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 | C | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 229 | 189 | 279 | 0 | 181 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.07 | 0.88 | 1.30 | 0.00 | 0.84 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.638 | 0.354 | 0.357 | 0.000 | 0.079 | 0.000 | 0.000 | 200.015 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 372 | 180 | 228 | 0 | 173 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.60 | 0.77 | 0.98 | 0.00 | 0.74 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.769 | 9.405 | 2.511 | 0.000 | 0.073 | 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 | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 353 | 164 | 230 | 0 | 175 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.57 | 0.73 | 1.02 | 0.00 | 0.78 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.797 | 6.851 | 2.316 | 0.000 | 0.081 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 223 | 97 | 147 | 0 | 97 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.52 | 0.66 | 1.00 | 0.00 | 0.66 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.550 | 6.741 | 2.237 | 0.000 | 0.071 | 0.000 | 0.000 | 0.171 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 358 | 168 | 230 | 0 | 159 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.50 | 0.70 | 0.96 | 0.00 | 0.67 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.775 | 6.866 | 1.758 | 0.000 | 0.076 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 368 | 172 | 228 | 0 | 173 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.61 | 0.75 | 1.00 | 0.00 | 0.76 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.776 | 7.061 | 2.266 | 0.000 | 0.081 | 0.000 | 0.000 | 0.187 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 358 | 172 | 230 | 0 | 177 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.52 | 0.73 | 0.98 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.776 | 6.733 | 1.780 | 0.000 | 0.073 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 211 | 98 | 122 | 0 | 90 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.50 | 0.70 | 0.87 | 0.00 | 0.64 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.550 | 6.738 | 1.770 | 0.000 | 0.082 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 132 | 47 | 40 | 0 | 52 | 32 | 0 | 25 | 34 |
N.S. |
1 | 2.20 | 0.78 | 0.67 | 0.00 | 0.87 | 0.53 | 0.00 | 0.42 | 0.57 |
time (sec) |
N/A | 0.351 | 4.687 | 0.708 | 0.000 | 0.072 | 0.712 | 0.000 | 0.164 | 17.597 |
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 | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 218 | 105 | 147 | 0 | 82 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.61 | 0.78 | 1.09 | 0.00 | 0.61 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.596 | 6.809 | 2.215 | 0.000 | 0.075 | 0.000 | 0.000 | 0.173 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 373 | 168 | 230 | 0 | 176 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.59 | 0.71 | 0.98 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.778 | 6.637 | 2.219 | 0.000 | 0.089 | 0.000 | 0.000 | 0.178 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 381 | 168 | 228 | 0 | 171 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.66 | 0.73 | 1.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.806 | 6.801 | 2.683 | 0.000 | 0.085 | 0.000 | 0.000 | 0.187 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 373 | 168 | 230 | 0 | 155 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.59 | 0.71 | 0.98 | 0.00 | 0.66 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.790 | 6.645 | 1.973 | 0.000 | 0.076 | 0.000 | 0.000 | 0.179 | 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 | 133 | 218 | 123 | 147 | 0 | 100 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.64 | 0.92 | 1.11 | 0.00 | 0.75 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.551 | 6.772 | 2.687 | 0.000 | 0.069 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 366 | 160 | 230 | 0 | 178 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.63 | 0.71 | 1.02 | 0.00 | 0.79 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.841 | 7.118 | 2.752 | 0.000 | 0.074 | 0.000 | 0.000 | 0.189 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 383 | 174 | 228 | 0 | 173 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.67 | 0.76 | 1.00 | 0.00 | 0.76 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.775 | 6.940 | 2.845 | 0.000 | 0.071 | 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 | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 372 | 168 | 228 | 0 | 179 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.56 | 0.70 | 0.95 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.754 | 7.472 | 2.474 | 0.000 | 0.075 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 373 | 158 | 228 | 0 | 148 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.66 | 0.70 | 1.01 | 0.00 | 0.66 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.746 | 6.595 | 1.788 | 0.000 | 0.077 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 223 | 97 | 147 | 0 | 97 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.52 | 0.66 | 1.00 | 0.00 | 0.66 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.543 | 6.514 | 2.293 | 0.000 | 0.084 | 0.000 | 0.000 | 0.172 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 371 | 172 | 230 | 0 | 