Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 415 | 256 | 3114 | 0 | 588 | 0 | 4112 | 1360 | 0 |
N.S. |
1 | 1.59 | 0.98 | 11.93 | 0.00 | 2.25 | 0.00 | 15.75 | 5.21 | 0.00 |
time (sec) |
N/A | 2.171 | 0.352 | 2.651 | 0.000 | 0.112 | 0.000 | 0.178 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 136 | 144 | 734 | 0 | 263 | 0 | 1218 | 483 | 0 |
N.S. |
1 | 1.01 | 1.07 | 5.44 | 0.00 | 1.95 | 0.00 | 9.02 | 3.58 | 0.00 |
time (sec) |
N/A | 0.603 | 0.083 | 0.851 | 0.000 | 0.080 | 0.000 | 0.136 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 703 | 95 | 22 | 26 | 1783 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 29.29 | 3.96 | 0.92 | 1.08 | 74.29 | 1.08 |
time (sec) |
N/A | 0.312 | 0.595 | 0.060 | 0.161 | 0.088 | 6.948 | 0.131 | 0.241 | 25.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 934 | 153 | 24 | 26 | 217 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 38.92 | 6.38 | 1.00 | 1.08 | 9.04 | 1.08 |
time (sec) |
N/A | 0.319 | 4.492 | 0.266 | 0.169 | 0.125 | 38.857 | 0.148 | 0.198 | 25.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 404 | 374 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.839 | 0.663 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 255 | 235 | 0 | 0 | 0 | 0 | 0 | 1044 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.09 | 0.00 |
time (sec) |
N/A | 1.122 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 109 | 106 | 0 | 0 | 0 | 0 | 0 | 344 | 0 |
N.S. |
1 | 0.98 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.10 | 0.00 |
time (sec) |
N/A | 0.590 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 22 | 26 | 564 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.85 | 1.00 | 21.69 | 1.00 |
time (sec) |
N/A | 0.339 | 5.695 | 0.616 | 0.493 | 0.000 | 0.497 | 0.158 | 0.295 | 25.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 24 | 26 | 252 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.92 | 1.00 | 9.69 | 1.00 |
time (sec) |
N/A | 0.531 | 0.497 | 0.622 | 0.522 | 0.000 | 2.906 | 0.151 | 0.235 | 25.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 24 | 26 | 1186 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.92 | 1.00 | 45.62 | 1.00 |
time (sec) |
N/A | 0.695 | 0.511 | 0.618 | 0.496 | 0.000 | 12.157 | 0.155 | 0.318 | 25.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 526 | 526 | 446 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.149 | 1.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.431 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 330 | 282 | 0 | 0 | 0 | 0 | 0 | 1373 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.16 | 0.00 |
time (sec) |
N/A | 1.336 | 0.523 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.378 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 140 | 127 | 0 | 0 | 0 | 0 | 0 | 437 | 0 |
N.S. |
1 | 0.98 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.06 | 0.00 |
time (sec) |
N/A | 0.696 | 0.157 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 22 | 26 | 892 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.85 | 1.00 | 34.31 | 1.00 |
time (sec) |
N/A | 0.351 | 4.369 | 0.621 | 0.544 | 0.000 | 10.232 | 0.208 | 0.430 | 26.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 0 | 26 | 2396 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.00 | 1.00 | 92.15 | 1.00 |
time (sec) |
N/A | 0.545 | 0.898 | 0.618 | 0.534 | 0.000 | 0.000 | 0.181 | 0.699 | 26.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 24 | 26 | 4886 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.92 | 1.00 | 187.92 | 1.00 |
time (sec) |
N/A | 0.693 | 0.856 | 0.624 | 0.533 | 0.000 | 106.518 | 0.196 | 0.864 | 26.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 660 | 660 | 511 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.607 | 2.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.448 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 413 | 326 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.584 | 0.811 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.383 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 171 | 152 | 0 | 0 | 0 | 0 | 0 | 699 | 0 |
