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 | C | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 214 | 813 | 451 | 0 | 474 | 0 | 0 | 161 | 0 |
N.S. |
1 | 0.98 | 3.73 | 2.07 | 0.00 | 2.17 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 1.339 | 10.843 | 5.718 | 0.000 | 0.106 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 241 | 573 | 465 | 0 | 487 | 0 | 0 | 161 | 0 |
N.S. |
1 | 0.97 | 2.30 | 1.87 | 0.00 | 1.96 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.501 | 9.664 | 6.659 | 0.000 | 0.107 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 276 | 623 | 479 | 0 | 500 | 0 | 0 | 161 | 0 |
N.S. |
1 | 0.95 | 2.15 | 1.65 | 0.00 | 1.72 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 1.608 | 12.282 | 7.974 | 0.000 | 0.118 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 241 | 124 | 486 | 659 | 115 | 0 | 0 | 70 | 581 |
N.S. |
1 | 1.13 | 0.58 | 2.28 | 3.09 | 0.54 | 0.00 | 0.00 | 0.33 | 2.73 |
time (sec) |
N/A | 1.258 | 0.800 | 27.227 | 0.186 | 0.085 | 0.000 | 0.000 | 0.263 | 3.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 198 | 101 | 434 | 567 | 97 | 0 | 0 | 70 | 441 |
N.S. |
1 | 1.18 | 0.60 | 2.58 | 3.38 | 0.58 | 0.00 | 0.00 | 0.42 | 2.62 |
time (sec) |
N/A | 1.062 | 0.597 | 18.868 | 0.196 | 0.101 | 0.000 | 0.000 | 0.253 | 3.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 156 | 73 | 382 | 474 | 80 | 0 | 0 | 70 | 172 |
N.S. |
1 | 1.27 | 0.59 | 3.11 | 3.85 | 0.65 | 0.00 | 0.00 | 0.57 | 1.40 |
time (sec) |
N/A | 0.890 | 0.364 | 10.776 | 0.211 | 0.079 | 0.000 | 0.000 | 0.264 | 1.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 145 | 90 | 461 | 1360 | 120 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.07 | 0.66 | 3.39 | 10.00 | 0.88 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.880 | 0.285 | 7.202 | 0.364 | 0.096 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 145 | 100 | 434 | 890 | 102 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.06 | 0.73 | 3.17 | 6.50 | 0.74 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.906 | 0.302 | 6.710 | 0.348 | 0.098 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 149 | 118 | 584 | 1207 | 122 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.03 | 0.82 | 4.06 | 8.38 | 0.85 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.885 | 0.374 | 7.909 | 0.377 | 0.122 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 193 | 132 | 0 | 2713 | 140 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.02 | 0.70 | 0.00 | 14.35 | 0.74 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.064 | 0.686 | 0.000 | 0.507 | 0.136 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 236 | 149 | 986 | 7700 | 157 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.01 | 0.64 | 4.21 | 32.91 | 0.67 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.263 | 1.067 | 18.324 | 0.751 | 0.162 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 295 | 146 | 148 | 712 | 138 | 0 | 0 | 143 | 387 |
N.S. |
1 | 1.11 | 0.55 | 0.56 | 2.68 | 0.52 | 0.00 | 0.00 | 0.54 | 1.45 |
time (sec) |
N/A | 1.701 | 0.814 | 1.740 | 0.227 | 0.085 | 0.000 | 0.000 | 0.345 | 3.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 252 | 123 | 128 | 619 | 119 | 0 | 0 | 143 | 320 |
N.S. |
1 | 1.15 | 0.56 | 0.58 | 2.83 | 0.54 | 0.00 | 0.00 | 0.65 | 1.46 |
time (sec) |
N/A | 1.496 | 0.855 | 1.603 | 0.233 | 0.083 | 0.000 | 0.000 | 0.340 | 3.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 208 | 102 | 108 | 527 | 100 | 0 | 0 | 143 | 299 |
N.S. |
1 | 1.21 | 0.59 | 0.63 | 3.06 | 0.58 | 0.00 | 0.00 | 0.83 | 1.74 |
time (sec) |
N/A | 1.262 | 0.655 | 1.605 | 0.230 | 0.100 | 0.000 | 0.000 | 0.353 | 3.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 190 | 121 | 159 | 1700 | 146 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.04 | 0.66 | 0.87 | 9.29 | 0.80 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 1.213 | 0.828 | 1.721 | 0.388 | 0.112 | 0.000 | 0.000 | 0.350 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 190 | 116 | 148 | 1393 | 138 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.05 | 0.64 | 0.82 | 7.70 | 0.76 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 1.227 | 0.587 | 2.023 | 0.433 | 0.100 | 0.000 | 0.000 | 0.346 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 203 | 119 | 191 | 0 | 132 | 0 | 0 | 135 | 0 |
N.S. |
