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 | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 207 | 417 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.450 | 0.424 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 207 | 337 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.417 | 0.585 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 207 | 399 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.420 | 0.789 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 213 | 452 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.423 | 0.778 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 221 | 505 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.438 | 0.898 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 264 | 292 | 194 | 0 | 0 | 0 | 257 | 0 | 0 |
| N.S. |
1 | 1.11 | 0.73 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.564 | 0.208 | 0.000 | 0.000 | 0.000 | 9.153 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 211 | 169 | 0 | 0 | 0 | 189 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.82 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.327 | 0.146 | 0.000 | 0.000 | 0.000 | 5.872 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 116 | 0 | 0 | 0 | 121 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.249 | 0.104 | 0.000 | 0.000 | 0.000 | 3.591 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 73 | 0 | 0 | 0 | 61 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.187 | 0.069 | 0.000 | 0.000 | 0.000 | 1.292 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 124 | 0 | 0 | 0 | 372 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 2.28 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.282 | 0.128 | 0.000 | 0.000 | 0.000 | 5.226 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 224 | 180 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.351 | 0.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 314 | 206 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.14 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.627 | 0.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 77 | 0 | 0 | 0 | 328 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 3.69 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.119 | 0.000 | 0.000 | 0.000 | 4.563 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.250 | 0.238 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 215 | 68 | 167 | 0 | 72 | 0 | 167 | 201 |
| N.S. |
1 | 1.00 | 0.32 | 0.78 | 0.00 | 0.34 | 0.00 | 0.78 | 0.94 |
| time (sec) |
N/A | 0.492 | 0.681 | 0.675 | 0.000 | 0.267 | 0.000 | 0.637 | 0.119 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 255 | 279 | 230 | 312 | 0 | 1104 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.90 | 1.22 | 0.00 | 4.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.859 | 0.658 | 0.443 | 0.000 | 4.061 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 225 | 199 | 266 | 0 | 963 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.94 | 1.26 | 0.00 | 4.56 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.552 | 0.443 | 0.437 | 0.000 | 4.133 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 162 | 161 | 227 | 0 | 776 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.05 | 1.48 | 0.00 | 5.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.346 | 0.366 | 0.421 | 0.000 | 0.632 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 134 | 133 | 203 | 0 | 684 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.05 | 1.60 | 0.00 | 5.39 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.298 | 0.297 | 0.421 | 0.000 | 0.607 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 108 | 110 | 184 | 0 | 574 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.07 | 1.79 | 0.00 | 5.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 0.015 | 0.422 | 0.000 | 0.464 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 122 | 137 | 305 | 122 | 1316 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.18 | 2.63 | 1.05 | 11.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.326 | 0.219 | 0.375 | 0.208 | 1.014 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 129 | 195 | 0 | 599 | 0 | 146 | 0 |
| N.S. |
1 | 1.00 | 1.23 | 1.86 | 0.00 | 5.70 | 0.00 | 1.39 | 0.00 |
| time (sec) |
N/A | 0.339 | 0.364 | 0.385 | 0.000 | 0.484 | 0.000 | 0.285 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 160 | 144 | 212 | 0 | 726 | 0 | 230 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 1.32 | 0.00 | 4.54 | 0.00 | 1.44 | 0.00 |
| time (sec) |
N/A | 0.383 | 0.445 | 0.443 | 0.000 | 0.461 | 0.000 | 0.302 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 173 | 241 | 0 | 824 | 0 | 313 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 1.26 | 0.00 | 4.31 | 0.00 | 1.64 | 0.00 |
| time (sec) |
N/A | 0.412 | 0.606 | 0.454 | 0.000 | 0.451 | 0.000 | 0.292 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 274 | 215 | 282 | 0 | 1007 | 0 | 605 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 1.03 | 0.00 | 3.68 | 0.00 | 2.21 | 0.00 |
| time (sec) |