N.S. |
1 | 0.96 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.91 | 0.00 |
time (sec) |
N/A | 0.775 | 0.196 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 0 | 26 | 1224 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.00 | 1.00 | 47.08 | 1.00 |
time (sec) |
N/A | 0.356 | 3.984 | 0.621 | 0.516 | 0.000 | 0.000 | 0.352 | 0.534 | 25.804 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 0 | 26 | 6409 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.00 | 1.00 | 246.50 | 1.00 |
time (sec) |
N/A | 0.557 | 12.497 | 0.622 | 0.573 | 0.000 | 0.000 | 0.236 | 1.307 | 26.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 0 | 26 | 13054 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.00 | 1.00 | 502.08 | 1.00 |
time (sec) |
N/A | 0.720 | 8.886 | 0.625 | 0.571 | 0.000 | 0.000 | 0.259 | 1.897 | 26.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 383 | 331 | 0 | 0 | 0 | 0 | 0 | 502 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 1.919 | 0.563 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.420 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 252 | 0 | 0 | 0 | 0 | 0 | 361 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 1.474 | 0.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 164 | 0 | 0 | 0 | 0 | 0 | 220 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.968 | 0.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.518 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 24 | 26 | 254 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.92 | 1.00 | 9.77 | 1.00 |
time (sec) |
N/A | 0.348 | 0.108 | 0.630 | 0.474 | 0.000 | 1.205 | 0.162 | 0.367 | 25.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 735 | 1281 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.74 | 3.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.182 | 2.926 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.584 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 533 | 828 | 0 | 0 | 0 | 0 | 0 | 1201 | 0 |
N.S. |
1 | 1.64 | 2.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.70 | 0.00 |
time (sec) |
N/A | 2.250 | 1.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.420 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 318 | 338 | 0 | 0 | 0 | 0 | 0 | 723 | 0 |
N.S. |
1 | 1.45 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.29 | 0.00 |
time (sec) |
N/A | 1.749 | 0.831 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 139 | 0 | 0 | 0 | 0 | 0 | 268 | 0 |
N.S. |
1 | 0.98 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.31 | 0.00 |
time (sec) |
N/A | 0.616 | 0.102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 0 | 26 | 890 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.00 | 1.00 | 34.23 | 1.00 |
time (sec) |
N/A | 0.355 | 0.348 | 0.625 | 0.527 | 0.000 | 0.000 | 0.243 | 0.301 | 26.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 520 | 1341 | 2647 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.58 | 5.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 5.430 | 6.402 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.870 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 924 | 527 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.19 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.616 | 4.668 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.531 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 501 | 353 | 0 | 0 | 0 | 0 | 0 | 1510 | 0 |
N.S. |
1 | 1.61 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.86 | 0.00 |
time (sec) |
N/A | 3.092 | 1.935 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 158 | 163 | 0 | 0 | 0 | 0 | 0 | 543 | 0 |
N.S. |