1 | 1.04 | 0.61 | 0.98 | 0.00 | 0.68 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 1.264 | 0.520 | 2.303 | 0.000 | 0.127 | 0.000 | 0.000 | 0.390 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 202 | 133 | 204 | 2746 | 147 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.06 | 0.70 | 1.07 | 14.38 | 0.77 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.236 | 0.774 | 2.388 | 0.633 | 0.128 | 0.000 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 244 | 148 | 217 | 7999 | 163 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.03 | 0.62 | 0.91 | 33.61 | 0.68 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 1.446 | 1.201 | 2.434 | 0.705 | 0.173 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 290 | 167 | 237 | 4470 | 183 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.02 | 0.59 | 0.83 | 15.68 | 0.64 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 1.709 | 2.107 | 2.411 | 0.730 | 0.171 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 347 | 171 | 164 | 763 | 170 | 0 | 0 | 221 | 897 |
N.S. |
1 | 1.11 | 0.55 | 0.52 | 2.44 | 0.54 | 0.00 | 0.00 | 0.71 | 2.87 |
time (sec) |
N/A | 2.107 | 1.487 | 0.629 | 0.200 | 0.098 | 0.000 | 0.000 | 0.488 | 3.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 300 | 149 | 144 | 671 | 148 | 0 | 0 | 221 | 751 |
N.S. |
1 | 1.13 | 0.56 | 0.54 | 2.52 | 0.56 | 0.00 | 0.00 | 0.83 | 2.82 |
time (sec) |
N/A | 1.852 | 1.098 | 0.622 | 0.239 | 0.088 | 0.000 | 0.000 | 0.472 | 3.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 256 | 127 | 124 | 579 | 129 | 0 | 0 | 221 | 721 |
N.S. |
1 | 1.17 | 0.58 | 0.57 | 2.64 | 0.59 | 0.00 | 0.00 | 1.01 | 3.29 |
time (sec) |
N/A | 1.655 | 0.997 | 1.002 | 0.182 | 0.084 | 0.000 | 0.000 | 0.490 | 3.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 242 | 151 | 179 | 2343 | 177 | 0 | 0 | 221 | 0 |
N.S. |
1 | 1.05 | 0.66 | 0.78 | 10.19 | 0.77 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 1.551 | 1.580 | 1.164 | 0.434 | 0.100 | 0.000 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 242 | 141 | 169 | 1673 | 172 | 0 | 0 | 221 | 0 |
N.S. |
1 | 1.05 | 0.61 | 0.73 | 7.27 | 0.75 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 1.597 | 1.141 | 1.236 | 0.347 | 0.105 | 0.000 | 0.000 | 0.463 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 248 | 141 | 223 | 0 | 174 | 0 | 0 | 221 | 0 |
N.S. |
1 | 1.04 | 0.59 | 0.94 | 0.00 | 0.73 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 1.626 | 0.930 | 1.223 | 0.000 | 0.126 | 0.000 | 0.000 | 0.463 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 256 | 142 | 217 | 0 | 163 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.06 | 0.59 | 0.90 | 0.00 | 0.67 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 1.598 | 0.878 | 3.925 | 0.000 | 0.132 | 0.000 | 0.000 | 0.394 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 254 | 151 | 225 | 8555 | 177 | 0 | 0 | 173 | 0 |
N.S. |
1 | 1.07 | 0.63 | 0.95 | 35.95 | 0.74 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 1.584 | 1.434 | 4.681 | 0.874 | 0.163 | 0.000 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 299 | 168 | 239 | 4556 | 197 | 0 | 0 | 221 | 0 |
N.S. |
1 | 1.05 | 0.59 | 0.84 | 15.99 | 0.69 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 1.845 | 2.521 | 3.757 | 0.805 | 0.170 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 336 | 190 | 260 | 42534 | 217 | 0 | 0 | 221 | 0 |
N.S. |
1 | 1.01 | 0.57 | 0.78 | 128.11 | 0.65 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 2.158 | 3.963 | 4.733 | 3.099 | 0.179 | 0.000 | 0.000 | 0.221 | 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 | 289 | 330 | 271 | 255 | 0 | 190 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.14 | 0.94 | 0.88 | 0.00 | 0.66 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.977 | 10.446 | 3.178 | 0.000 | 0.114 | 0.000 | 0.000 | 0.188 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 275 | 2440 | 235 | 0 | 173 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.13 | 10.00 | 0.96 | 0.00 | 0.71 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.581 | 9.774 | 3.181 | 0.000 | 0.128 | 0.000 | 0.000 | 0.184 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 220 | 1717 | 216 | 0 | 156 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.09 | 8.54 | 1.07 | 0.00 | 0.78 