N/A | 0.525 | 0.757 | 0.450 | 0.000 | 0.507 | 0.000 | 0.301 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 212 | 161 | 222 | 0 | 1060 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.83 | 1.14 | 0.00 | 5.44 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.728 | 0.512 | 0.443 | 0.000 | 2.393 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 159 | 137 | 201 | 0 | 924 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.90 | 1.32 | 0.00 | 6.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.448 | 0.382 | 0.425 | 0.000 | 2.406 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 111 | 128 | 172 | 0 | 745 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.17 | 1.58 | 0.00 | 6.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.264 | 0.445 | 0.419 | 0.000 | 0.471 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 98 | 151 | 0 | 631 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 1.76 | 0.00 | 7.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.226 | 0.240 | 0.411 | 0.000 | 0.453 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 54 | 64 | 127 | 60 | 211 | 0 | 60 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 2.35 | 1.11 | 3.91 | 0.00 | 1.11 | 0.00 |
| time (sec) |
N/A | 0.177 | 0.004 | 0.382 | 0.199 | 0.341 | 0.000 | 0.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 104 | 158 | 0 | 634 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.21 | 1.84 | 0.00 | 7.37 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.269 | 0.241 | 0.398 | 0.000 | 0.407 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 111 | 128 | 180 | 0 | 767 | 0 | 143 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 1.62 | 0.00 | 6.91 | 0.00 | 1.29 | 0.00 |
| time (sec) |
N/A | 0.283 | 0.329 | 0.425 | 0.000 | 0.438 | 0.000 | 0.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 198 | 209 | 0 | 956 | 0 | 240 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 1.24 | 0.00 | 5.69 | 0.00 | 1.43 | 0.00 |
| time (sec) |
N/A | 0.335 | 0.480 | 0.435 | 0.000 | 0.571 | 0.000 | 0.287 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 146 | 157 | 178 | 351 | 0 | 1525 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.22 | 2.40 | 0.00 | 10.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.460 | 0.806 | 0.471 | 0.000 | 3.477 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 129 | 137 | 397 | 0 | 1323 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.11 | 3.23 | 0.00 | 10.76 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.319 | 0.528 | 0.425 | 0.000 | 2.923 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 109 | 355 | 179 | 455 | 0 | 181 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 3.74 | 1.88 | 4.79 | 0.00 | 1.91 | 0.00 |
| time (sec) |
N/A | 0.237 | 0.470 | 0.417 | 0.217 | 0.358 | 0.000 | 0.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 99 | 335 | 156 | 425 | 0 | 168 | 0 |
| N.S. |
1 | 1.00 | 1.12 | 3.81 | 1.77 | 4.83 | 0.00 | 1.91 | 0.00 |
| time (sec) |
N/A | 0.225 | 0.376 | 0.404 | 0.215 | 0.332 | 0.000 | 0.301 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 94 | 104 | 315 | 131 | 456 | 0 | 180 | 0 |
| N.S. |
1 | 1.00 | 1.11 | 3.35 | 1.39 | 4.85 | 0.00 | 1.91 | 0.00 |
| time (sec) |
N/A | 0.230 | 0.045 | 0.348 | 0.204 | 0.321 | 0.000 | 0.281 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 147 | 144 | 363 | 0 | 1325 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 2.47 | 0.00 | 9.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.341 | 0.703 | 0.368 | 0.000 | 0.471 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 194 | 178 | 361 | 0 | 1556 | 0 | 273 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.86 | 0.00 | 8.02 | 0.00 | 1.41 | 0.00 |
| time (sec) |
N/A | 0.365 | 0.688 | 0.388 | 0.000 | 0.501 | 0.000 | 0.280 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 276 | 276 | 217 | 407 | 0 | 1943 | 0 | 365 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 1.47 | 0.00 | 7.04 | 0.00 | 1.32 | 0.00 |
| time (sec) |
N/A | 0.453 | 0.765 | 0.453 | 0.000 | 0.696 | 0.000 | 0.303 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 316 | 251 | 440 | 0 | 2025 | 0 | 0 | 0 |
| N.S. |
1 | 1.30 | 1.03 | 1.80 | 0.00 | 8.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.190 | 1.136 | 0.481 | 0.000 | 25.370 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 256 | 223 | 420 | 0 | 1786 | 0 | 0 | 0 |
| N.S. |
1 | 1.25 | 1.09 | 2.06 | 0.00 | 8.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.795 | 1.461 | 0.452 | 0.000 | 46.200 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 196 | 173 | 386 | 0 | 1449 | 0 | 0 | 0 |
| N.S. |
1 | 1.22 | 1.08 | 2.41 | 0.00 | 9.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.509 | 0.796 | 0.443 | 0.000 | 5.640 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 169 | 158 | 369 | 0 | 1260 | 0 | 0 | 0 |
| N.S. |
1 | 1.23 | 1.15 | 2.69 | 0.00 | 9.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.326 | 0.851 | 0.424 | 0.000 | 5.491 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 100 | 344 | 0 | 382 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.11 | 3.82 | 0.00 | 4.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.217 | 0.404 | 0.415 | 0.000 | 0.450 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 101 | 215 | 0 | 381 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.11 | 2.36 | 0.00 | 4.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.214 | 0.037 | 0.398 | 0.000 | 0.453 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 179 | 153 | 376 | 0 | 1261 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 2.10 | 0.00 | 7.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.356 | 0.707 | 0.379 | 0.000 | 0.817 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 212 | 212 | 183 | 395 | 0 | 1512 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 1.86 | 0.00 | 7.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.381 | 0.913 | 0.392 | 0.000 | 0.671 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 268 | 268 | 224 | 424 | 0 | 1867 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 1.58 | 0.00 | 6.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.453 | 1.126 | 0.419 | 0.000 | 1.020 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 114 | 320 | 210 | 368 | 4134 | 624 | 363 |
