.33 | 0.00 | 0.86 | 7.32 |
time (sec) |
N/A | 0.653 | 0.318 | 2.089 | 0.000 | 0.919 | 0.000 | 0.252 | 30.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 25 | 28 | 12 | 11 | 17 | 0 | 13 | 11 |
N.S. |
1 | 1.32 | 1.47 | 0.63 | 0.58 | 0.89 | 0.00 | 0.68 | 0.58 |
time (sec) |
N/A | 0.261 | 0.224 | 0.127 | 0.199 | 0.252 | 0.000 | 0.254 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 62 | 54 | 53 | 0 | 244 | 0 | 46 | 78 |
N.S. |
1 | 1.24 | 1.08 | 1.06 | 0.00 | 4.88 | 0.00 | 0.92 | 1.56 |
time (sec) |
N/A | 0.299 | 0.069 | 0.244 | 0.000 | 0.265 | 0.000 | 0.254 | 0.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 108 | 124 | 0 | 546 | 0 | 122 | 1069 |
N.S. |
1 | 1.00 | 0.92 | 1.05 | 0.00 | 4.63 | 0.00 | 1.03 | 9.06 |
time (sec) |
N/A | 0.628 | 1.565 | 0.429 | 0.000 | 0.900 | 0.000 | 0.274 | 8.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 115 | 104 | 200 | 0 | 505 | 0 | 122 | 377 |
N.S. |
1 | 0.96 | 0.87 | 1.67 | 0.00 | 4.21 | 0.00 | 1.02 | 3.14 |
time (sec) |
N/A | 0.392 | 1.008 | 0.371 | 0.000 | 0.279 | 0.000 | 0.257 | 0.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 130 | 224 | 0 | 2211 | 0 | 179 | 0 |
N.S. |
1 | 1.05 | 1.20 | 2.07 | 0.00 | 20.47 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.402 | 0.540 | 1.709 | 0.000 | 0.305 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 219 | 373 | 836 | 0 | 12285 | 0 | 625 | 0 |
N.S. |
1 | 1.11 | 1.88 | 4.22 | 0.00 | 62.05 | 0.00 | 3.16 | 0.00 |
time (sec) |
N/A | 0.696 | 0.997 | 11.623 | 0.000 | 0.594 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 116 | 104 | 197 | 0 | 508 | 0 | 122 | 375 |
N.S. |
1 | 0.96 | 0.86 | 1.63 | 0.00 | 4.20 | 0.00 | 1.01 | 3.10 |
time (sec) |
N/A | 0.388 | 0.211 | 0.345 | 0.000 | 0.276 | 0.000 | 0.262 | 0.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 125 | 225 | 0 | 2228 | 0 | 177 | 0 |
N.S. |
1 | 1.05 | 1.16 | 2.08 | 0.00 | 20.63 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.397 | 0.237 | 1.701 | 0.000 | 0.314 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 216 | 336 | 857 | 0 | 12366 | 0 | 625 | 0 |
N.S. |
1 | 1.11 | 1.73 | 4.42 | 0.00 | 63.74 | 0.00 | 3.22 | 0.00 |
time (sec) |
N/A | 0.706 | 0.504 | 11.589 | 0.000 | 0.603 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 130 | 107 | 226 | 0 | 583 | 0 | 125 | 376 |
N.S. |
1 | 1.04 | 0.86 | 1.81 | 0.00 | 4.66 | 0.00 | 1.00 | 3.01 |
time (sec) |
N/A | 0.398 | 0.838 | 0.375 | 0.000 | 0.285 | 0.000 | 0.256 | 0.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 123 | 225 | 0 | 2119 | 0 | 179 | 0 |
N.S. |
1 | 1.05 | 1.14 | 2.08 | 0.00 | 19.62 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.406 | 0.494 | 1.722 | 0.000 | 0.306 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 215 | 319 | 800 | 0 | 10107 | 0 | 577 | 0 |
N.S. |
1 | 1.11 | 1.64 | 4.12 | 0.00 | 52.10 | 0.00 | 2.97 | 0.00 |
time (sec) |
N/A | 0.673 | 1.039 | 11.484 | 0.000 | 0.589 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 142 | 119 | 237 | 0 | 605 | 0 | 136 | 454 |
N.S. |
1 | 1.04 | 0.87 | 1.73 | 0.00 | 4.42 | 0.00 | 0.99 | 3.31 |
time (sec) |
N/A | 0.425 | 0.941 | 0.413 | 0.000 | 0.296 | 0.000 | 0.279 | 3.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 126 | 143 | 249 | 0 | 2541 | 0 | 207 | 0 |
N.S. |
1 | 1.04 | 1.18 | 2.06 | 0.00 | 21.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.416 | 0.713 | 1.736 | 0.000 | 0.309 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 255 | 465 | 1084 | 0 | 13813 | 0 | 819 | 0 |
N.S. |
1 | 1.09 | 2.00 | 4.65 | 0.00 | 59.28 | 0.00 | 3.52 | 0.00 |
time (sec) |
N/A | 0.776 | 1.317 | 11.799 | 0.000 | 0.728 | 0.000 | 0.296 | 0.000 |