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 1.230 | 8.022 | 3.016 | 0.000 | 0.110 | 0.000 | 0.000 | 0.237 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 165 | 576 | 184 | 0 | 135 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.06 | 3.69 | 1.18 | 0.00 | 0.87 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.933 | 6.972 | 2.858 | 0.000 | 0.110 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 161 | 251 | 208 | 0 | 156 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.92 | 1.43 | 1.19 | 0.00 | 0.89 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.004 | 4.131 | 2.808 | 0.000 | 0.872 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 163 | 124 | 169 | 0 | 153 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.94 | 0.72 | 0.98 | 0.00 | 0.88 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.015 | 0.366 | 3.333 | 0.000 | 0.848 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 217 | 496 | 208 | 0 | 186 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.97 | 2.22 | 0.93 | 0.00 | 0.83 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.355 | 2.355 | 3.325 | 0.000 | 1.936 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 272 | 439 | 247 | 0 | 203 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.02 | 1.65 | 0.93 | 0.00 | 0.76 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.709 | 2.861 | 3.501 | 0.000 | 1.980 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 342 | 3122 | 275 | 0 | 231 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.09 | 9.91 | 0.87 | 0.00 | 0.73 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 2.003 | 9.912 | 3.483 | 0.000 | 0.121 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 283 | 2281 | 255 | 0 | 214 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.06 | 8.51 | 0.95 | 0.00 | 0.80 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 1.629 | 8.083 | 3.260 | 0.000 | 0.114 | 0.000 | 0.000 | 0.183 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 232 | 1055 | 236 | 0 | 193 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.05 | 4.77 | 1.07 | 0.00 | 0.87 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.293 | 7.008 | 3.161 | 0.000 | 0.109 | 0.000 | 0.000 | 0.211 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 175 | 460 | 199 | 0 | 161 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.02 | 2.67 | 1.16 | 0.00 | 0.94 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.955 | 5.355 | 2.991 | 0.000 | 0.111 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 171 | 245 | 226 | 0 | 207 | 0 | 0 | 97 | 0 |
N.S. |
1 | 0.92 | 1.32 | 1.22 | 0.00 | 1.12 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 1.065 | 3.249 | 2.977 | 0.000 | 2.664 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 215 | 251 | 243 | 0 | 222 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.94 | 1.10 | 1.07 | 0.00 | 0.97 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.385 | 3.028 | 3.423 | 0.000 | 2.657 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 278 | 896 | 293 | 0 | 258 | 0 | 0 | 145 | 0 |
N.S. |
1 | 0.98 | 3.14 | 1.03 | 0.00 | 0.91 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.814 | 8.090 | 3.589 | 0.000 | 5.234 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 342 | 261 | 315 | 0 | 262 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.09 | 0.83 | 1.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 2.063 | 13.071 | 3.544 | 0.000 | 0.124 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 285 | 865 | 295 | 0 | 240 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.07 | 3.25 | 1.11 | 0.00 | 0.90 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 1.663 | 9.017 | 3.326 | 0.000 | 0.117 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 230 | 730 | 259 | 0 | 208 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.05 | 3.33 | 1.18 | 0.00 | 0.95 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 1.300 | 7.423 | 3.176 | 0.000 | 0.114 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 181 | 412 | 244 | 0 | 207 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.04 | 2.37 | 1.40 | 0.00 | 1.19 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.966 | 4.011 | 3.062 | 0.000 | 0.112 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 224 | 262 | 289 | 0 | 275 | 0 | 0 | 165 | 0 |
N.S. |
