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 | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 87 | 283 | 0 | 147 | 0 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 2.53 | 0.00 | 1.31 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 0.719 | 0.680 | 9.628 | 0.000 | 0.095 | 0.000 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 142 | 100 | 357 | 0 | 170 | 0 | 0 | 81 | 0 |
| N.S. |
1 | 1.01 | 0.71 | 2.53 | 0.00 | 1.21 | 0.00 | 0.00 | 0.57 | 0.00 |
| time (sec) |
N/A | 0.871 | 0.897 | 15.895 | 0.000 | 0.093 | 0.000 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 170 | 120 | 362 | 0 | 191 | 0 | 0 | 81 | 0 |
| N.S. |
1 | 0.97 | 0.69 | 2.07 | 0.00 | 1.09 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 1.015 | 1.149 | 16.997 | 0.000 | 0.094 | 0.000 | 0.000 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 198 | 135 | 398 | 0 | 203 | 0 | 0 | 81 | 0 |
| N.S. |
1 | 0.99 | 0.68 | 1.99 | 0.00 | 1.02 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 1.233 | 1.521 | 25.181 | 0.000 | 0.111 | 0.000 | 0.000 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 218 | 191 | 820 | 0 | 270 | 0 | 0 | 115 | 0 |
| N.S. |
1 | 0.93 | 0.82 | 3.50 | 0.00 | 1.15 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 1.406 | 1.387 | 965.345 | 0.000 | 0.101 | 0.000 | 0.000 | 0.310 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 181 | 134 | 711 | 0 | 244 | 0 | 0 | 115 | 0 |
| N.S. |
1 | 0.96 | 0.71 | 3.76 | 0.00 | 1.29 | 0.00 | 0.00 | 0.61 | 0.00 |
| time (sec) |
N/A | 1.215 | 1.482 | 983.105 | 0.000 | 0.098 | 0.000 | 0.000 | 0.322 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 161 | 106 | 630 | 0 | 214 | 0 | 0 | 115 | 0 |
| N.S. |
1 | 1.01 | 0.66 | 3.94 | 0.00 | 1.34 | 0.00 | 0.00 | 0.72 | 0.00 |
| time (sec) |
N/A | 1.038 | 1.114 | 1001.356 | 0.000 | 0.104 | 0.000 | 0.000 | 0.312 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 167 | 108 | 303 | 0 | 182 | 0 | 0 | 107 | 0 |
| N.S. |
1 | 1.01 | 0.65 | 1.83 | 0.00 | 1.10 | 0.00 | 0.00 | 0.64 | 0.00 |
| time (sec) |
N/A | 1.084 | 0.978 | 14.298 | 0.000 | 0.097 | 0.000 | 0.000 | 0.278 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 157 | 106 | 412 | 0 | 193 | 0 | 0 | 82 | 0 |
| N.S. |
1 | 1.01 | 0.68 | 2.64 | 0.00 | 1.24 | 0.00 | 0.00 | 0.53 | 0.00 |
| time (sec) |
N/A | 1.045 | 0.920 | 17.013 | 0.000 | 0.100 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 194 | 132 | 421 | 0 | 216 | 0 | 0 | 115 | 0 |
| N.S. |
1 | 0.97 | 0.66 | 2.12 | 0.00 | 1.09 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 1.234 | 1.279 | 21.117 | 0.000 | 0.098 | 0.000 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 222 | 159 | 470 | 0 | 238 | 0 | 0 | 115 | 0 |
| N.S. |
1 | 0.95 | 0.68 | 2.01 | 0.00 | 1.02 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 1.397 | 1.603 | 24.120 | 0.000 | 0.106 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 201 | 165 | 425 | 0 | 0 | 0 | 0 | 30 | 0 |
| N.S. |
1 | 1.07 | 0.88 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.617 | 35.377 | 19.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 116 | 83 | 354 | 0 | 0 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 0.99 | 0.71 | 3.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.855 | 15.286 | 4.115 | 0.000 | 0.000 | 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 | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 49 | 63 | 150 | 0 | 0 | 0 | 0 | 22 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 3.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.395 | 0.294 | 2.575 | 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(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 74 | 47 | 188 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 0.80 | 0.51 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.564 | 0.258 | 4.690 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 176 | 227 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.00 | 1.30 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.978 | 19.698 | 6.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 178 | 196 | 552 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.03 | 1.14 | 3.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 1.323 | 21.657 | 7.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 341 | 324 | 294 | 981 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 0.95 | 0.86 | 2.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 2.578 | 4.881 | 66.315 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 266 | 351 | 847 | 0 | 0 | 0 | 0 | 44 | 0 |
| N.S. |
