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 | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 122 | 112 | 0 | 0 | 0 | 950 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.90 | 0.00 | 0.00 | 0.00 | 7.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.429 | 0.088 | 0.000 | 0.000 | 0.000 | 12.666 | 0.000 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 122 | 112 | 0 | 0 | 0 | 950 | 0 | 1250 | 0 |
| N.S. |
1 | 0.98 | 0.90 | 0.00 | 0.00 | 0.00 | 7.60 | 0.00 | 10.00 | 0.00 |
| time (sec) |
N/A | 0.427 | 0.068 | 0.000 | 0.000 | 0.000 | 8.377 | 0.000 | 0.270 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 99 | 87 | 0 | 0 | 0 | 364 | 0 | 953 | 0 |
| N.S. |
1 | 0.99 | 0.87 | 0.00 | 0.00 | 0.00 | 3.64 | 0.00 | 9.53 | 0.00 |
| time (sec) |
N/A | 0.393 | 0.066 | 0.000 | 0.000 | 0.000 | 6.804 | 0.000 | 0.278 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 99 | 87 | 0 | 0 | 0 | 364 | 0 | 643 | 0 |
| N.S. |
1 | 0.99 | 0.87 | 0.00 | 0.00 | 0.00 | 3.64 | 0.00 | 6.43 | 0.00 |
| time (sec) |
N/A | 0.383 | 0.073 | 0.000 | 0.000 | 0.000 | 4.416 | 0.000 | 0.319 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 71 | 0 | 0 | 0 | 65 | 0 | 436 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 5.81 | 0.00 |
| time (sec) |
N/A | 0.312 | 0.035 | 0.000 | 0.000 | 0.000 | 3.588 | 0.000 | 0.306 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 98 | 0 | 0 | 0 | 61 | 0 | 223 | 65 |
| N.S. |
1 | 1.00 | 1.40 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 3.19 | 0.93 |
| time (sec) |
N/A | 0.299 | 0.051 | 0.000 | 0.000 | 0.000 | 2.401 | 0.000 | 0.341 | 9.525 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 88 | 0 | 0 | 0 | 65 | 0 | 253 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 | 2.88 | 0.00 |
| time (sec) |
N/A | 0.342 | 0.045 | 0.000 | 0.000 | 0.000 | 3.522 | 0.000 | 0.255 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 91 | 0 | 0 | 0 | 68 | 0 | 287 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 3.15 | 0.00 |
| time (sec) |
N/A | 0.358 | 0.065 | 0.000 | 0.000 | 0.000 | 3.790 | 0.000 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 92 | 89 | 0 | 0 | 0 | 70 | 0 | 388 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 4.22 | 0.00 |
| time (sec) |
N/A | 0.339 | 0.053 | 0.000 | 0.000 | 0.000 | 5.276 | 0.000 | 0.324 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 182 | 205 | 0 | 0 | 0 | 2883 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.09 | 0.00 | 0.00 | 0.00 | 15.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.577 | 0.171 | 0.000 | 0.000 | 0.000 | 17.331 | 0.000 | 0.236 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 167 | 156 | 0 | 0 | 0 | 986 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.92 | 0.00 | 0.00 | 0.00 | 5.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.567 | 0.145 | 0.000 | 0.000 | 0.000 | 16.601 | 0.000 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 146 | 152 | 0 | 0 | 0 | 1294 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 8.68 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.520 | 0.124 | 0.000 | 0.000 | 0.000 | 9.313 | 0.000 | 0.226 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 139 | 0 | 0 | 0 | 400 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 2.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.526 | 0.135 | 0.000 | 0.000 | 0.000 | 8.836 | 0.000 | 0.217 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 112 | 184 | 0 | 0 | 0 | 408 | 0 | 833 | 0 |
| N.S. |
1 | 0.93 | 1.53 | 0.00 | 0.00 | 0.00 | 3.40 | 0.00 | 6.94 | 0.00 |
| time (sec) |
N/A | 0.447 | 0.147 | 0.000 | 0.000 | 0.000 | 4.731 | 0.000 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 126 | 133 | 0 | 0 | 0 | 97 | 0 | 808 | 0 |
| N.S. |
1 | 1.18 | 1.24 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 | 7.55 | 0.00 |
| time (sec) |
N/A | 0.415 | 0.095 | 0.000 | 0.000 | 0.000 | 4.525 | 0.000 | 0.225 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 101 | 0 | 0 | 0 | 109 | 0 | 476 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 | 4.03 | 0.00 |
| time (sec) |
N/A | 0.406 | 0.075 | 0.000 | 0.000 | 0.000 | 4.135 | 0.000 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 127 | 134 | 0 | 0 | 0 | 95 | 0 | 633 | 0 |
| N.S. |
1 | 0.89 | 0.94 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 | 4.43 | 0.00 |
| time (sec) |
N/A | 0.424 | 0.054 | 0.000 | 0.000 | 0.000 | 4.882 | 0.000 | 0.229 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 128 | 119 | 0 | 0 | 0 | 117 | 0 | 593 | 0 |
| N.S. |
1 | 0.96 | 0.89 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 4.46 | 0.00 |
| time (sec) |
N/A | 0.435 | 0.062 | 0.000 | 0.000 | 0.000 | 6.519 | 0.000 | 0.215 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 233 | 249 | 0 | 0 | 0 | 2919 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.01 | 0.00 | 0.00 | 0.00 | 11.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.747 | 0.173 | 0.000 | 0.000 | 0.000 | 31.349 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 234 | 249 | 0 | 0 | 0 | 2919 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.00 | 0.00 | 0.00 | 0.00 | 11.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.739 | 0.135 | 0.000 | 0.000 | 0.000 | 21.825 | 0.000 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 197 | 196 | 0 | 0 | 0 | 1329 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.95 | 0.00 | 0.00 | 0.00 | 6.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.661 | 0.090 | 0.000 | 0.000 | 0.000 | 17.735 | 0.000 | 0.249 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 198 | 196 | 0 | 0 | 0 | 1329 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.93 | 0.00 | 0.00 | 0.00 | 6.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.651 | 0.097 | 0.000 | 0.000 | 0.000 | 11.762 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 158 | 228 | 0 | 0 | 0 | 440 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.41 | 0.00 | 0.00 | 0.00 | 2.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.604 | 0.214 | 0.000 | 0.000 | 0.000 | 9.786 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 185 | 223 | 0 | 0 | 0 | 437 | 0 | 1314 | 0 |