1 | 0.97 | 1.13 | 1.25 | 0.00 | 1.19 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 1.434 | 4.162 | 2.872 | 0.000 | 5.841 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 272 | 274 | 297 | 0 | 288 | 0 | 0 | 181 | 0 |
N.S. |
1 | 0.98 | 0.99 | 1.07 | 0.00 | 1.04 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.770 | 4.529 | 4.415 | 0.000 | 5.806 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 332 | 968 | 362 | 0 | 324 | 0 | 0 | 181 | 0 |
N.S. |
1 | 0.99 | 2.90 | 1.08 | 0.00 | 0.97 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 2.254 | 8.693 | 4.768 | 0.000 | 10.133 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 134 | 97 | 502 | 0 | 188 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.89 | 0.64 | 3.32 | 0.00 | 1.25 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.708 | 0.589 | 126.902 | 0.000 | 0.092 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 106 | 85 | 397 | 0 | 167 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.86 | 0.69 | 3.23 | 0.00 | 1.36 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.605 | 0.467 | 87.632 | 0.000 | 0.090 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 79 | 71 | 150 | 0 | 124 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.81 | 0.73 | 1.55 | 0.00 | 1.28 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.554 | 0.319 | 126.792 | 0.000 | 0.088 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 56 | 52 | 152 | 0 | 107 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.75 | 0.69 | 2.03 | 0.00 | 1.43 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.482 | 0.347 | 2.645 | 0.000 | 0.094 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 83 | 76 | 229 | 0 | 125 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.82 | 0.75 | 2.27 | 0.00 | 1.24 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.560 | 0.380 | 8.691 | 0.000 | 0.088 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 110 | 88 | 383 | 0 | 145 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.87 | 0.69 | 3.02 | 0.00 | 1.14 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.581 | 0.608 | 8.884 | 0.000 | 0.093 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 138 | 99 | 403 | 0 | 156 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.91 | 0.66 | 2.67 | 0.00 | 1.03 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.695 | 0.879 | 23.385 | 0.000 | 0.091 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 142 | 112 | 755 | 0 | 206 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.87 | 0.69 | 4.63 | 0.00 | 1.26 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.682 | 1.873 | 129.325 | 0.000 | 0.103 | 0.000 | 0.000 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 113 | 89 | 500 | 0 | 177 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.89 | 0.70 | 3.94 | 0.00 | 1.39 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.650 | 0.799 | 83.702 | 0.000 | 0.092 | 0.000 | 0.000 | 0.375 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 82 | 75 | 195 | 0 | 134 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.81 | 0.74 | 1.93 | 0.00 | 1.33 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.530 | 0.679 | 4.127 | 0.000 | 0.090 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 89 | 80 | 274 | 0 | 135 | 0 | 0 | 50 | 0 |
N.S. |
1 | 0.85 | 0.76 | 2.61 | 0.00 | 1.29 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.542 | 0.646 | 5.421 | 0.000 | 0.086 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 119 | 94 | 308 | 0 | 157 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.89 | 0.71 | 2.32 | 0.00 | 1.18 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.652 | 0.829 | 9.738 | 0.000 | 0.095 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 146 | 108 | 342 | 0 | 174 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.90 | 0.66 | 2.10 | 0.00 | 1.07 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.698 | 1.267 | 16.284 | 0.000 | 0.094 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 189 | 172 | 822 | 0 | 263 | 0 | 0 | 159 | 0 |
N.S. |
1 | 0.87 | 0.79 | 3.79 | 0.00 | 1.21 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.991 | 4.469 | 134.950 | 0.000 | 0.099 | 0.000 | 0.000 | 0.407 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 157 | 147 | 712 | 0 | 234 | 0 | 0 | 159 | 0 |
N.S. |