| N.S. |
1 | 1.00 | 0.84 | 2.37 | 1.56 | 2.73 | 30.62 | 4.62 | 2.69 |
| time (sec) |
N/A | 0.285 | 0.107 | 0.368 | 0.200 | 0.301 | 1.258 | 0.289 | 11.633 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 109 | 195 | 146 | 250 | 2181 | 410 | 255 |
| N.S. |
1 | 1.00 | 1.07 | 1.91 | 1.43 | 2.45 | 21.38 | 4.02 | 2.50 |
| time (sec) |
N/A | 0.256 | 0.109 | 0.402 | 0.199 | 0.286 | 0.783 | 0.283 | 11.563 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 65 | 100 | 89 | 148 | 952 | 237 | 163 |
| N.S. |
1 | 1.00 | 0.93 | 1.43 | 1.27 | 2.11 | 13.60 | 3.39 | 2.33 |
| time (sec) |
N/A | 0.214 | 0.058 | 0.388 | 0.190 | 0.308 | 0.495 | 0.269 | 11.522 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 64 | 0 | 0 | 0 | 279 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 3.62 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.220 | 0.064 | 0.000 | 0.000 | 0.000 | 2.287 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 232 | 199 | 754 | 447 | 1027 | 14317 | 1750 | 932 |
| N.S. |
1 | 1.00 | 0.86 | 3.25 | 1.93 | 4.43 | 61.71 | 7.54 | 4.02 |
| time (sec) |
N/A | 0.409 | 0.171 | 0.475 | 0.210 | 0.319 | 4.186 | 0.299 | 11.960 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 185 | 323 | 601 | 335 | 757 | 8940 | 1266 | 723 |
| N.S. |
1 | 1.00 | 1.75 | 3.25 | 1.81 | 4.09 | 48.32 | 6.84 | 3.91 |
| time (sec) |
N/A | 0.349 | 0.344 | 0.431 | 0.212 | 0.299 | 2.449 | 0.300 | 11.735 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 160 | 420 | 235 | 519 | 5097 | 851 | 496 |
| N.S. |
1 | 1.00 | 1.14 | 3.00 | 1.68 | 3.71 | 36.41 | 6.08 | 3.54 |
| time (sec) |
N/A | 0.287 | 0.162 | 0.420 | 0.192 | 0.306 | 1.436 | 0.277 | 11.625 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 132 | 0 | 0 | 0 | 1608 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 10.86 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.299 | 0.141 | 0.000 | 0.000 | 0.000 | 3.316 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 343 | 302 | 2232 | 795 | 2165 | 35984 | 3713 | 1796 |
| N.S. |
1 | 1.00 | 0.88 | 6.51 | 2.32 | 6.31 | 104.91 | 10.83 | 5.24 |
| time (sec) |
N/A | 0.523 | 0.220 | 0.453 | 0.244 | 0.311 | 11.304 | 0.297 | 12.660 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 282 | 282 | 709 | 1214 | 625 | 1675 | 24687 | 2851 | 1459 |
| N.S. |
1 | 1.00 | 2.51 | 4.30 | 2.22 | 5.94 | 87.54 | 10.11 | 5.17 |
| time (sec) |
N/A | 0.469 | 0.874 | 0.480 | 0.232 | 0.308 | 6.425 | 0.309 | 12.260 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 223 | 347 | 958 | 472 | 1244 | 15990 | 2085 | 1144 |
| N.S. |
1 | 1.00 | 1.56 | 4.30 | 2.12 | 5.58 | 71.70 | 9.35 | 5.13 |
| time (sec) |
N/A | 0.383 | 0.387 | 0.443 | 0.212 | 0.270 | 4.078 | 0.279 | 12.107 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 246 | 246 | 226 | 0 | 0 | 0 | 5622 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 22.85 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.409 | 0.189 | 0.000 | 0.000 | 0.000 | 4.956 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 276 | 217 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.757 | 0.401 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 232 | 168 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.513 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 195 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.339 | 0.146 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 151 | 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 |
| time (sec) |
N/A | 0.280 | 0.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 145 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.275 | 0.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 207 | 189 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.353 | 0.152 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 207 | 167 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.366 | 0.246 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 342 | 413 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.663 | 0.550 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 292 | 247 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.501 | 0.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 306 | 295 | 403 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.492 | 0.426 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 279 | 263 | 230 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.416 | 0.271 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 304 | 299 | 253 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.490 | 0.251 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 489 | 484 | 391 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.751 | 0.594 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 513 | 513 | 437 | 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 |
| time (sec) |