179 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.58 | 0.73 | 0.98 | 0.00 | 0.76 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.742 | 6.920 | 2.263 | 0.000 | 0.075 | 0.000 | 0.000 | 0.186 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 365 | 166 | 228 | 0 | 177 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.55 | 0.71 | 0.97 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.762 | 7.006 | 1.953 | 0.000 | 0.077 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 368 | 170 | 228 | 0 | 175 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.58 | 0.73 | 0.98 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.745 | 6.990 | 1.808 | 0.000 | 0.084 | 0.000 | 0.000 | 0.186 | 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 | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 210 | 113 | 141 | 0 | 74 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.63 | 0.88 | 1.09 | 0.00 | 0.57 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.535 | 6.471 | 1.840 | 0.000 | 0.070 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 132 | 47 | 40 | 0 | 46 | 32 | 0 | 25 | 34 |
N.S. |
1 | 2.20 | 0.78 | 0.67 | 0.00 | 0.77 | 0.53 | 0.00 | 0.42 | 0.57 |
time (sec) |
N/A | 0.355 | 4.691 | 0.711 | 0.000 | 0.074 | 0.410 | 0.000 | 0.166 | 17.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 220 | 101 | 128 | 0 | 98 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.50 | 0.69 | 0.87 | 0.00 | 0.67 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.563 | 6.643 | 2.244 | 0.000 | 0.084 | 0.000 | 0.000 | 0.177 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 383 | 166 | 228 | 0 | 175 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.64 | 0.71 | 0.98 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.759 | 6.840 | 2.257 | 0.000 | 0.078 | 0.000 | 0.000 | 0.179 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 380 | 162 | 228 | 0 | 176 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.62 | 0.69 | 0.97 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.771 | 7.035 | 2.304 | 0.000 | 0.089 | 0.000 | 0.000 | 0.194 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 384 | 172 | 230 | 0 | 177 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.66 | 0.74 | 1.00 | 0.00 | 0.77 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.833 | 6.760 | 2.630 | 0.000 | 0.081 | 0.000 | 0.000 | 0.194 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 218 | 123 | 147 | 0 | 100 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.64 | 0.92 | 1.11 | 0.00 | 0.75 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.542 | 7.035 | 2.769 | 0.000 | 0.082 | 0.000 | 0.000 | 0.176 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 388 | 154 | 228 | 0 | 145 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.71 | 0.68 | 1.00 | 0.00 | 0.64 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.788 | 6.906 | 2.001 | 0.000 | 0.078 | 0.000 | 0.000 | 0.186 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 383 | 168 | 228 | 0 | 178 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.63 | 0.71 | 0.97 | 0.00 | 0.76 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.741 | 6.793 | 2.812 | 0.000 | 0.090 | 0.000 | 0.000 | 0.175 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 286 | 186 | 224 | 0 | 174 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.22 | 0.79 | 0.96 | 0.00 | 0.74 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.666 | 6.285 | 2.602 | 0.000 | 0.078 | 0.000 | 0.000 | 0.185 | 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 | 120 | 173 | 123 | 125 | 0 | 88 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.44 | 1.02 | 1.04 | 0.00 | 0.73 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.510 | 5.771 | 2.652 | 0.000 | 0.092 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 263 | 328 | 237 | 0 | 148 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.26 | 0.91 | 0.00 | 0.57 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.641 | 5.992 | 1.609 | 0.000 | 0.078 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 269 | 344 | 237 | 0 | 161 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.32 | 0.91 | 0.00 | 0.62 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.631 | 6.244 | 2.265 | 0.000 | 0.078 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 267 | 328 | 237 | 0 | 166 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.24 | 0.90 | 0.00 | 0.63 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.604 | 6.001 | 1.831 | 0.000 | 0.075 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 255 | 326 | 231 | 0 | 151 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.91 | 0.00 | 0.59 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.604 | 6.102 | 1.847 | 0.000 | 0.079 | 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 | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 44 | 18 | 0 | 52 | 36 | 0 | 25 | 16 |
N.S. |
1 | 1.00 | 0.49 | 0.20 | 0.00 | 0.58 | 0.40 | 0.00 | 0.28 | 0.18 |
time (sec) |