1 | 0.88 | 0.82 | 3.98 | 0.00 | 1.31 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.962 | 2.959 | 130.835 | 0.000 | 0.101 | 0.000 | 0.000 | 0.417 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 124 | 99 | 488 | 0 | 200 | 0 | 0 | 159 | 0 |
N.S. |
1 | 0.89 | 0.71 | 3.49 | 0.00 | 1.43 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.845 | 3.225 | 129.556 | 0.000 | 0.106 | 0.000 | 0.000 | 0.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 124 | 101 | 381 | 0 | 170 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.88 | 0.72 | 2.70 | 0.00 | 1.21 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.834 | 3.346 | 5.168 | 0.000 | 0.109 | 0.000 | 0.000 | 0.350 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 134 | 105 | 447 | 0 | 181 | 0 | 0 | 110 | 0 |
N.S. |
1 | 0.91 | 0.71 | 3.04 | 0.00 | 1.23 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.812 | 3.294 | 5.702 | 0.000 | 0.093 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 165 | 125 | 481 | 0 | 210 | 0 | 0 | 159 | 0 |
N.S. |
1 | 0.90 | 0.68 | 2.61 | 0.00 | 1.14 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.946 | 3.279 | 11.095 | 0.000 | 0.113 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 193 | 149 | 512 | 0 | 231 | 0 | 0 | 159 | 0 |
N.S. |
1 | 0.89 | 0.69 | 2.36 | 0.00 | 1.06 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 1.000 | 3.464 | 25.069 | 0.000 | 0.111 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 266 | 209 | 1154 | 0 | 304 | 0 | 0 | 248 | 0 |
N.S. |
1 | 0.91 | 0.72 | 3.97 | 0.00 | 1.04 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 1.687 | 5.887 | 227.964 | 0.000 | 0.109 | 0.000 | 0.000 | 0.552 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 238 | 177 | 905 | 0 | 281 | 0 | 0 | 248 | 0 |
N.S. |
1 | 0.93 | 0.69 | 3.55 | 0.00 | 1.10 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 1.642 | 5.604 | 221.954 | 0.000 | 0.100 | 0.000 | 0.000 | 0.545 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 205 | 135 | 879 | 0 | 248 | 0 | 0 | 248 | 0 |
N.S. |
1 | 0.96 | 0.63 | 4.11 | 0.00 | 1.16 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 1.457 | 4.256 | 213.848 | 0.000 | 0.102 | 0.000 | 0.000 | 0.555 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 205 | 118 | 801 | 0 | 229 | 0 | 0 | 248 | 0 |
N.S. |
1 | 0.97 | 0.56 | 3.78 | 0.00 | 1.08 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 1.481 | 4.211 | 219.019 | 0.000 | 0.100 | 0.000 | 0.000 | 0.550 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 204 | 121 | 595 | 0 | 199 | 0 | 0 | 230 | 0 |
N.S. |
1 | 0.96 | 0.57 | 2.81 | 0.00 | 0.94 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 1.435 | 4.105 | 9.400 | 0.000 | 0.099 | 0.000 | 0.000 | 0.473 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 214 | 133 | 483 | 0 | 226 | 0 | 0 | 175 | 0 |
N.S. |
1 | 0.98 | 0.61 | 2.21 | 0.00 | 1.03 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 1.466 | 4.166 | 14.347 | 0.000 | 0.094 | 0.000 | 0.000 | 0.338 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 242 | 151 | 514 | 0 | 249 | 0 | 0 | 248 | 0 |
N.S. |
1 | 0.95 | 0.59 | 2.02 | 0.00 | 0.98 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 1.621 | 3.545 | 25.025 | 0.000 | 0.103 | 0.000 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 270 | 174 | 545 | 0 | 272 | 0 | 0 | 248 | 0 |
N.S. |
1 | 0.93 | 0.60 | 1.87 | 0.00 | 0.93 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 1.713 | 4.258 | 35.740 | 0.000 | 0.148 | 0.000 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 320 | 242 | 1397 | 0 | 327 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.93 | 0.71 | 4.07 | 0.00 | 0.95 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 2.157 | 8.501 | 617.898 | 0.000 | 0.105 | 0.000 | 0.000 | 0.690 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 285 | 209 | 1235 | 0 | 304 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.93 | 0.68 | 4.02 | 0.00 | 0.99 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 2.081 | 6.777 | 607.014 | 0.000 | 0.104 | 0.000 | 0.000 | 0.724 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 261 | 176 | 1070 | 0 | 281 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.96 | 0.65 | 3.95 | 0.00 | 1.04 | 0.00 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 1.919 | 7.656 | 599.491 | 0.000 | 0.105 | 0.000 | 0.000 | 0.692 