1 | 0.96 | 1.27 | 3.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 2.073 | 2.992 | 7.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 213 | 297 | 612 | 0 | 0 | 0 | 0 | 38 | 0 |
| N.S. |
1 | 0.98 | 1.37 | 2.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 1.449 | 5.380 | 3.934 | 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 | A | B | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 203 | 574 | 713 | 0 | 0 | 0 | 0 | 57 | 0 |
| N.S. |
1 | 0.98 | 2.76 | 3.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 1.383 | 6.422 | 6.905 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 211 | 250 | 794 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.95 | 1.12 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 1.420 | 3.567 | 7.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 233 | 319 | 815 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 0.95 | 1.30 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 1.618 | 3.880 | 9.663 | 0.000 | 0.000 | 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(-1) | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 455 | 446 | 747 | 2101 | 0 | 0 | 0 | 0 | 62 | 0 |
| N.S. |
1 | 0.98 | 1.64 | 4.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 3.540 | 6.626 | 290.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 388 | 383 | 532 | 1965 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 0.99 | 1.37 | 5.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 2.914 | 6.481 | 10.434 | 0.000 | 0.000 | 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 | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 321 | 324 | 341 | 1176 | 0 | 0 | 0 | 0 | 54 | 0 |
| N.S. |
1 | 1.01 | 1.06 | 3.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 2.328 | 5.723 | 3.976 | 0.000 | 0.000 | 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 | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 314 | 395 | 1736 | 0 | 0 | 0 | 0 | 79 | 0 |
| N.S. |
1 | 0.99 | 1.25 | 5.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 2.205 | 3.943 | 7.411 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 302 | 303 | 429 | 1836 | 0 | 0 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 1.00 | 1.42 | 6.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 2.108 | 5.244 | 9.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 319 | 317 | 280 | 1914 | 0 | 0 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 0.99 | 0.88 | 6.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 2.174 | 3.759 | 9.712 | 0.000 | 0.000 | 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 | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 369 | 359 | 353 | 971 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.97 | 0.96 | 2.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 1.453 | 24.087 | 22.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 311 | 293 | 261 | 560 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.94 | 0.84 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 0.987 | 14.776 | 22.123 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 269 | 250 | 215 | 477 | 0 | 0 | 0 | 0 | 27 | 0 |
| N.S. |
1 | 0.93 | 0.80 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 0.782 | 4.730 | 17.516 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 146 | 179 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.412 | 1.583 | 14.198 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 431 | 405 | 2995 | 467 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.94 | 6.95 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 1.508 | 19.304 | 8.378 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 498 | 456 | 837 | 716 | 0 | 0 | 0 | 0 | 29 | 0 |
| N.S. |
1 | 0.92 | 1.68 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
| time (sec) |
N/A | 2.025 | 16.239 | 11.478 | 0.000 | 0.000 | 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 | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 419 | 441 | 1150 | 0 | 0 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 0.98 | 1.03 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.895 | 11.192 | 31.155 | 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 | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 347 | 345 | 967 | 0 | 0 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 0.95 | 0.95 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 1.445 | 7.891 | 26.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 299 | 291 | 671 | 0 | 0 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 0.94 | 0.92 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 1.076 | 5.037 | 22.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 397 | 367 | 639 | 696 | 0 | 0 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 0.92 | 1.61 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.274 | 16.088 | 19.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 435 | 402 | 322 | 592 | 0 | 0 | 0 | 0 | 53 | 0 |