| N.S. |
1 | 1.09 | 1.32 | 0.00 | 0.00 | 0.00 | 2.59 | 0.00 | 7.78 | 0.00 |
| time (sec) |
N/A | 0.587 | 0.211 | 0.000 | 0.000 | 0.000 | 6.087 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 166 | 170 | 0 | 0 | 0 | 144 | 0 | 1294 | 0 |
| N.S. |
1 | 1.01 | 1.03 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 7.84 | 0.00 |
| time (sec) |
N/A | 0.494 | 0.081 | 0.000 | 0.000 | 0.000 | 6.459 | 0.000 | 0.208 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 159 | 154 | 0 | 0 | 0 | 143 | 0 | 1162 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 | 7.31 | 0.00 |
| time (sec) |
N/A | 0.482 | 0.081 | 0.000 | 0.000 | 0.000 | 5.492 | 0.000 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 169 | 174 | 0 | 0 | 0 | 148 | 0 | 1321 | 0 |
| N.S. |
1 | 0.92 | 0.95 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 | 7.22 | 0.00 |
| time (sec) |
N/A | 0.498 | 0.083 | 0.000 | 0.000 | 0.000 | 8.394 | 0.000 | 0.236 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 176 | 174 | 0 | 0 | 0 | 156 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.96 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.501 | 0.439 | 0.000 | 0.000 | 0.000 | 10.551 | 0.000 | 0.237 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 199 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.670 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.350 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 260 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.519 | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 172 | 0 | 0 | 0 | 0 | 0 | 546 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.17 | 0.00 |
| time (sec) |
N/A | 0.462 | 0.198 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.314 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 177 | 170 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.01 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.511 | 0.268 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 218 | 256 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.02 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.653 | 0.356 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 198 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.630 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 162 | 227 | 0 | 0 | 0 | 0 | 0 | 818 | 0 |
| N.S. |
1 | 1.01 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.08 | 0.00 |
| time (sec) |
N/A | 0.509 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 125 | 131 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
| N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.410 | 0.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 178 | 214 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.520 | 0.422 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 220 | 314 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.01 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.618 | 0.734 | 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 | F | F | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 484 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.686 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.372 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 309 | 343 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.39 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.097 | 0.680 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 249 | 223 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.35 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.724 | 0.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 306 | 303 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.31 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.981 | 0.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 306 | 488 | 403 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.59 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 1.561 | 0.909 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 389 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.774 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.412 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 267 | 300 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.755 | 0.297 | 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 | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 191 | 141 | 0 | 0 | 0 | 0 | 0 | 996 | 0 |
| N.S. |
1 | 1.27 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 6.64 | 0.00 |
| time (sec) |
N/A | 0.640 | 0.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 296 | 296 | 342 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.964 | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 366 | 366 | 448 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 1.244 | 0.722 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 415 | 528 | 510 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.27 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.777 | 1.437 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.647 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 387 | 436 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.18 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.285 | 0.481 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.519 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 255 | 326 | 229 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.28 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.960 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.390 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 388 | 464 | 434 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
