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 | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 284 | 190 | 199 | 867 | 167 | 0 | 0 | 809 |
| N.S. |
1 | 1.00 | 0.67 | 0.70 | 3.05 | 0.59 | 0.00 | 0.00 | 2.85 |
| time (sec) |
N/A | 1.067 | 1.002 | 13.932 | 0.412 | 0.310 | 0.000 | 0.000 | 9.702 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 334 | 334 | 224 | 232 | 1004 | 191 | 0 | 0 | 941 |
| N.S. |
1 | 1.00 | 0.67 | 0.69 | 3.01 | 0.57 | 0.00 | 0.00 | 2.82 |
| time (sec) |
N/A | 1.146 | 1.171 | 13.311 | 0.415 | 0.296 | 0.000 | 0.000 | 10.705 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 241 | 346 | 403 | 0 | 213 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.44 | 1.67 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.972 | 1.039 | 27.222 | 0.000 | 15.850 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 195 | 265 | 305 | 0 | 193 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.36 | 1.56 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.716 | 0.738 | 27.859 | 0.000 | 15.748 | 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(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 112 | 210 | 0 | 171 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 1.49 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.514 | 0.333 | 33.449 | 0.000 | 6.151 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | C | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 266 | 204 | 1884 | 185 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.93 | 1.48 | 13.65 | 1.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.510 | 5.637 | 13.059 | 1.350 | 4.686 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | C | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 701 | 357 | 2006 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.90 | 2.50 | 14.03 | 1.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.456 | 6.949 | 12.722 | 1.337 | 0.304 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | C | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 1973 | 424 | 2490 | 185 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 10.33 | 2.22 | 13.04 | 0.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.682 | 7.603 | 12.398 | 1.319 | 0.303 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | C | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 237 | 2797 | 475 | 3203 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 11.80 | 2.00 | 13.51 | 0.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.874 | 9.456 | 13.169 | 1.393 | 0.307 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 213 | 342 | 397 | 0 | 245 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.61 | 1.86 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.860 | 0.842 | 28.190 | 0.000 | 14.956 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 260 | 260 | 366 | 595 | 0 | 273 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.41 | 2.29 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.968 | 2.341 | 27.763 | 0.000 | 45.393 | 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(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 202 | 279 | 457 | 0 | 241 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.38 | 2.26 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.731 | 1.983 | 29.201 | 0.000 | 21.845 | 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(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 178 | 357 | 0 | 213 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 2.40 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.533 | 1.120 | 14.316 | 0.000 | 16.570 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 161 | 455 | 363 | 0 | 211 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.83 | 2.25 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.506 | 4.996 | 13.283 | 0.000 | 0.330 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 213 | 1207 | 565 | 0 | 233 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 5.67 | 2.65 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.728 | 6.573 | 12.965 | 0.000 | 0.338 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 263 | 263 | 2470 | 622 | 0 | 255 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 9.39 | 2.37 | 0.00 | 0.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.960 | 7.767 | 14.105 | 0.000 | 0.337 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 254 | 364 | 729 | 0 | 319 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.43 | 2.87 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.077 | 5.070 | 30.771 | 0.000 | 47.253 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 201 | 305 | 589 | 0 | 283 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.52 | 2.93 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.922 | 2.843 | 9.285 | 0.000 | 35.861 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 711 | 485 | 0 | 235 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.36 | 2.98 | 0.00 | 1.44 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.491 | 6.468 | 14.329 | 0.000 | 0.305 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 946 | 561 | 0 | 264 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.48 | 2.66 | 0.00 | 1.25 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.760 | 7.266 | 14.055 | 0.000 | 0.332 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 261 | 1368 | 763 | 0 | 288 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 5.24 | 2.92 | 0.00 | 1.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.026 | 9.179 | 13.633 | 0.000 | 0.327 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 89 | 89 | 113 | 94 | 279 | 109 | 279 |
| N.S. |
1 | 1.00 | 0.68 | 0.68 | 0.86 | 0.72 | 2.13 | 0.83 | 2.13 |
| time (sec) |
N/A | 0.220 | 0.321 | 5.113 | 0.201 | 0.258 | 0.252 | 0.326 | 2.774 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 108 | 84 | 69 | 90 | 76 | 226 | 86 | 243 |
| N.S. |
1 | 1.00 | 0.78 | 0.64 | 0.83 | 0.70 | 2.09 | 0.80 | 2.25 |
| time (sec) |
N/A | 0.128 | 0.283 | 2.541 | 0.195 | 0.277 | 0.172 | 0.301 | 2.769 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 64 | 56 | 67 | 56 | 121 | 64 | 67 |
| N.S. |
1 | 1.00 | 0.67 | 0.58 | 0.70 | 0.58 | 1.26 | 0.67 | 0.70 |
| time (sec) |
N/A | 0.081 | 0.114 | 3.513 | 0.196 | 0.253 | 0.120 | 0.304 | 1.710 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 73 | 65 | 63 | 63 | 0 | 127 | 115 |
| N.S. |
1 | 1.00 | 1.26 | 1.12 | 1.09 | 1.09 | 0.00 | 2.19 | 1.98 |
| time (sec) |
N/A | 0.135 | 0.190 | 3.060 | 0.200 | 0.284 | 0.000 | 0.311 | 2.037 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 54 | 49 | 59 | 86 | 0 | 117 | 91 |
| N.S. |
1 | 1.00 | 1.29 | 1.17 | 1.40 | 2.05 | 0.00 | 2.79 | 2.17 |
| time (sec) |
N/A | 0.124 | 0.038 | 4.430 | 0.200 | 0.276 | 0.000 | 0.315 | 1.470 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 67 | 74 | 95 | 101 | 0 | 132 | 135 |
| N.S. |
1 | 1.00 | 1.16 | 1.28 | 1.64 | 1.74 | 0.00 | 2.28 | 2.33 |
| time (sec) |
N/A | 0.152 | 0.015 | 5.814 | 0.210 | 0.284 | 0.000 | 0.322 | 1.578 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 59 | 88 | 107 | 107 | 0 | 184 | 137 |
| N.S. |
1 | 1.00 | 0.69 | 1.02 | 1.24 | 1.24 | 0.00 | 2.14 | 1.59 |
| time (sec) |
N/A | 0.184 | 0.335 | 7.423 | 0.209 | 0.279 | 0.000 | 0.309 | 3.552 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 80 | 118 | 152 | 129 | 0 | 304 | 195 |
| N.S. |
1 | 1.00 | 0.68 | 1.01 | 1.30 | 1.10 | 0.00 | 2.60 | 1.67 |
| time (sec) |
N/A | 0.214 | 0.464 | 10.876 | 0.208 | 0.283 | 0.000 | 0.318 | 5.120 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 96 | 141 | 175 | 147 | 0 | 334 | 233 |
| N.S. |
1 | 1.00 | 0.69 | 1.01 | 1.25 | 1.05 | 0.00 | 2.39 | 1.66 |
| time (sec) |
N/A | 0.231 | 0.866 | 10.138 | 0.207 | 0.298 | 0.000 | 0.317 | 5.115 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 214 | 160 | 152 | 202 | 159 | 592 | 183 | 252 |
| N.S. |
1 | 1.00 | 0.75 | 0.71 | 0.94 | 0.74 | 2.77 | 0.86 | 1.18 |
| time (sec) |
N/A | 0.542 | 2.054 | 8.040 | 0.212 | 0.302 | 0.382 | 0.312 | 2.112 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 178 | 126 | 120 | 154 | 123 | 350 | 142 | 371 |
| N.S. |
1 | 1.00 | 0.71 | 0.67 | 0.87 | 0.69 | 1.97 | 0.80 | 2.08 |
| time (sec) |
N/A | 0.333 | 1.660 | 5.941 | 0.211 | 0.287 | 0.262 | 0.308 | 2.823 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 161 | 106 | 99 | 130 | 104 | 309 | 116 | 145 |
| N.S. |
1 | 1.00 | 0.66 | 0.61 | 0.81 | 0.65 | 1.92 | 0.72 | 0.90 |
| time (sec) |
N/A | 0.234 | 1.172 | 3.265 | 0.201 | 0.292 | 0.183 | 0.300 | 1.726 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 145 | 105 | 105 | 99 | 0 | 256 | 170 |
| N.S. |
1 | 1.00 | 1.41 | 1.02 | 1.02 | 0.96 | 0.00 | 2.49 | 1.65 |
| time (sec) |
N/A | 0.305 | 1.792 | 4.178 | 0.215 | 0.297 | 0.000 | 0.376 | 2.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 132 | 94 | 99 | 119 | 0 | 175 | 193 |
| N.S. |
1 | 1.00 | 1.21 | 0.86 | 0.91 | 1.09 | 0.00 | 1.61 | 1.77 |
| time (sec) |
N/A | 0.362 | 2.403 | 4.541 | 0.202 | 0.284 | 0.000 | 0.334 | 1.927 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 249 | 111 | 140 | 139 | 0 | 189 | 188 |
| N.S. |
1 | 1.00 | 2.42 | 1.08 | 1.36 | 1.35 | 0.00 | 1.83 | 1.83 |
| time (sec) |
N/A | 0.357 | 2.669 | 6.451 | 0.203 | 0.286 | 0.000 | 0.316 | 2.439 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 76 | 117 | 136 | 136 | 0 | 262 | 209 |
| N.S. |
1 | 1.00 | 0.68 | 1.04 | 1.21 | 1.21 | 0.00 | 2.34 | 1.87 |
| time (sec) |
N/A | 0.342 | 0.468 | 7.774 | 0.203 | 0.294 | 0.000 | 0.318 | 1.675 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 107 | 162 | 232 | 171 | 0 | 426 | 307 |
| N.S. |
1 | 1.00 | 0.69 | 1.05 | 1.51 | 1.11 | 0.00 | 2.77 | 1.99 |
| time (sec) |
N/A | 0.460 | 0.672 | 9.677 | 0.207 | 0.300 | 0.000 | 0.335 | 5.772 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 115 | 178 | 216 | 180 | 0 | 532 | 322 |
| N.S. |
1 | 1.00 | 0.61 | 0.95 | 1.16 | 0.96 | 0.00 | 2.84 | 1.72 |
| time (sec) |
N/A | 0.490 | 1.181 | 10.855 | 0.200 | 0.280 | 0.000 | 0.338 | 5.855 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 264 | 264 | 252 | 181 | 243 | 189 | 668 | 216 | 617 |
| N.S. |
1 | 1.00 | 0.95 | 0.69 | 0.92 | 0.72 | 2.53 | 0.82 | 2.34 |
| time (sec) |
N/A | 0.598 | 2.031 | 8.815 | 0.209 | 0.293 | 0.400 | 0.339 | 3.373 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 225 | 225 | 160 | 146 | 194 | 153 | 440 | 174 | 488 |
| N.S. |
1 | 1.00 | 0.71 | 0.65 | 0.86 | 0.68 | 1.96 | 0.77 | 2.17 |
| time (sec) |
N/A | 0.387 | 1.731 | 6.084 | 0.210 | 0.276 | 0.283 | 0.344 | 3.901 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 180 | 150 | 167 | 146 | 0 | 503 | 2008 |
| N.S. |
1 | 1.00 | 1.08 | 0.90 | 1.00 | 0.87 | 0.00 | 3.01 | 12.02 |
| time (sec) |
N/A | 0.599 | 2.286 | 4.510 | 0.203 | 0.294 | 0.000 | 0.318 | 3.586 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 185 | 135 | 141 | 158 | 0 | 306 | 238 |
| N.S. |
1 | 1.00 | 1.11 | 0.81 | 0.84 | 0.95 | 0.00 | 1.83 | 1.43 |
| time (sec) |
N/A | 0.546 | 2.855 | 5.845 | 0.202 | 0.294 | 0.000 | 0.325 | 2.665 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 285 | 156 | 179 | 171 | 0 | 385 | 282 |
| N.S. |
1 | 1.00 | 1.70 | 0.93 | 1.07 | 1.02 | 0.00 | 2.29 | 1.68 |
| time (sec) |
N/A | 0.630 | 4.064 | 7.441 | 0.215 | 0.310 | 0.000 | 0.348 | 3.693 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 377 | 153 | 181 | 178 | 0 | 322 | 464 |
| N.S. |
1 | 1.00 | 2.31 | 0.94 | 1.11 | 1.09 | 0.00 | 1.98 | 2.85 |
| time (sec) |
N/A | 0.577 | 6.763 | 8.271 | 0.199 | 0.294 | 0.000 | 0.318 | 3.399 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 182 | 127 | 190 | 261 | 199 | 0 | 526 | 1547 |
| N.S. |
1 | 1.00 | 0.70 | 1.04 | 1.43 | 1.09 | 0.00 | 2.89 | 8.50 |
| time (sec) |
N/A | 0.641 | 0.926 | 9.462 | 0.213 | 0.295 | 0.000 | 0.349 | 4.111 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 227 | 150 | 215 | 296 | 225 | 0 | 656 | 445 |
| N.S. |
1 | 1.00 | 0.66 | 0.95 | 1.30 | 0.99 | 0.00 | 2.89 | 1.96 |
| time (sec) |
N/A | 0.764 | 2.505 | 11.625 | 0.215 | 0.291 | 0.000 | 0.340 | 5.545 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 273 | 184 | 254 | 386 | 262 | 0 | 932 | 572 |
| N.S. |
1 | 1.00 | 0.67 | 0.93 | 1.41 | 0.96 | 0.00 | 3.41 | 2.10 |
| time (sec) |
N/A | 0.845 | 1.722 | 12.615 | 0.207 | 0.295 | 0.000 | 0.365 | 5.980 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 345 | 351 | 236 | 329 | 251 | 850 | 290 | 798 |
| N.S. |
1 | 1.00 | 1.02 | 0.68 | 0.95 | 0.73 | 2.46 | 0.84 | 2.31 |
| time (sec) |
N/A | 0.971 | 2.300 | 7.832 | 0.212 | 0.291 | 0.542 | 0.340 | 3.407 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 301 | 301 | 204 | 283 | 212 | 748 | 247 | 359 |
| N.S. |
1 | 1.00 | 1.00 | 0.68 | 0.94 | 0.70 | 2.49 | 0.82 | 1.19 |
| time (sec) |
N/A | 0.600 | 2.055 | 6.883 | 0.218 | 0.305 | 0.414 | 0.312 | 2.319 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 227 | 226 | 195 | 232 | 195 | 0 | 753 | 2241 |
| N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.02 | 0.86 | 0.00 | 3.32 | 9.87 |
| time (sec) |
N/A | 0.865 | 2.891 | 6.204 | 0.207 | 0.291 | 0.000 | 0.347 | 3.619 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 229 | 274 | 197 | 204 | 203 | 0 | 558 | 395 |
| N.S. |
1 | 1.00 | 1.20 | 0.86 | 0.89 | 0.89 | 0.00 | 2.44 | 1.72 |
| time (sec) |
N/A | 0.839 | 4.292 | 6.613 | 0.206 | 0.292 | 0.000 | 0.376 | 2.381 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 219 | 219 | 323 | 196 | 221 | 210 | 0 | 396 | 2658 |
| N.S. |
1 | 1.00 | 1.47 | 0.89 | 1.01 | 0.96 | 0.00 | 1.81 | 12.14 |
| time (sec) |
N/A | 0.946 | 7.843 | 9.098 | 0.206 | 0.312 | 0.000 | 0.373 | 3.530 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 412 | 198 | 221 | 208 | 0 | 397 | 2662 |
| N.S. |
1 | 1.00 | 1.64 | 0.79 | 0.88 | 0.83 | 0.00 | 1.58 | 10.61 |
| time (sec) |
N/A | 0.970 | 10.292 | 9.197 | 0.219 | 0.293 | 0.000 | 0.371 | 3.915 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 246 | 246 | 612 | 219 | 306 | 236 | 0 | 590 | 1988 |
| N.S. |
1 | 1.00 | 2.49 | 0.89 | 1.24 | 0.96 | 0.00 | 2.40 | 8.08 |
| time (sec) |
N/A | 0.992 | 9.180 | 10.309 | 0.210 | 0.293 | 0.000 | 0.381 | 4.233 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 250 | 169 | 243 | 325 | 251 | 0 | 778 | 1738 |
| N.S. |
1 | 1.00 | 0.68 | 0.97 | 1.30 | 1.00 | 0.00 | 3.11 | 6.95 |
| time (sec) |
N/A | 0.993 | 1.163 | 11.337 | 0.214 | 0.294 | 0.000 | 0.391 | 4.422 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 307 | 204 | 291 | 466 | 297 | 0 | 1100 | 690 |
| N.S. |
1 | 1.00 | 0.66 | 0.95 | 1.52 | 0.97 | 0.00 | 3.58 | 2.25 |
| time (sec) |
N/A | 1.207 | 4.952 | 13.322 | 0.217 | 0.294 | 0.000 | 0.400 | 4.368 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 355 | 355 | 233 | 317 | 472 | 325 | 0 | 1280 | 755 |
| N.S. |
1 | 1.00 | 0.66 | 0.89 | 1.33 | 0.92 | 0.00 | 3.61 | 2.13 |
| time (sec) |
N/A | 1.283 | 2.223 | 14.071 | 0.206 | 0.321 | 0.000 | 0.384 | 5.724 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 183 | 139 | 133 | 146 | 132 | 321 | 147 | 406 |
| N.S. |
1 | 1.00 | 0.76 | 0.73 | 0.80 | 0.72 | 1.75 | 0.80 | 2.22 |
| time (sec) |
N/A | 0.337 | 1.480 | 5.011 | 0.192 | 0.284 | 0.260 | 0.305 | 3.376 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 89 | 87 | 84 | 80 | 190 | 91 | 107 |
| N.S. |
1 | 1.00 | 0.69 | 0.67 | 0.65 | 0.62 | 1.47 | 0.71 | 0.83 |
| time (sec) |
N/A | 0.222 | 0.346 | 3.491 | 0.198 | 0.287 | 0.169 | 0.288 | 1.815 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 92 | 75 | 74 | 73 | 67 | 131 | 74 | 76 |
| N.S. |
1 | 1.00 | 0.82 | 0.80 | 0.79 | 0.73 | 1.42 | 0.80 | 0.83 |
| time (sec) |
N/A | 0.129 | 0.287 | 3.121 | 0.196 | 0.285 | 0.128 | 0.287 | 1.624 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 233 | 194 | 353 | 0 | 609 | 0 | 574 | 5844 |
| N.S. |
1 | 1.00 | 0.83 | 1.52 | 0.00 | 2.61 | 0.00 | 2.46 | 25.08 |
| time (sec) |
N/A | 0.931 | 1.920 | 2.510 | 0.000 | 0.342 | 0.000 | 0.320 | 8.395 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 152 | 225 | 0 | 485 | 0 | 326 | 3953 |
| N.S. |
1 | 1.00 | 0.86 | 1.27 | 0.00 | 2.74 | 0.00 | 1.84 | 22.33 |
| time (sec) |
N/A | 0.580 | 1.488 | 2.378 | 0.000 | 0.318 | 0.000 | 0.314 | 5.577 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 126 | 117 | 160 | 0 | 385 | 9489 | 199 | 2398 |
| N.S. |
1 | 0.98 | 0.91 | 1.25 | 0.00 | 3.01 | 74.13 | 1.55 | 18.73 |
| time (sec) |
N/A | 0.427 | 1.126 | 1.671 | 0.000 | 0.296 | 164.048 | 0.306 | 5.171 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 82 | 106 | 0 | 297 | 2518 | 136 | 916 |
| N.S. |
1 | 1.00 | 0.95 | 1.23 | 0.00 | 3.45 | 29.28 | 1.58 | 10.65 |
| time (sec) |
N/A | 0.194 | 0.409 | 1.494 | 0.000 | 0.309 | 54.110 | 0.306 | 4.009 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 234 | 116 | 0 | 353 | 0 | 143 | 2862 |
| N.S. |
1 | 1.00 | 2.66 | 1.32 | 0.00 | 4.01 | 0.00 | 1.62 | 32.52 |
| time (sec) |
N/A | 0.201 | 1.309 | 2.661 | 0.000 | 0.679 | 0.000 | 0.343 | 4.685 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 306 | 135 | 0 | 412 | 0 | 164 | 1328 |
| N.S. |
1 | 1.00 | 3.22 | 1.42 | 0.00 | 4.34 | 0.00 | 1.73 | 13.98 |
| time (sec) |
N/A | 0.414 | 3.026 | 2.099 | 0.000 | 0.676 | 0.000 | 0.305 | 3.467 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 399 | 218 | 0 | 535 | 0 | 242 | 3926 |
| N.S. |
1 | 1.00 | 2.91 | 1.59 | 0.00 | 3.91 | 0.00 | 1.77 | 28.66 |
| time (sec) |
N/A | 0.557 | 3.055 | 2.380 | 0.000 | 1.742 | 0.000 | 0.326 | 5.515 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 184 | 413 | 299 | 0 | 633 | 0 | 372 | 3927 |
| N.S. |
1 | 1.00 | 2.24 | 1.62 | 0.00 | 3.44 | 0.00 | 2.02 | 21.34 |
| time (sec) |
N/A | 0.834 | 3.812 | 3.057 | 0.000 | 1.737 | 0.000 | 0.344 | 5.754 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 332 | 215 | 323 | 0 | 985 | 0 | 439 | 6989 |
| N.S. |
1 | 1.00 | 0.65 | 0.97 | 0.00 | 2.97 | 0.00 | 1.32 | 21.05 |
| time (sec) |
N/A | 1.265 | 2.762 | 2.180 | 0.000 | 0.365 | 0.000 | 0.329 | 11.277 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 262 | 262 | 178 | 259 | 0 | 809 | 0 | 311 | 6546 |
| N.S. |
1 | 1.00 | 0.68 | 0.99 | 0.00 | 3.09 | 0.00 | 1.19 | 24.98 |
| time (sec) |
N/A | 0.747 | 2.143 | 1.894 | 0.000 | 0.354 | 0.000 | 0.322 | 11.378 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 136 | 198 | 0 | 632 | 0 | 998 | 4124 |
| N.S. |
1 | 1.00 | 0.94 | 1.38 | 0.00 | 4.39 | 0.00 | 6.93 | 28.64 |
| time (sec) |
N/A | 0.376 | 1.843 | 2.199 | 0.000 | 0.333 | 0.000 | 0.418 | 9.411 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 126 | 123 | 164 | 0 | 534 | 0 | 201 | 3862 |
| N.S. |
1 | 1.00 | 0.98 | 1.30 | 0.00 | 4.24 | 0.00 | 1.60 | 30.65 |
| time (sec) |
N/A | 0.217 | 0.935 | 1.688 | 0.000 | 0.307 | 0.000 | 0.338 | 9.172 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 134 | 306 | 183 | 0 | 666 | 0 | 226 | 3850 |
| N.S. |
1 | 1.00 | 2.28 | 1.37 | 0.00 | 4.97 | 0.00 | 1.69 | 28.73 |
| time (sec) |
N/A | 0.373 | 2.842 | 2.308 | 0.000 | 1.471 | 0.000 | 0.341 | 9.020 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 180 | 219 | 227 | 0 | 842 | 0 | 382 | 4118 |
| N.S. |
1 | 1.00 | 1.22 | 1.26 | 0.00 | 4.68 | 0.00 | 2.12 | 22.88 |
| time (sec) |
N/A | 0.657 | 3.302 | 3.051 | 0.000 | 2.280 | 0.000 | 0.348 | 9.332 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 265 | 712 | 319 | 0 | 1149 | 0 | 353 | 6465 |
| N.S. |
1 | 1.00 | 2.69 | 1.20 | 0.00 | 4.34 | 0.00 | 1.33 | 24.40 |
| time (sec) |
N/A | 1.164 | 8.106 | 2.935 | 0.000 | 7.376 | 0.000 | 0.373 | 11.249 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 335 | 335 | 593 | 399 | 0 | 1305 | 0 | 483 | 6976 |
| N.S. |
1 | 1.00 | 1.77 | 1.19 | 0.00 | 3.90 | 0.00 | 1.44 | 20.82 |
| time (sec) |
N/A | 1.555 | 7.507 | 3.038 | 0.000 | 6.137 | 0.000 | 0.377 | 11.496 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 372 | 372 | 256 | 400 | 0 | 1535 | 0 | 2494 | 10483 |
| N.S. |
1 | 1.00 | 0.69 | 1.08 | 0.00 | 4.13 | 0.00 | 6.70 | 28.18 |
| time (sec) |
N/A | 1.636 | 4.254 | 3.003 | 0.000 | 0.406 | 0.000 | 0.621 | 15.134 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 262 | 262 | 214 | 323 | 0 | 1202 | 0 | 489 | 7216 |
| N.S. |
1 | 1.00 | 0.82 | 1.23 | 0.00 | 4.59 | 0.00 | 1.87 | 27.54 |
| time (sec) |
N/A | 0.905 | 3.022 | 2.442 | 0.000 | 0.347 | 0.000 | 0.369 | 11.829 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 203 | 194 | 294 | 0 | 1051 | 0 | 479 | 6587 |
| N.S. |
1 | 1.00 | 0.96 | 1.45 | 0.00 | 5.18 | 0.00 | 2.36 | 32.45 |
| time (sec) |
N/A | 0.533 | 2.204 | 1.842 | 0.000 | 0.338 | 0.000 | 0.373 | 10.920 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 170 | 226 | 0 | 709 | 0 | 369 | 241 |
| N.S. |
1 | 1.00 | 0.96 | 1.28 | 0.00 | 4.01 | 0.00 | 2.08 | 1.36 |
| time (sec) |
N/A | 0.312 | 1.128 | 2.170 | 0.000 | 0.304 | 0.000 | 0.326 | 5.179 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 409 | 313 | 0 | 1308 | 0 | 504 | 6574 |
| N.S. |
1 | 1.00 | 1.94 | 1.48 | 0.00 | 6.20 | 0.00 | 2.39 | 31.16 |
| time (sec) |
N/A | 0.761 | 4.528 | 2.629 | 0.000 | 4.635 | 0.000 | 0.361 | 10.705 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 275 | 649 | 354 | 0 | 1548 | 0 | 517 | 7211 |
| N.S. |
1 | 1.00 | 2.36 | 1.29 | 0.00 | 5.63 | 0.00 | 1.88 | 26.22 |
| time (sec) |
N/A | 1.255 | 8.002 | 3.197 | 0.000 | 8.496 | 0.000 | 0.377 | 11.260 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 378 | 378 | 856 | 458 | 0 | 2078 | 0 | 1191 | 10422 |
| N.S. |
1 | 1.00 | 2.26 | 1.21 | 0.00 | 5.50 | 0.00 | 3.15 | 27.57 |
| time (sec) |
N/A | 1.949 | 8.548 | 4.350 | 0.000 | 18.866 | 0.000 | 0.374 | 15.585 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 514 | 514 | 1452 | 615 | 0 | 2395 | 0 | 1029 | 14280 |
| N.S. |
1 | 1.00 | 2.82 | 1.20 | 0.00 | 4.66 | 0.00 | 2.00 | 27.78 |
| time (sec) |
N/A | 2.351 | 9.607 | 3.985 | 0.000 | 0.563 | 0.000 | 0.387 | 20.710 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 369 | 369 | 849 | 499 | 0 | 1919 | 0 | 846 | 10081 |
| N.S. |
1 | 1.00 | 2.30 | 1.35 | 0.00 | 5.20 | 0.00 | 2.29 | 27.32 |
| time (sec) |
N/A | 1.695 | 6.180 | 3.174 | 0.000 | 0.452 | 0.000 | 0.397 | 13.796 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 304 | 304 | 723 | 479 | 0 | 1735 | 0 | 845 | 9774 |
| N.S. |
1 | 1.00 | 2.38 | 1.58 | 0.00 | 5.71 | 0.00 | 2.78 | 32.15 |
| time (sec) |
N/A | 1.518 | 8.055 | 2.539 | 0.000 | 0.421 | 0.000 | 0.354 | 17.356 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 261 | 224 | 370 | 0 | 1103 | 0 | 689 | 491 |
| N.S. |
1 | 1.00 | 0.86 | 1.42 | 0.00 | 4.23 | 0.00 | 2.64 | 1.88 |
| time (sec) |
N/A | 0.670 | 2.412 | 2.119 | 0.000 | 0.349 | 0.000 | 0.365 | 5.320 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 252 | 252 | 224 | 369 | 0 | 1105 | 0 | 689 | 491 |
| N.S. |
1 | 1.00 | 0.89 | 1.46 | 0.00 | 4.38 | 0.00 | 2.73 | 1.95 |
| time (sec) |
N/A | 0.533 | 1.562 | 2.358 | 0.000 | 0.350 | 0.000 | 0.352 | 4.960 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 301 | 498 | 498 | 0 | 2159 | 0 | 868 | 9766 |
| N.S. |
1 | 1.00 | 1.65 | 1.65 | 0.00 | 7.17 | 0.00 | 2.88 | 32.45 |
| time (sec) |
N/A | 1.470 | 7.196 | 3.510 | 0.000 | 15.175 | 0.000 | 0.382 | 17.549 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 376 | 376 | 515 | 528 | 0 | 2410 | 0 | 871 | 10078 |
| N.S. |
1 | 1.00 | 1.37 | 1.40 | 0.00 | 6.41 | 0.00 | 2.32 | 26.80 |
| time (sec) |
N/A | 2.258 | 5.471 | 3.957 | 0.000 | 20.055 | 0.000 | 0.377 | 15.079 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 522 | 522 | 740 | 673 | 0 | 3269 | 0 | 1070 | 14213 |
| N.S. |
1 | 1.00 | 1.42 | 1.29 | 0.00 | 6.26 | 0.00 | 2.05 | 27.23 |
| time (sec) |
N/A | 2.820 | 8.118 | 6.394 | 0.000 | 51.138 | 0.000 | 0.404 | 19.788 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 193 | 168 | 252 | 0 | 369 | 0 | 370 | 240 |
| N.S. |
1 | 1.00 | 0.87 | 1.31 | 0.00 | 1.91 | 0.00 | 1.92 | 1.24 |
| time (sec) |
N/A | 0.656 | 1.272 | 1.875 | 0.000 | 0.323 | 0.000 | 0.327 | 2.763 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 125 | 179 | 0 | 304 | 0 | 229 | 183 |
| N.S. |
1 | 1.00 | 0.83 | 1.19 | 0.00 | 2.03 | 0.00 | 1.53 | 1.22 |
| time (sec) |
N/A | 0.405 | 0.737 | 1.626 | 0.000 | 0.306 | 0.000 | 0.303 | 2.253 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 98 | 146 | 0 | 251 | 2958 | 186 | 147 |
| N.S. |
1 | 1.00 | 0.90 | 1.34 | 0.00 | 2.30 | 27.14 | 1.71 | 1.35 |
| time (sec) |
N/A | 0.231 | 0.319 | 1.435 | 0.000 | 0.290 | 159.029 | 0.311 | 1.886 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 69 | 102 | 0 | 202 | 1039 | 122 | 112 |
| N.S. |
1 | 1.00 | 0.95 | 1.40 | 0.00 | 2.77 | 14.23 | 1.67 | 1.53 |
| time (sec) |
N/A | 0.114 | 0.310 | 1.688 | 0.000 | 0.307 | 52.507 | 0.308 | 1.935 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 115 | 108 | 0 | 243 | 0 | 130 | 121 |
| N.S. |
1 | 1.00 | 1.51 | 1.42 | 0.00 | 3.20 | 0.00 | 1.71 | 1.59 |
| time (sec) |
N/A | 0.131 | 0.346 | 1.720 | 0.000 | 0.326 | 0.000 | 0.303 | 1.824 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 112 | 129 | 0 | 297 | 0 | 150 | 436 |
| N.S. |
1 | 1.00 | 1.37 | 1.57 | 0.00 | 3.62 | 0.00 | 1.83 | 5.32 |
| time (sec) |
N/A | 0.229 | 0.505 | 2.577 | 0.000 | 0.317 | 0.000 | 0.324 | 1.712 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 236 | 199 | 0 | 373 | 0 | 219 | 176 |
| N.S. |
1 | 1.00 | 2.02 | 1.70 | 0.00 | 3.19 | 0.00 | 1.87 | 1.50 |
| time (sec) |
N/A | 0.424 | 1.444 | 2.115 | 0.000 | 0.327 | 0.000 | 0.333 | 1.997 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 256 | 245 | 0 | 431 | 0 | 266 | 224 |
| N.S. |
1 | 1.00 | 1.65 | 1.58 | 0.00 | 2.78 | 0.00 | 1.72 | 1.45 |
| time (sec) |
N/A | 0.646 | 3.033 | 2.398 | 0.000 | 0.361 | 0.000 | 0.331 | 1.935 |