1 | 1.01 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.48 | 0.00 |
time (sec) |
N/A | 0.752 | 0.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 0 | 0 | 26 | 1914 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 0.00 | 0.00 | 1.00 | 73.62 | 1.00 |
time (sec) |
N/A | 0.360 | 0.691 | 0.625 | 0.536 | 0.000 | 0.000 | 0.342 | 0.318 | 26.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 161 | 137 | 0 | 0 | 538 | 0 | 0 | 394 | 0 |
N.S. |
1 | 0.99 | 0.84 | 0.00 | 0.00 | 3.30 | 0.00 | 0.00 | 2.42 | 0.00 |
time (sec) |
N/A | 0.530 | 0.243 | 0.000 | 0.000 | 0.127 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 118 | 0 | 0 | 311 | 0 | 0 | 223 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 2.36 | 0.00 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 0.457 | 0.150 | 0.000 | 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(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 99 | 83 | 113 | 0 | 185 | 0 | 110 | 95 | 0 |
N.S. |
1 | 1.02 | 0.86 | 1.16 | 0.00 | 1.91 | 0.00 | 1.13 | 0.98 | 0.00 |
time (sec) |
N/A | 0.408 | 0.094 | 2.977 | 0.000 | 0.107 | 0.000 | 0.140 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 80 | 0 | 0 | 206 | 0 | 101 | 123 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 2.54 | 0.00 | 1.25 | 1.52 | 0.00 |
time (sec) |
N/A | 0.376 | 0.175 | 0.000 | 0.000 | 0.134 | 0.000 | 0.137 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 110 | 85 | 0 | 0 | 405 | 0 | 164 | 303 | 0 |
N.S. |
1 | 0.96 | 0.75 | 0.00 | 0.00 | 3.55 | 0.00 | 1.44 | 2.66 | 0.00 |
time (sec) |
N/A | 0.423 | 0.047 | 0.000 | 0.000 | 0.124 | 0.000 | 0.129 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 146 | 78 | 0 | 0 | 769 | 0 | 0 | 562 | 0 |
N.S. |
1 | 1.01 | 0.54 | 0.00 | 0.00 | 5.30 | 0.00 | 0.00 | 3.88 | 0.00 |
time (sec) |
N/A | 0.470 | 0.054 | 0.000 | 0.000 | 0.156 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 182 | 78 | 0 | 0 | 1232 | 0 | 0 | 866 | 0 |
N.S. |
1 | 1.03 | 0.44 | 0.00 | 0.00 | 7.00 | 0.00 | 0.00 | 4.92 | 0.00 |
time (sec) |
N/A | 0.495 | 0.057 | 0.000 | 0.000 | 0.195 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 590 | 1007 | 854 | 0 | 0 | 0 | 0 | 0 | 1280 | 0 |
N.S. |
1 | 1.71 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.17 | 0.00 |
time (sec) |
N/A | 7.659 | 2.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.414 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 763 | 680 | 0 | 0 | 0 | 0 | 0 | 782 | 0 |
N.S. |
1 | 1.50 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.53 | 0.00 |
time (sec) |
N/A | 5.666 | 1.304 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 418 | 553 | 566 | 0 | 0 | 0 | 0 | 0 | 322 | 0 |
N.S. |
1 | 1.32 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 3.721 | 1.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 389 | 424 | 0 | 0 | 0 | 0 | 0 | 518 | 0 |
N.S. |
1 | 1.25 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 2.400 | 0.751 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 423 | 529 | 557 | 0 | 0 | 0 | 0 | 0 | 1518 | 0 |
N.S. |
1 | 1.25 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.59 | 0.00 |
time (sec) |
N/A | 3.748 | 1.419 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 709 | 639 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.41 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 5.454 | 2.194 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.370 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 583 | 940 | 728 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.61 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 7.539 | 3.945 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.526 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 204 | 26 | 22 | 26 | 56 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 7.85 | 1.00 | 0.85 | 1.00 | 2.15 | 1.00 |
time (sec) |