| N.S. |
1 | 0.92 | 0.74 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 1.592 | 9.171 | 16.768 | 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 | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 493 | 467 | 845 | 806 | 0 | 0 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 0.95 | 1.71 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 2.372 | 15.996 | 12.638 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 568 | 532 | 961 | 969 | 0 | 0 | 0 | 0 | 69 | 0 |
| N.S. |
1 | 0.94 | 1.69 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 2.592 | 15.311 | 14.963 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 494 | 489 | 521 | 1563 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.99 | 1.05 | 3.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 2.519 | 13.334 | 2216.853 | 0.000 | 0.000 | 0.000 | 0.000 | 0.293 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 416 | 387 | 1150 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.97 | 0.91 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 1.988 | 11.000 | 2600.338 | 0.000 | 0.000 | 0.000 | 0.000 | 0.299 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 378 | 362 | 376 | 1080 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.96 | 0.99 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 1.549 | 10.405 | 2233.612 | 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 | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 452 | 414 | 377 | 901 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.92 | 0.83 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 1.723 | 10.072 | 2925.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 505 | 479 | 421 | 940 | 0 | 0 | 0 | 0 | 108 | 0 |
| N.S. |
1 | 0.95 | 0.83 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 2.132 | 11.852 | 22.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 503 | 473 | 421 | 945 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 0.94 | 0.84 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 2.237 | 8.349 | 18.916 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 566 | 544 | 970 | 1054 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.96 | 1.71 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 2.667 | 15.145 | 14.848 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 638 | 616 | 1226 | 1334 | 0 | 0 | 0 | 0 | 114 | 0 |
| N.S. |
1 | 0.97 | 1.92 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 3.334 | 14.107 | 17.137 | 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(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 299 | 322 | 564 | 0 | 0 | 0 | 0 | 41 | 0 |
| N.S. |
1 | 0.95 | 1.03 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 1.028 | 10.975 | 24.757 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 264 | 245 | 296 | 381 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 0.93 | 1.12 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.761 | 11.255 | 20.274 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 103 | 109 | 0 | 0 | 0 | 0 | 33 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.401 | 0.774 | 14.695 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 146 | 139 | 0 | 0 | 0 | 0 | 46 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.398 | 1.714 | 12.612 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 474 | 445 | 235 | 373 | 0 | 0 | 0 | 0 | 50 | 0 |
| N.S. |
1 | 0.94 | 0.50 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 1.794 | 5.414 | 14.843 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 505 | 468 | 678 | 736 | 0 | 0 | 0 | 0 | 50 | 0 |
| N.S. |
1 | 0.93 | 1.34 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 2.024 | 12.789 | 17.058 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 397 | 397 | 440 | 1088 | 0 | 0 | 0 | 0 | 57 | 0 |
| N.S. |
1 | 1.00 | 1.11 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 1.585 | 11.471 | 27.602 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 332 | 369 | 869 | 0 | 0 | 0 | 0 | 55 | 0 |
| N.S. |
1 | 1.02 | 1.14 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 1.169 | 7.796 | 23.491 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 311 | 237 | 498 | 0 | 0 | 0 | 0 | 49 | 0 |
| N.S. |
1 | 1.01 | 0.77 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.068 | 6.396 | 17.744 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 306 | 311 | 235 | 466 | 0 | 0 | 0 | 0 | 68 | 0 |