N/A | 0.295 | 3.963 | 0.711 | 0.000 | 0.082 | 0.387 | 0.000 | 0.169 | 17.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 264 | 328 | 237 | 0 | 159 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.25 | 0.90 | 0.00 | 0.61 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.591 | 5.944 | 2.292 | 0.000 | 0.093 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 264 | 328 | 237 | 0 | 165 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.25 | 0.90 | 0.00 | 0.63 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.617 | 5.917 | 2.241 | 0.000 | 0.080 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 266 | 345 | 237 | 0 | 158 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.04 | 1.34 | 0.92 | 0.00 | 0.61 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.619 | 6.153 | 2.672 | 0.000 | 0.079 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 260 | 328 | 237 | 0 | 153 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.27 | 0.92 | 0.00 | 0.59 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.589 | 6.006 | 2.162 | 0.000 | 0.076 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 269 | 104 | 118 | 0 | 82 | 0 | 0 | 40 | 0 |
N.S. |
1 | 2.05 | 0.79 | 0.90 | 0.00 | 0.63 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.608 | 5.827 | 2.135 | 0.000 | 0.069 | 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 | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 267 | 184 | 224 | 0 | 179 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.17 | 0.80 | 0.98 | 0.00 | 0.78 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.641 | 6.324 | 2.178 | 0.000 | 0.080 | 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 | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 299 | 211 | 222 | 0 | 178 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.27 | 0.89 | 0.94 | 0.00 | 0.75 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.715 | 6.181 | 2.721 | 0.000 | 0.074 | 0.000 | 0.000 | 0.185 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 298 | 223 | 224 | 0 | 178 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.25 | 0.93 | 0.94 | 0.00 | 0.74 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.740 | 6.222 | 2.604 | 0.000 | 0.071 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 183 | 119 | 138 | 0 | 98 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.50 | 0.98 | 1.13 | 0.00 | 0.80 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.497 | 5.858 | 2.647 | 0.000 | 0.074 | 0.000 | 0.000 | 0.177 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 279 | 201 | 222 | 0 | 141 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.19 | 0.86 | 0.95 | 0.00 | 0.60 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.657 | 6.076 | 1.980 | 0.000 | 0.080 | 0.000 | 0.000 | 0.187 | 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 | 135 | 173 | 123 | 140 | 0 | 98 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.28 | 0.91 | 1.04 | 0.00 | 0.73 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.478 | 5.837 | 2.570 | 0.000 | 0.072 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 265 | 322 | 237 | 0 | 165 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.07 | 1.30 | 0.96 | 0.00 | 0.67 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.634 | 5.939 | 2.200 | 0.000 | 0.070 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 267 | 320 | 237 | 0 | 166 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.23 | 0.91 | 0.00 | 0.64 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.593 | 6.037 | 1.832 | 0.000 | 0.075 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 267 | 326 | 235 | 0 | 164 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.05 | 1.28 | 0.93 | 0.00 | 0.65 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.588 | 5.915 | 1.803 | 0.000 | 0.074 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 255 | 318 | 231 | 0 | 157 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.02 | 1.28 | 0.93 | 0.00 | 0.63 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.595 | 5.901 | 1.842 | 0.000 | 0.072 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 44 | 18 | 0 | 46 | 36 | 0 | 25 | 16 |
N.S. |
1 | 1.00 | 0.49 | 0.20 | 0.00 | 0.52 | 0.40 | 0.00 | 0.28 | 0.18 |
time (sec) |
N/A | 0.302 | 3.992 | 0.701 | 0.000 | 0.081 | 0.391 | 0.000 | 0.165 | 19.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 264 | 320 | 237 | 0 | 165 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.25 | 0.92 | 0.00 | 0.64 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.614 | 5.988 | 2.255 | 0.000 | 0.074 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 262 | 326 | 235 | 0 | 164 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.05 | 1.30 | 0.94 | 0.00 | 0.66 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.598 | 6.045 | 2.246 | 0.000 | 0.077 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 264 | 320 | 237 | 0 | 163 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.25 | 0.92 | 0.00 | 0.63 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.683 | 6.146 | 2.302 | 0.000 | 0.070 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 262 | 323 | 237 | 0 | 166 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.07 | 1.32 | 0.97 | 0.00 | 0.68 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.591 | 6.173 | 2.606 | 0.000 | 0.084 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 269 | 105 | 118 | 0 | 83 | 0 | 0 | 40 | 0 |
N.S. |