N/A | 0.340 | 0.772 | 0.644 | 0.134 | 0.104 | 7.413 | 0.165 | 0.648 | 25.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 174 | 26 | 22 | 26 | 25 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 6.69 | 1.00 | 0.85 | 1.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.315 | 0.217 | 0.599 | 0.137 | 0.110 | 0.616 | 0.131 | 0.325 | 26.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 174 | 39 | 24 | 26 | 46 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 6.69 | 1.50 | 0.92 | 1.00 | 1.77 | 1.00 |
time (sec) |
N/A | 0.316 | 0.742 | 0.637 | 0.145 | 0.082 | 1.362 | 0.133 | 0.223 | 26.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 166 | 63 | 24 | 26 | 80 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 6.38 | 2.42 | 0.92 | 1.00 | 3.08 | 1.00 |
time (sec) |
N/A | 0.320 | 1.218 | 0.638 | 0.136 | 0.095 | 5.390 | 0.173 | 0.263 | 26.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 24 | 26 | 0 | 26 | 26 | 5097 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.86 | 0.93 | 0.00 | 0.93 | 0.93 | 182.04 | 0.93 |
time (sec) |
N/A | 0.774 | 1.440 | 0.644 | 0.486 | 0.000 | 2.700 | 0.432 | 1.365 | 25.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 24 | 26 | 0 | 26 | 26 | 1934 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.86 | 0.93 | 0.00 | 0.93 | 0.93 | 69.07 | 0.93 |
time (sec) |
N/A | 0.746 | 1.532 | 0.639 | 0.496 | 0.000 | 1.246 | 0.320 | 0.605 | 25.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 24 | 26 | 0 | 26 | 26 | 4743 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.86 | 0.93 | 0.00 | 0.93 | 0.93 | 169.39 | 0.93 |
time (sec) |
N/A | 0.777 | 2.554 | 0.636 | 0.497 | 0.000 | 16.086 | 0.231 | 0.644 | 25.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 24 | 26 | 0 | 26 | 26 | 40 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.86 | 0.93 | 0.00 | 0.93 | 0.93 | 1.43 | 0.93 |
time (sec) |
N/A | 0.354 | 4.333 | 0.641 | 0.522 | 0.000 | 0.975 | 0.149 | 1.341 | 25.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 24 | 26 | 0 | 27 | 26 | 61 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.86 | 0.93 | 0.00 | 0.96 | 0.93 | 2.18 | 0.93 |
time (sec) |
N/A | 0.362 | 0.283 | 0.641 | 0.534 | 0.000 | 2.910 | 0.140 | 0.761 | 26.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 24 | 26 | 0 | 27 | 26 | 95 | 26 |
N.S. |
1 | 1.00 | 1.07 | 0.86 | 0.93 | 0.00 | 0.96 | 0.93 | 3.39 | 0.93 |
time (sec) |
N/A | 0.350 | 0.125 | 0.640 | 0.486 | 0.000 | 25.755 | 0.186 | 0.885 | 26.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 81 | 0 | 0 | 0 | 0 | 0 | 820 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.72 | 0.00 |
time (sec) |
N/A | 0.371 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 20 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.83 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.307 | 0.373 | 0.644 | 0.114 | 0.090 | 26.020 | 0.138 | 0.229 | 27.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 131 | 46 | 0 | 26 | 46 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 5.46 | 1.92 | 0.00 | 1.08 | 1.92 | 1.08 |
time (sec) |
N/A | 0.318 | 9.035 | 0.012 | 0.137 | 0.084 | 0.000 | 0.163 | 0.243 | 26.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 48 | 0 | 26 | 14410 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.85 | 0.00 | 1.00 | 554.23 | 1.00 |
time (sec) |
N/A | 0.345 | 14.616 | 0.641 | 0.550 | 0.109 | 0.000 | 1.245 | 2.948 | 26.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 26 | 0 | 26 | 33476 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.00 | 1.00 | 1287.54 | 1.00 |
time (sec) |
N/A | 0.335 | 0.082 | 0.640 | 0.572 | 0.098 | 0.000 | 0.437 | 0.977 | 26.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 26 | 24 | 26 | 41 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.92 | 1.00 | 1.58 | 1.00 |
time (sec) |