| N.S. |
1 | 1.20 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 1.498 | 0.606 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 473 | 744 | 537 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
| N.S. |
1 | 1.57 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 2.237 | 1.386 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 416 | 433 | 462 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.813 | 0.778 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.437 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 364 | 290 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.023 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.388 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 322 | 142 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
| N.S. |
1 | 1.49 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.607 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.338 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 389 | 460 | 478 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
| N.S. |
1 | 1.18 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.913 | 0.643 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.315 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 440 | 229 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.36 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.257 | 0.559 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.330 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 291 | 390 | 141 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
| N.S. |
1 | 1.34 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 1.119 | 0.546 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 81 | 0 | 0 | 0 | 90 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.352 | 0.026 | 0.000 | 0.000 | 0.000 | 154.723 | 0.000 | 0.261 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 81 | 0 | 0 | 0 | 90 | 0 | 1015 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 8.83 | 0.00 |
| time (sec) |
N/A | 0.352 | 0.015 | 0.000 | 0.000 | 0.000 | 25.045 | 0.000 | 0.279 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 80 | 0 | 0 | 0 | 90 | 0 | 559 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 | 4.95 | 0.00 |
| time (sec) |
N/A | 0.347 | 0.018 | 0.000 | 0.000 | 0.000 | 23.120 | 0.000 | 0.258 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 80 | 0 | 0 | 0 | 90 | 0 | 559 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 | 4.95 | 0.00 |
| time (sec) |
N/A | 0.344 | 0.001 | 0.000 | 0.000 | 0.000 | 23.180 | 0.000 | 0.236 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 188 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.500 | 0.835 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.321 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 188 | 110 | 0 | 0 | 0 | 139 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 0.64 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.498 | 0.711 | 0.000 | 0.000 | 0.000 | 50.547 | 0.000 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 185 | 109 | 0 | 0 | 0 | 139 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.62 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.504 | 0.712 | 0.000 | 0.000 | 0.000 | 45.468 | 0.000 | 0.292 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 185 | 109 | 0 | 0 | 0 | 139 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.62 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.514 | 0.002 | 0.000 | 0.000 | 0.000 | 40.580 | 0.000 | 0.295 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 248 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.864 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.346 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 191 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.766 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.458 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 141 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.655 | 0.000 | 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 | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 202 | 0 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.803 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.342 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 402 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.395 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.769 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 356 | 0 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.239 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.434 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 215 | 0 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.849 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.481 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 418 | 0 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 1.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.573 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 470 | 1467 | 400 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 3.12 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.349 | 3.326 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.593 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 727 | 325 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.95 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.192 | 2.546 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.643 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 357 | 248 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.80 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.678 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.859 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 155 | 0 | 0 | 0 | 0 | 0 | 863 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.75 | 0.00 |
| time (sec) |
N/A | 0.404 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.682 | 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 | 22 | 22 | 24 | 20 | 22 | 22 | 19 | 22 | 207 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.86 | 1.00 | 9.41 | 1.00 |
| time (sec) |
N/A | 0.251 | 5.873 | 0.171 | 0.071 | 0.088 | 4.268 | 0.255 | 0.469 | 8.764 |
| 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 | 22 | 22 | 24 | 20 | 22 | 22 | 20 | 22 | 579 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.91 | 1.00 | 26.32 | 1.00 |
| time (sec) |
N/A | 0.255 | 5.245 | 0.168 | 0.073 | 0.115 | 8.354 | 0.222 | 0.759 | 8.731 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 470 | 1469 | 401 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 3.13 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.205 | 3.576 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.891 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 729 | 325 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.95 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.205 | 2.469 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.478 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 359 | 248 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.81 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.692 | 0.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.654 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 173 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.400 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.217 | 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 | 22 | 22 | 24 | 20 | 22 | 22 | 19 | 22 | 1267 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.86 | 1.00 | 57.59 | 1.00 |
| time (sec) |
N/A | 0.255 | 6.985 | 0.170 | 0.076 | 0.084 | 20.255 | 0.344 | 0.890 | 8.615 |
| 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 | 22 | 22 | 24 | 20 | 22 | 22 | 20 | 22 | 1703 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.91 | 1.00 | 77.41 | 1.00 |
| time (sec) |
N/A | 0.253 | 6.079 | 0.165 | 0.073 | 0.102 | 91.434 | 0.384 | 1.547 | 8.782 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 468 | 1406 | 628 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 3.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.257 | 0.433 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.017 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 370 | 668 | 495 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.81 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.251 | 0.244 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.391 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 300 | 223 | 0 | 0 | 0 | 0 | 0 | 870 | 0 |
| N.S. |
1 | 1.52 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.39 | 0.00 |
| time (sec) |
N/A | 0.582 | 0.106 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.758 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 153 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.436 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.407 | 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 | 22 | 22 | 24 | 20 | 22 | 30 | 19 | 22 | 29 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.36 | 0.86 | 1.00 | 1.32 | 1.00 |
| time (sec) |
N/A | 0.264 | 0.481 | 0.004 | 0.073 | 0.085 | 5.042 | 0.169 | 0.424 | 8.978 |
| 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 | 22 | 22 | 24 | 20 | 22 | 32 | 20 | 22 | 31 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.45 | 0.91 | 1.00 | 1.41 | 1.00 |
| time (sec) |
N/A | 0.264 | 0.371 | 0.007 | 0.073 | 0.104 | 7.614 | 0.165 | 0.577 | 8.977 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 487 | 487 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.286 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.369 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 368 | 390 | 294 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.838 | 1.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.960 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 373 | 220 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.88 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.739 | 0.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.953 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 153 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.398 | 0.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.427 | 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 | 22 | 22 | 24 | 20 | 22 | 41 | 19 | 22 | 40 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.86 | 0.86 | 1.00 | 1.82 | 1.00 |
| time (sec) |
N/A | 0.257 | 2.938 | 0.167 | 0.076 | 0.088 | 10.783 | 0.173 | 0.499 | 9.059 |
| 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 | 22 | 22 | 24 | 20 | 22 | 43 | 20 | 22 | 42 | 22 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.95 | 0.91 | 1.00 | 1.91 | 1.00 |
| time (sec) |
N/A | 0.259 | 2.818 | 0.174 | 0.075 | 0.125 | 13.366 | 0.185 | 0.853 | 9.193 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 103 | 142 | 162 | 471 | 2783 | 816 | 565 | 393 |
| N.S. |
1 | 1.00 | 0.72 | 0.99 | 1.13 | 3.29 | 19.46 | 5.71 | 3.95 | 2.75 |
| time (sec) |
N/A | 0.500 | 0.070 | 0.256 | 0.045 | 0.086 | 0.487 | 0.135 | 0.242 | 9.234 |