N/A | 0.815 | 0.537 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 399 | 378 | 275 | 0 | 0 | 0 | 128 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.69 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.732 | 0.130 | 0.000 | 0.000 | 0.000 | 16.572 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 157 | 113 | 0 | 0 | 0 | 80 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.69 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.281 | 0.075 | 0.000 | 0.000 | 0.000 | 6.299 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 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 |
| time (sec) |
N/A | 0.346 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 295 | 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 |
| time (sec) |
N/A | 0.546 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 122 | 112 | 0 | 0 | 0 | 950 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.90 | 0.00 | 0.00 | 0.00 | 7.60 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.271 | 0.138 | 0.000 | 0.000 | 0.000 | 12.803 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 122 | 112 | 0 | 0 | 0 | 950 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.90 | 0.00 | 0.00 | 0.00 | 7.60 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.273 | 0.122 | 0.000 | 0.000 | 0.000 | 8.511 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 99 | 87 | 0 | 0 | 0 | 364 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.87 | 0.00 | 0.00 | 0.00 | 3.64 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.243 | 0.118 | 0.000 | 0.000 | 0.000 | 6.896 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 99 | 87 | 0 | 0 | 0 | 364 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.87 | 0.00 | 0.00 | 0.00 | 3.64 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.248 | 0.106 | 0.000 | 0.000 | 0.000 | 4.564 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 71 | 0 | 0 | 0 | 65 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.190 | 0.073 | 0.000 | 0.000 | 0.000 | 3.694 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 98 | 0 | 0 | 0 | 61 | 0 | 65 |
| N.S. |
1 | 1.00 | 1.40 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 0.93 |
| time (sec) |
N/A | 0.180 | 0.108 | 0.000 | 0.000 | 0.000 | 2.451 | 0.000 | 12.309 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 88 | 0 | 0 | 0 | 65 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.204 | 0.097 | 0.000 | 0.000 | 0.000 | 3.697 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 91 | 0 | 0 | 0 | 68 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.213 | 0.105 | 0.000 | 0.000 | 0.000 | 3.952 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 92 | 89 | 0 | 0 | 0 | 70 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.216 | 0.101 | 0.000 | 0.000 | 0.000 | 5.504 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 182 | 205 | 0 | 0 | 0 | 2883 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.09 | 0.00 | 0.00 | 0.00 | 15.34 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.347 | 0.266 | 0.000 | 0.000 | 0.000 | 17.848 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 167 | 156 | 0 | 0 | 0 | 986 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.88 | 0.00 | 0.00 | 0.00 | 5.57 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.332 | 0.253 | 0.000 | 0.000 | 0.000 | 16.936 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 146 | 152 | 0 | 0 | 0 | 1294 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 8.68 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.305 | 0.196 | 0.000 | 0.000 | 0.000 | 9.547 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 144 | 139 | 0 | 0 | 0 | 400 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.91 | 0.00 | 0.00 | 0.00 | 2.63 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.309 | 0.216 | 0.000 | 0.000 | 0.000 | 8.843 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 112 | 184 | 0 | 0 | 0 | 408 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.63 | 0.00 | 0.00 | 0.00 | 3.61 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.269 | 0.200 | 0.000 | 0.000 | 0.000 | 4.841 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 126 | 133 | 0 | 0 | 0 | 97 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.260 | 0.174 | 0.000 | 0.000 | 0.000 | 4.566 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 101 | 0 | 0 | 0 | 109 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.244 | 0.167 | 0.000 | 0.000 | 0.000 | 4.186 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 134 | 0 | 0 | 0 | 95 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.255 | 0.192 | 0.000 | 0.000 | 0.000 | 4.985 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 128 | 119 | 0 | 0 | 0 | 117 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.94 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.252 | 0.164 | 0.000 | 0.000 | 0.000 | 6.649 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 233 | 249 | 0 | 0 | 0 | 2919 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.01 | 0.00 | 0.00 | 0.00 | 11.82 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.429 | 0.344 | 0.000 | 0.000 | 0.000 | 31.281 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 234 | 249 | 0 | 0 | 0 | 2919 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.00 | 0.00 | 0.00 | 0.00 | 11.72 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.428 | 0.315 | 0.000 | 0.000 | 0.000 | 21.453 | 0.000 | 0.000 |