1 | 2.07 | 0.81 | 0.91 | 0.00 | 0.64 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.627 | 5.825 | 2.152 | 0.000 | 0.074 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 265 | 174 | 222 | 0 | 141 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.17 | 0.77 | 0.98 | 0.00 | 0.62 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.614 | 6.127 | 1.759 | 0.000 | 0.074 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 269 | 101 | 136 | 0 | 97 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.78 | 0.67 | 0.90 | 0.00 | 0.64 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.642 | 6.023 | 2.155 | 0.000 | 0.071 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 231 | 229 | 249 | 0 | 171 | 0 | 0 | 598 | 0 |
N.S. |
1 | 0.88 | 0.87 | 0.95 | 0.00 | 0.65 | 0.00 | 0.00 | 2.27 | 0.00 |
time (sec) |
N/A | 0.576 | 7.937 | 1.141 | 0.000 | 0.081 | 0.000 | 0.000 | 0.415 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 76 | 101 | 133 | 0 | 97 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.07 | 1.42 | 1.87 | 0.00 | 1.37 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.381 | 6.280 | 2.737 | 0.000 | 0.074 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 130 | 176 | 221 | 0 | 157 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.39 | 1.74 | 0.00 | 1.24 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.500 | 6.503 | 2.116 | 0.000 | 0.073 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 64 | 104 | 139 | 0 | 83 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.05 | 1.70 | 2.28 | 0.00 | 1.36 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.369 | 6.359 | 2.668 | 0.000 | 0.082 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 263 | 322 | 237 | 0 | 179 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.07 | 1.31 | 0.96 | 0.00 | 0.73 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.663 | 6.538 | 2.168 | 0.000 | 0.067 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 264 | 320 | 237 | 0 | 175 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.25 | 0.92 | 0.00 | 0.68 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.613 | 6.574 | 1.784 | 0.000 | 0.072 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 263 | 326 | 235 | 0 | 164 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.05 | 1.30 | 0.94 | 0.00 | 0.66 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.586 | 6.461 | 1.754 | 0.000 | 0.072 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 256 | 318 | 231 | 0 | 163 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.03 | 1.28 | 0.93 | 0.00 | 0.65 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.607 | 6.384 | 1.783 | 0.000 | 0.074 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 47 | 19 | 0 | 46 | 37 | 0 | 25 | 34 |
N.S. |
1 | 1.00 | 0.53 | 0.21 | 0.00 | 0.52 | 0.42 | 0.00 | 0.28 | 0.38 |
time (sec) |
N/A | 0.296 | 4.130 | 0.667 | 0.000 | 0.071 | 0.420 | 0.000 | 0.156 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 263 | 320 | 237 | 0 | 159 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.25 | 0.92 | 0.00 | 0.62 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.592 | 6.346 | 2.190 | 0.000 | 0.067 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 266 | 326 | 235 | 0 | 164 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.05 | 1.28 | 0.93 | 0.00 | 0.65 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.608 | 6.370 | 2.160 | 0.000 | 0.066 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 267 | 320 | 237 | 0 | 176 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.23 | 0.91 | 0.00 | 0.67 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.605 | 6.521 | 2.208 | 0.000 | 0.066 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 264 | 323 | 237 | 0 | 175 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.07 | 1.31 | 0.96 | 0.00 | 0.71 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.610 | 6.497 | 2.546 | 0.000 | 0.073 | 0.000 | 0.000 | 0.177 | 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 | 104 | 174 | 123 | 125 | 0 | 98 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.67 | 1.18 | 1.20 | 0.00 | 0.94 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.486 | 6.236 | 2.180 | 0.000 | 0.073 | 0.000 | 0.000 | 0.161 | 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 | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 304 | 201 | 221 | 0 | 149 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.52 | 1.00 | 1.10 | 0.00 | 0.74 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.737 | 6.563 | 1.505 | 0.000 | 0.072 | 0.000 | 0.000 | 0.186 | 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 | 94 | 166 | 119 | 144 | 0 | 98 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.77 | 1.27 | 1.53 | 0.00 | 1.04 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.511 | 6.326 | 2.186 | 0.000 | 0.073 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 76 | 101 | 133 | 0 | 97 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.07 | 1.42 | 1.87 | 0.00 | 1.37 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.374 | 6.278 | 2.652 | 0.000 | 0.082 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 130 | 185 | 223 | 0 | 179 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.47 | 1.77 | 0.00 | 1.42 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.514 | 6.639 | 2.533 | 0.000 | 0.091 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 50 | 105 | 118 | 0 | 82 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.16 | 2.44 | 2.74 | 0.00 | 1.91 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.357 | 6.454 | 2.630 | 0.000 | 0.081 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 260 | 328 | 237 | 0 | 144 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.27 | 0.92 | 0.00 | 0.56 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.638 | 6.591 | 1.716 | 0.000 | 0.085 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 267 | 344 | 237 | 0 | 158 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.04 | 1.34 | 0.92 | 0.00 | 0.61 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.619 | 6.772 | 2.208 | 0.000 | 0.088 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 264 | 328 | 237 | 0 | 165 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.25 | 0.90 | 0.00 | 0.63 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.615 | 6.445 | 1.742 | 0.000 | 0.076 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 256 | 326 | 231 | 0 | 157 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 1.28 | 0.91 | 0.00 | 0.62 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.610 | 6.761 | 1.769 | 0.000 | 0.079 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 47 | 19 | 0 | 52 | 37 | 0 | 25 | 34 |
N.S. |
1 | 1.00 | 0.53 | 0.21 | 0.00 | 0.58 | 0.42 | 0.00 | 0.28 | 0.38 |
time (sec) |
N/A | 0.298 | 4.426 | 0.678 | 0.000 | 0.077 | 0.402 | 0.000 | 0.158 | 17.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 263 | 328 | 237 | 0 | 153 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.90 | 0.00 | 0.58 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.613 | 6.597 | 2.174 | 0.000 | 0.073 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 267 | 328 | 237 | 0 | 166 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.24 | 0.90 | 0.00 | 0.63 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.610 | 6.679 | 2.151 | 0.000 | 0.075 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 268 | 345 | 237 | 0 | 161 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.32 | 0.91 | 0.00 | 0.62 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.628 | 7.049 | 2.611 | 0.000 | 0.075 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 263 | 328 | 237 | 0 | 144 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.26 | 0.91 | 0.00 | 0.55 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.636 | 6.905 | 1.923 | 0.000 | 0.071 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 168 | 123 | 140 | 0 | 87 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.83 | 1.34 | 1.52 | 0.00 | 0.95 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.488 | 6.459 | 2.159 | 0.000 | 0.082 | 0.000 | 0.000 | 0.165 | 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 | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 303 | 188 | 223 | 0 | 174 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.53 | 0.95 | 1.13 | 0.00 | 0.88 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.727 | 6.683 | 2.095 | 0.000 | 0.068 | 0.000 | 0.000 | 0.172 | 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 | 94 | 166 | 119 | 144 | 0 | 98 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.77 | 1.27 | 1.53 | 0.00 | 1.04 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.507 | 6.257 | 2.154 | 0.000 | 0.064 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 125 | 185 | 221 | 0 | 159 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.06 | 1.57 | 1.87 | 0.00 | 1.35 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.522 | 5.046 | 1.148 | 0.000 | 0.079 | 0.000 | 0.000 | 0.176 | 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 | 92 | 168 | 123 | 140 | 0 | 87 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.83 | 1.34 | 1.52 | 0.00 | 0.95 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.489 | 0.036 | 2.076 | 0.000 | 0.074 | 0.000 | 0.000 | 0.171 | 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 | 96 | 135 | 118 | 112 | 0 | 89 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.41 | 1.23 | 1.17 | 0.00 | 0.93 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.394 | 2.633 | 5.987 | 0.000 | 0.071 | 0.000 | 0.000 | 0.236 | 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 | 96 | 168 | 123 | 141 | 0 | 87 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.75 | 1.28 | 1.47 | 0.00 | 0.91 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.520 | 0.006 | 0.590 | 0.000 | 0.074 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 269 | 342 | 237 | 0 | 160 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.31 | 0.91 | 0.00 | 0.61 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.675 | 6.473 | 2.359 | 0.000 | 0.075 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 262 | 332 | 237 | 0 | 162 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.29 | 0.92 | 0.00 | 0.63 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.633 | 5.462 | 1.932 | 0.000 | 0.083 | 0.000 | 0.000 | 0.171 | 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 | 120 | 173 | 123 | 125 | 0 | 88 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.44 | 1.02 | 1.04 | 0.00 | 0.73 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.489 | 0.014 | 2.545 | 0.000 | 0.079 | 0.000 | 0.000 | 0.172 | 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 | 122 | 172 | 109 | 132 | 0 | 98 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.41 | 0.89 | 1.08 | 0.00 | 0.80 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.508 | 4.673 | 1.782 | 0.000 | 0.079 | 0.000 | 0.000 | 0.160 | 0.000 |