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 263 | 157 | 1262 | 0 | 272 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.97 | 0.58 | 4.67 | 0.00 | 1.01 | 0.00 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 1.930 | 5.759 | 603.539 | 0.000 | 0.102 | 0.000 | 0.000 | 0.701 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 259 | 149 | 950 | 0 | 259 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.97 | 0.56 | 3.56 | 0.00 | 0.97 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 1.817 | 4.314 | 604.244 | 0.000 | 0.106 | 0.000 | 0.000 | 0.710 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 263 | 149 | 727 | 0 | 232 | 0 | 0 | 311 | 0 |
N.S. |
1 | 0.98 | 0.55 | 2.70 | 0.00 | 0.86 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 1.879 | 4.596 | 16.543 | 0.000 | 0.101 | 0.000 | 0.000 | 0.577 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 261 | 153 | 514 | 0 | 249 | 0 | 0 | 238 | 0 |
N.S. |
1 | 0.96 | 0.56 | 1.90 | 0.00 | 0.92 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.868 | 5.075 | 24.934 | 0.000 | 0.102 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 296 | 174 | 545 | 0 | 272 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.96 | 0.57 | 1.78 | 0.00 | 0.89 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 2.061 | 4.696 | 35.807 | 0.000 | 0.112 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 324 | 197 | 576 | 0 | 295 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.94 | 0.57 | 1.68 | 0.00 | 0.86 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 2.109 | 5.606 | 51.483 | 0.000 | 0.116 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 202 | 200 | 785 | 0 | 369 | 0 | 0 | 109 | 0 |
N.S. |
1 | 0.81 | 0.80 | 3.14 | 0.00 | 1.48 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.085 | 7.094 | 73.711 | 0.000 | 0.100 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 172 | 162 | 467 | 0 | 335 | 0 | 0 | 109 | 0 |
N.S. |
1 | 0.84 | 0.79 | 2.28 | 0.00 | 1.63 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.917 | 5.373 | 71.909 | 0.000 | 0.096 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 142 | 132 | 353 | 0 | 275 | 0 | 0 | 103 | 0 |
N.S. |
1 | 0.86 | 0.80 | 2.14 | 0.00 | 1.67 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.875 | 4.586 | 2.469 | 0.000 | 0.092 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 117 | 126 | 281 | 0 | 266 | 0 | 0 | 85 | 0 |
N.S. |
1 | 0.90 | 0.97 | 2.16 | 0.00 | 2.05 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.750 | 4.067 | 2.946 | 0.000 | 0.117 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 149 | 163 | 300 | 0 | 287 | 0 | 0 | 121 | 0 |
N.S. |
1 | 0.86 | 0.94 | 1.72 | 0.00 | 1.65 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.862 | 3.601 | 4.738 | 0.000 | 0.101 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 178 | 178 | 319 | 0 | 307 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.83 | 0.83 | 1.49 | 0.00 | 1.43 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.921 | 4.355 | 5.852 | 0.000 | 0.113 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 206 | 198 | 341 | 0 | 327 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.82 | 0.79 | 1.36 | 0.00 | 1.31 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.091 | 5.494 | 8.490 | 0.000 | 0.112 | 0.000 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 223 | 212 | 724 | 0 | 464 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.89 | 0.84 | 2.88 | 0.00 | 1.85 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.290 | 7.178 | 27.264 | 0.000 | 0.109 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | C | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 196 | 172 | 563 | 0 | 386 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.91 | 0.80 | 2.62 | 0.00 | 1.80 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.230 | 6.718 | 3.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 163 | 164 | 507 | 0 | 383 | 0 | 0 | 115 | 0 |
N.S. |
1 | 0.94 | 0.95 | 2.93 | 0.00 | 2.21 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 1.050 | 5.427 | 3.941 | 0.000 | 0.096 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 166 | 162 | 507 | 0 | 381 | 0 | 0 | 169 | 0 |
N.S. |
1 | 0.93 | 0.91 | 2.83 | 0.00 | 2.13 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 1.043 | 5.206 | 4.697 | 0.000 | 0.112 | 0.000 | 0.000 | 0.179 | 0.000 |