N/A | 0.338 | 11.457 | 0.645 | 0.543 | 0.102 | 4.758 | 0.158 | 1.582 | 27.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 62 | 0 | 26 | 61 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.38 | 0.00 | 1.00 | 2.35 | 1.00 |
time (sec) |
N/A | 0.353 | 12.739 | 0.636 | 0.563 | 0.103 | 0.000 | 0.203 | 2.624 | 27.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 0 | 26 | 0 | 0 | 34142 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 1.08 | 0.00 | 0.00 | 1422.58 | 1.08 |
time (sec) |
N/A | 0.307 | 0.407 | 0.669 | 0.000 | 0.100 | 0.000 | 0.000 | 0.854 | 27.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 474 | 474 | 343 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.729 | 1.609 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 348 | 262 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.297 | 0.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 181 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.889 | 0.156 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 103 | 0 | 0 | 60 | 0 | 0 | 655 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.58 | 0.00 | 0.00 | 6.36 | 0.00 |
time (sec) |
N/A | 0.446 | 0.070 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 0 | 26 | 20 | 26 | 1087 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 1.08 | 0.83 | 1.08 | 45.29 | 1.08 |
time (sec) |
N/A | 0.315 | 0.258 | 0.634 | 0.000 | 0.102 | 4.481 | 0.159 | 0.271 | 26.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 265 | 589 | 554 | 757 | 478 | 682 | 572 | 676 | 661 |
N.S. |
1 | 0.84 | 1.87 | 1.76 | 2.40 | 1.52 | 2.17 | 1.82 | 2.15 | 2.10 |
time (sec) |
N/A | 0.872 | 0.567 | 2.111 | 0.062 | 0.106 | 0.853 | 0.123 | 0.195 | 26.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 207 | 375 | 356 | 539 | 308 | 427 | 369 | 434 | 393 |
N.S. |
1 | 0.85 | 1.54 | 1.46 | 2.21 | 1.26 | 1.75 | 1.51 | 1.78 | 1.61 |
time (sec) |
N/A | 0.810 | 0.322 | 1.481 | 0.048 | 0.083 | 0.593 | 0.126 | 0.182 | 28.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 141 | 214 | 202 | 351 | 170 | 226 | 209 | 233 | 208 |
N.S. |
1 | 0.90 | 1.36 | 1.29 | 2.24 | 1.08 | 1.44 | 1.33 | 1.48 | 1.32 |
time (sec) |
N/A | 0.706 | 0.165 | 1.465 | 0.052 | 0.091 | 0.384 | 0.129 | 0.185 | 28.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 70 | 66 | 92 | 201 | 71 | 85 | 92 | 103 | 100 |
N.S. |
1 | 0.89 | 0.84 | 1.16 | 2.54 | 0.90 | 1.08 | 1.16 | 1.30 | 1.27 |
time (sec) |
N/A | 0.570 | 0.062 | 1.289 | 0.048 | 0.119 | 0.210 | 0.126 | 0.174 | 28.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 35 | 101 | 34 | 31 | 35 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 3.74 | 1.26 | 1.15 | 1.30 | 1.15 | 1.15 |
time (sec) |
N/A | 0.355 | 0.007 | 0.976 | 0.040 | 0.086 | 0.067 | 0.121 | 0.188 | 28.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 85 | 91 | 177 | 0 | 0 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.98 | 1.05 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.693 | 0.082 | 3.684 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 189 | 141 | 317 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.25 | 0.93 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 1.129 | 0.171 | 3.671 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 335 | 226 | 510 | 0 | 0 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.34 | 0.90 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 1.909 | 0.246 | 3.797 | 0.000 | 0.000 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 579 | 838 | 374 | 1135 | 1427 | 939 | 1479 | 1213 | 1603 | 1346 |
N.S. |
1 | 1.45 | 0.65 | 1.96 | 2.46 | 1.62 | 2.55 | 2.09 | 2.77 | 2.32 |
time (sec) |
N/A | 4.976 | 0.621 | 2.167 | 0.088 | 0.120 | 1.736 | 0.131 | 0.257 | 27.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 521 | 267 | 721 | 964 | 606 | 918 | 769 | 1020 | 803 |
N.S. |
1 | 1.12 | 0.58 | 1.55 | 2.08 | 1.31 | 1.98 | 1.66 | 2.20 | 1.73 |
time (sec) |