| N.S. |
1 | 1.02 | 0.77 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 1.016 | 2.700 | 9.004 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 447 | 434 | 893 | 694 | 0 | 0 | 0 | 0 | 74 | 0 |
| N.S. |
1 | 0.97 | 2.00 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 1.540 | 16.016 | 15.647 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 525 | 515 | 1025 | 961 | 0 | 0 | 0 | 0 | 74 | 0 |
| N.S. |
1 | 0.98 | 1.95 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 2.244 | 13.438 | 17.938 | 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(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 513 | 512 | 546 | 2027 | 0 | 0 | 0 | 0 | 73 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 3.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 2.225 | 14.292 | 30.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 438 | 444 | 525 | 1705 | 0 | 0 | 0 | 0 | 71 | 0 |
| N.S. |
1 | 1.01 | 1.20 | 3.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
| time (sec) |
N/A | 1.691 | 13.754 | 25.615 | 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 | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 421 | 421 | 471 | 1310 | 0 | 0 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 1.00 | 1.12 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 1.553 | 11.763 | 19.945 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 399 | 399 | 455 | 1137 | 0 | 0 | 0 | 0 | 90 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 2.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 1.509 | 11.360 | 13.582 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 382 | 382 | 359 | 877 | 0 | 0 | 0 | 0 | 98 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 1.416 | 6.700 | 13.527 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 557 | 546 | 1335 | 1952 | 0 | 0 | 0 | 0 | 98 | 0 |
| N.S. |
1 | 0.98 | 2.40 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 2.378 | 12.821 | 17.894 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | 330 | 330 | 242 | 0 | 0 | 0 | 0 | 0 | 113 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 1.338 | 1.193 | 0.000 | 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 | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 247 | 197 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 0.99 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.848 | 0.633 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 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 | 179 | 175 | 168 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 0.98 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
| time (sec) |
N/A | 0.517 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 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 | 131 | 131 | 112 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.310 | 0.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 190 | 6534 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 34.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.522 | 23.944 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 294 | 7214 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.00 | 24.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.682 | 29.152 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 282 | 282 | 222 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 1.515 | 0.641 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 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 | 200 | 194 | 159 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 0.97 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.900 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 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 | 143 | 143 | 107 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 0.505 | 0.136 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | C | F(-2) | A | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 47 | 58 | 0 | 30 | 0 | 71 | 27 | 0 |
| N.S. |
1 | 1.00 | 1.81 | 2.23 | 0.00 | 1.15 | 0.00 | 2.73 | 1.04 | 0.00 |
| time (sec) |
N/A | 0.245 | 0.106 | 4.043 | 0.000 | 0.103 | 0.000 | 0.393 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 64 | 65 | 0 | 32 | 0 | 46 | 23 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 1.00 | 0.00 | 0.49 | 0.00 | 0.71 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.357 | 0.103 | 2.964 | 0.000 | 0.105 | 0.000 | 0.428 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 29 | 26 | 45 | 24 | 87 | 30 | 21 | 25 |
| N.S. |
1 | 1.00 | 0.78 | 0.70 | 1.22 | 0.65 | 2.35 | 0.81 | 0.57 | 0.68 |
| time (sec) |
N/A | 0.200 | 0.107 | 3.327 | 0.028 | 0.072 | 0.105 | 0.367 | 0.152 | 43.002 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 27 | 34 | 144 | 70 | 333 | 88 | 59 | 29 |
| N.S. |
1 | 1.00 | 1.04 | 1.31 | 5.54 | 2.69 | 12.81 | 3.38 | 2.27 | 1.12 |
| time (sec) |
N/A | 0.209 | 0.523 | 174.898 | 0.034 | 0.074 | 0.337 | 0.446 | 0.164 | 43.875 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 28 | 29 | 143 | 27 | 114 | 795 | 69 | 28 |
| N.S. |
1 | 1.00 | 1.00 | 1.04 | 5.11 | 0.96 | 4.07 | 28.39 | 2.46 | 1.00 |
| time (sec) |
N/A | 0.232 | 0.866 | 13.172 | 0.253 | 0.079 | 1.834 | 1.904 | 0.164 | 42.662 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 27 | 30 | 115 | 56 | 80 | 47 | 46 | 33 |
| N.S. |
1 | 1.00 | 1.04 | 1.15 | 4.42 | 2.15 | 3.08 | 1.81 | 1.77 | 1.27 |
| time (sec) |
N/A | 0.216 | 0.558 | 2.079 | 0.071 | 0.070 | 0.808 | 0.388 | 0.152 | 42.498 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 45 | 48 | 92 | 36 | 0 | 80 | 62 | 0 |
| N.S. |
1 | 1.00 | 1.61 | 1.71 | 3.29 | 1.29 | 0.00 | 2.86 | 2.21 | 0.00 |
| time (sec) |
N/A | 0.228 | 0.090 | 5.273 | 0.243 | 0.071 | 0.000 | 0.423 | 0.171 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 33 | 43 | 19040 | 36 | 0 | 33 | 18 | 37 |
| N.S. |
1 | 1.00 | 1.27 | 1.65 | 732.31 | 1.38 | 0.00 | 1.27 | 0.69 | 1.42 |
| time (sec) |
N/A | 0.209 | 0.075 | 4.185 | 0.404 | 0.070 | 0.000 | 0.414 | 0.162 | 42.074 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-1) | B | F | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 28 | 48 | 0 | 68 | 0 | 0 | 103 | 85 |
| N.S. |
1 | 1.00 | 1.00 | 1.71 | 0.00 | 2.43 | 0.00 | 0.00 | 3.68 | 3.04 |
| time (sec) |
N/A | 0.223 | 0.061 | 4.709 | 0.000 | 0.075 | 0.000 | 0.000 | 0.168 | 51.674 |
| 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 | 104 | 104 | 164 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.411 | 0.677 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 304 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 2.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.409 | 4.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 101 | 101 | 133 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 0.407 | 0.406 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 254 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.420 | 2.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 70 | 64 | 77 | 0 | 194 | 233 | 281 | 62 | 93 |
| N.S. |
1 | 1.11 | 1.02 | 1.22 | 0.00 | 3.08 | 3.70 | 4.46 | 0.98 | 1.48 |
| time (sec) |
N/A | 0.321 | 0.157 | 1.829 | 0.000 | 0.096 | 14.334 | 0.379 | 0.163 | 42.913 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 22 | 22 | 22 | 23 | 0 | 22 | 267 | 50 | 22 | 37 |
| N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.00 | 12.14 | 2.27 | 1.00 | 1.68 |
| time (sec) |
N/A | 0.211 | 0.220 | 1.802 | 0.000 | 0.070 | 160.674 | 0.357 | 0.166 | 42.003 |
| 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 | 47 | 49 | 31 | 37 | 52 | 43 | 56 | 72 | 30 | 74 |
| N.S. |
1 | 1.04 | 0.66 | 0.79 | 1.11 | 0.91 | 1.19 | 1.53 | 0.64 | 1.57 |
| time (sec) |
N/A | 0.279 | 0.082 | 1.634 | 0.132 | 0.083 | 0.938 | 0.376 | 0.152 | 42.927 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 58 | 171 | 0 | 359 | 0 | 0 | 15 | 56 |
| N.S. |
1 | 1.00 | 1.00 | 2.95 | 0.00 | 6.19 | 0.00 | 0.00 | 0.26 | 0.97 |
| time (sec) |
N/A | 0.313 | 0.102 | 9.518 | 0.000 | 0.090 | 0.000 | 0.000 | 0.157 | 43.201 |
| 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 | 226 | 229 | 259 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.01 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.488 | 1.575 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 226 | 229 | 253 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.01 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.444 | 1.488 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 226 | 226 | 189 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.451 | 0.466 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 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 | 226 | 226 | 188 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.445 | 0.502 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 186 | 100 | 299 | 0 | 162 | 0 | 0 | 44 | 0 |
| N.S. |
1 | 1.11 | 0.60 | 1.78 | 0.00 | 0.96 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.752 | 0.743 | 15.523 | 0.000 | 0.087 | 0.000 | 0.000 | 0.169 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 152 | 91 | 271 | 0 | 151 | 0 | 0 | 42 | 0 |
| N.S. |
1 | 1.09 | 0.65 | 1.95 | 0.00 | 1.09 | 0.00 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.613 | 0.351 | 11.446 | 0.000 | 0.088 | 0.000 | 0.000 | 0.171 | 0.000 |