N/A | 2.979 | 0.338 | 1.619 | 0.070 | 0.086 | 1.055 | 0.135 | 0.196 | 27.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 262 | 171 | 397 | 586 | 336 | 473 | 420 | 542 | 408 |
N.S. |
1 | 1.10 | 0.72 | 1.67 | 2.46 | 1.41 | 1.99 | 1.76 | 2.28 | 1.71 |
time (sec) |
N/A | 1.522 | 0.178 | 1.575 | 0.058 | 0.079 | 0.592 | 0.130 | 0.193 | 26.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 94 | 89 | 176 | 304 | 141 | 175 | 178 | 228 | 163 |
N.S. |
1 | 0.83 | 0.79 | 1.56 | 2.69 | 1.25 | 1.55 | 1.58 | 2.02 | 1.44 |
time (sec) |
N/A | 0.758 | 0.068 | 1.382 | 0.053 | 0.103 | 0.306 | 0.127 | 0.179 | 26.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 54 | 128 | 53 | 51 | 59 | 50 | 50 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 4.74 | 1.96 | 1.89 | 2.19 | 1.85 | 1.85 |
time (sec) |
N/A | 0.399 | 0.008 | 1.022 | 0.037 | 0.084 | 0.090 | 0.122 | 0.178 | 27.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 126 | 189 | 334 | 331 | 0 | 0 | 0 | 193 | 0 |
N.S. |
1 | 0.89 | 1.33 | 2.35 | 2.33 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.991 | 0.275 | 3.507 | 0.087 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 275 | 360 | 0 | 622 | 0 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.01 | 1.32 | 0.00 | 2.28 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 2.141 | 0.669 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 485 | 530 | 664 | 0 | 1271 | 0 | 0 | 0 | 225 | 0 |
N.S. |
1 | 1.09 | 1.37 | 0.00 | 2.62 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 4.090 | 1.127 | 0.000 | 0.205 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 207 | 0 | 567 | 0 | 401 | 0 | 0 | 215 | 0 |
N.S. |
1 | 0.90 | 0.00 | 2.47 | 0.00 | 1.74 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 1.333 | 0.000 | 8.149 | 0.000 | 0.092 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 160 | 0 | 361 | 0 | 260 | 0 | 0 | 168 | 0 |
N.S. |
1 | 0.90 | 0.00 | 2.04 | 0.00 | 1.47 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 1.074 | 0.000 | 7.003 | 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 | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 113 | 112 | 200 | 0 | 149 | 0 | 0 | 119 | 0 |
N.S. |
1 | 0.91 | 0.90 | 1.61 | 0.00 | 1.20 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.920 | 0.401 | 5.813 | 0.000 | 0.100 | 0.000 | 0.000 | 0.195 | 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 | 71 | 66 | 69 | 88 | 0 | 70 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.93 | 0.97 | 1.24 | 0.00 | 0.99 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.690 | 0.197 | 4.257 | 0.000 | 0.067 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 24 | 29 | 24 | 17 | 24 | 24 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.26 | 1.04 | 0.74 | 1.04 | 1.04 | 1.00 |
time (sec) |
N/A | 0.407 | 0.061 | 1.485 | 0.033 | 0.076 | 0.092 | 0.128 | 0.185 | 27.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 68 | 99 | 34 | 87 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.12 | 3.09 | 1.06 | 2.72 | 1.06 |
time (sec) |
N/A | 0.713 | 0.211 | 3.550 | 0.075 | 0.065 | 2.544 | 0.121 | 0.193 | 28.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 122 | 180 | 34 | 149 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 3.81 | 5.62 | 1.06 | 4.66 | 1.06 |
time (sec) |
N/A | 0.857 | 0.263 | 5.990 | 0.077 | 0.072 | 5.034 | 0.148 | 0.254 | 28.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 485 | 969 | 818 | 0 | 0 | 0 | 0 | 0 | 945 | 0 |
N.S. |
1 | 2.00 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 7.536 | 1.271 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 725 | 644 | 0 | 0 | 0 | 0 | 0 | 576 | 0 |
N.S. |
1 | 1.74 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 5.205 | 0.848 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 519 | 534 | 0 | 0 | 0 | 0 | 0 | 238 | 0 |
N.S. |
1 | 1.49 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 3.462 | 0.617 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |