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 | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 143 | 1041 | 466 | 0 | 318 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 6.85 | 3.07 | 0.00 | 2.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.751 | 8.485 | 15.514 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 200 | 1158 | 465 | 0 | 384 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 5.68 | 2.28 | 0.00 | 1.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.104 | 8.810 | 13.436 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 173 | 1114 | 435 | 0 | 366 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 6.51 | 2.54 | 0.00 | 2.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.035 | 8.546 | 9.453 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 144 | 1079 | 421 | 0 | 356 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 7.88 | 3.07 | 0.00 | 2.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.895 | 8.114 | 9.212 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 131 | 800 | 350 | 0 | 314 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 6.61 | 2.89 | 0.00 | 2.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.845 | 7.921 | 9.231 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 130 | 801 | 350 | 0 | 318 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 6.62 | 2.89 | 0.00 | 2.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.850 | 7.973 | 9.027 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 166 | 1113 | 492 | 0 | 407 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 6.79 | 3.00 | 0.00 | 2.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.016 | 8.109 | 10.300 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 195 | 1154 | 723 | 0 | 436 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 5.86 | 3.67 | 0.00 | 2.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.054 | 8.756 | 18.831 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 231 | 463 | 465 | 0 | 478 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 2.10 | 2.10 | 0.00 | 2.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.409 | 6.051 | 10.616 | 0.000 | 0.124 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 203 | 422 | 451 | 0 | 467 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 2.24 | 2.40 | 0.00 | 2.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.239 | 5.443 | 10.581 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 197 | 379 | 451 | 0 | 465 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 2.08 | 2.48 | 0.00 | 2.55 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.214 | 4.368 | 9.938 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 193 | 189 | 451 | 0 | 465 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.06 | 2.53 | 0.00 | 2.61 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.176 | 3.886 | 10.689 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 195 | 1171 | 451 | 0 | 465 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 6.51 | 2.51 | 0.00 | 2.58 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.192 | 8.231 | 10.541 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 227 | 1211 | 685 | 0 | 521 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 5.48 | 3.10 | 0.00 | 2.36 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.396 | 10.120 | 12.430 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 220 | 235 | 119 | 116 | 547 | 116 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.54 | 0.53 | 2.49 | 0.53 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.282 | 0.926 | 4.516 | 0.443 | 0.277 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 192 | 96 | 96 | 418 | 99 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 0.55 | 0.55 | 2.39 | 0.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.954 | 0.555 | 4.367 | 0.451 | 0.275 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 149 | 79 | 76 | 296 | 81 | 0 | 0 | 0 |
| N.S. |
1 | 1.15 | 0.61 | 0.58 | 2.28 | 0.62 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.788 | 0.293 | 4.526 | 0.418 | 0.271 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 103 | 56 | 55 | 141 | 64 | 0 | 0 | 0 |
| N.S. |
1 | 1.26 | 0.68 | 0.67 | 1.72 | 0.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.595 | 0.348 | 4.480 | 0.415 | 0.268 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 97 | 94 | 163 | 262 | 298 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.98 | 1.70 | 2.73 | 3.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.591 | 0.601 | 7.182 | 0.413 | 0.316 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 99 | 119 | 277 | 905 | 351 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.21 | 2.83 | 9.23 | 3.58 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.602 | 0.742 | 7.125 | 0.474 | 0.322 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 144 | 141 | 344 | 1927 | 401 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.93 | 2.28 | 12.76 | 2.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.775 | 1.632 | 7.336 | 0.488 | 0.328 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 196 | 187 | 176 | 406 | 3342 | 439 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.90 | 2.07 | 17.05 | 2.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.958 | 1.657 | 6.981 | 0.559 | 0.382 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 288 | 131 | 137 | 703 | 142 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.48 | 0.50 | 2.56 | 0.52 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.613 | 1.855 | 5.384 | 0.467 | 0.277 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 245 | 118 | 117 | 558 | 124 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.52 | 0.51 | 2.45 | 0.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.346 | 0.991 | 5.129 | 0.451 | 0.278 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 202 | 100 | 97 | 451 | 105 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.55 | 0.54 | 2.49 | 0.58 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.106 | 0.704 | 5.251 | 0.431 | 0.271 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 150 | 80 | 77 | 276 | 86 | 0 | 0 | 0 |
| N.S. |
1 | 1.15 | 0.61 | 0.59 | 2.11 | 0.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.780 | 0.578 | 5.203 | 0.433 | 0.281 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 149 | 101 | 217 | 583 | 343 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.70 | 1.50 | 4.02 | 2.37 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.913 | 0.875 | 8.187 | 0.449 | 0.298 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 152 | 133 | 308 | 1417 | 389 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.92 | 2.14 | 9.84 | 2.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.879 | 0.901 | 7.830 | 0.466 | 0.313 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 170 | 345 | 3389 | 409 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.11 | 2.25 | 22.15 | 2.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.898 | 0.792 | 8.218 | 0.539 | 0.316 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 197 | 177 | 407 | 4606 | 449 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.88 | 2.04 | 23.03 | 2.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.095 | 1.469 | 7.783 | 0.655 | 0.315 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 240 | 211 | 469 | 5879 | 485 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.85 | 1.90 | 23.80 | 1.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.355 | 1.768 | 8.083 | 0.876 | 0.366 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 299 | 137 | 139 | 754 | 154 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.50 | 0.51 | 2.74 | 0.56 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.786 | 0.714 | 3.860 | 0.492 | 0.263 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 256 | 116 | 119 | 596 | 133 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.51 | 0.52 | 2.61 | 0.58 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.475 | 0.568 | 3.151 | 0.491 | 0.264 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 194 | 99 | 99 | 482 | 112 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.56 | 0.56 | 2.71 | 0.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.982 | 0.435 | 3.173 | 0.465 | 0.257 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 201 | 118 | 279 | 352 | 399 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.61 | 1.45 | 1.83 | 2.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.215 | 0.711 | 2.844 | 0.465 | 0.304 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 205 | 117 | 370 | 2589 | 449 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.59 | 1.88 | 13.14 | 2.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.250 | 0.669 | 8.372 | 0.534 | 0.323 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 204 | 173 | 378 | 14322 | 453 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.86 | 1.89 | 71.61 | 2.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.233 | 1.012 | 8.159 | 3.383 | 0.322 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 206 | 152 | 409 | 6297 | 469 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.76 | 2.04 | 31.48 | 2.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.241 | 1.561 | 8.202 | 3.424 | 0.357 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 251 | 210 | 471 | 7331 | 509 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.85 | 1.91 | 29.68 | 2.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.509 | 1.375 | 8.346 | 0.937 | 0.345 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 294 | 607 | 533 | 9242 | 549 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.06 | 1.81 | 31.44 | 1.87 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.797 | 6.301 | 9.028 | 1.361 | 0.345 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 281 | 170 | 375 | 749 | 400 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.68 | 1.50 | 3.00 | 1.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.751 | 1.198 | 4.177 | 0.504 | 0.272 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 226 | 154 | 341 | 581 | 368 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.74 | 1.65 | 2.81 | 1.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.283 | 0.815 | 4.815 | 0.509 | 0.282 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 171 | 124 | 309 | 478 | 336 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.77 | 1.91 | 2.95 | 2.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.927 | 0.347 | 4.607 | 0.455 | 0.299 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 120 | 140 | 159 | 195 | 306 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.18 | 1.34 | 1.64 | 2.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.642 | 0.319 | 4.224 | 0.455 | 0.279 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 121 | 115 | 226 | 699 | 357 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.82 | 1.61 | 4.99 | 2.55 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.779 | 0.232 | 7.260 | 0.468 | 0.296 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 171 | 193 | 376 | 1509 | 575 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.07 | 2.08 | 8.34 | 3.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.071 | 0.451 | 6.924 | 0.545 | 0.343 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 224 | 254 | 447 | 2704 | 621 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.10 | 1.94 | 11.76 | 2.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.432 | 0.808 | 6.606 | 0.572 | 0.344 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 289 | 178 | 503 | 0 | 480 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.66 | 1.86 | 0.00 | 1.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.724 | 1.453 | 4.909 | 0.000 | 0.303 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 234 | 155 | 469 | 36231 | 442 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.70 | 2.10 | 162.47 | 1.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.326 | 1.299 | 5.163 | 0.946 | 0.296 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 179 | 194 | 309 | 8208 | 410 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.10 | 1.76 | 46.64 | 2.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.973 | 1.906 | 5.384 | 0.547 | 0.302 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | A | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 128 | 325 | 278 | 2166 | 376 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.56 | 2.19 | 17.06 | 2.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.643 | 1.206 | 5.440 | 0.485 | 0.268 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 171 | 325 | 472 | 0 | 592 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.76 | 2.55 | 0.00 | 3.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.057 | 1.619 | 8.220 | 0.000 | 0.310 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 226 | 449 | 747 | 7057 | 716 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.89 | 3.15 | 29.78 | 3.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.451 | 2.608 | 7.997 | 0.806 | 0.382 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 287 | 280 | 517 | 821 | 13364 | 764 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.80 | 2.86 | 46.56 | 2.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.857 | 5.014 | 7.439 | 1.434 | 0.351 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 344 | 207 | 665 | 244922 | 572 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.65 | 2.10 | 772.62 | 1.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.130 | 2.274 | 5.504 | 5.909 | 0.286 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 289 | 183 | 662 | 154245 | 542 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.68 | 2.45 | 571.28 | 2.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.698 | 1.849 | 5.845 | 3.884 | 0.301 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 234 | 228 | 580 | 261506 | 504 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.02 | 2.60 | 1172.67 | 2.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.313 | 2.562 | 5.561 | 3.469 | 0.296 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 234 | 481 | 438 | 5924 | 482 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 2.16 | 1.96 | 26.57 | 2.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.313 | 6.273 | 5.363 | 1.052 | 0.286 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 175 | 657 | 557 | 5356 | 478 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 3.73 | 3.16 | 30.43 | 2.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.851 | 6.224 | 5.296 | 0.995 | 0.292 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 226 | 772 | 690 | 0 | 720 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 3.30 | 2.95 | 0.00 | 3.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.431 | 6.211 | 8.217 | 0.000 | 0.329 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 283 | 842 | 1082 | 14037 | 850 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 2.94 | 3.78 | 49.08 | 2.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.860 | 6.238 | 7.936 | 2.891 | 0.387 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 134 | 103 | 413 | 0 | 192 | 0 | 0 | 166 |
| N.S. |
1 | 0.96 | 0.74 | 2.95 | 0.00 | 1.37 | 0.00 | 0.00 | 1.19 |
| time (sec) |
N/A | 0.748 | 2.480 | 28.877 | 0.000 | 0.128 | 0.000 | 0.000 | 0.791 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 107 | 86 | 371 | 0 | 175 | 0 | 0 | 128 |
| N.S. |
1 | 0.99 | 0.80 | 3.44 | 0.00 | 1.62 | 0.00 | 0.00 | 1.19 |
| time (sec) |
N/A | 0.687 | 1.716 | 27.952 | 0.000 | 0.103 | 0.000 | 0.000 | 0.645 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 78 | 67 | 326 | 0 | 156 | 0 | 0 | 85 |
| N.S. |
1 | 1.04 | 0.89 | 4.35 | 0.00 | 2.08 | 0.00 | 0.00 | 1.13 |
| time (sec) |
N/A | 0.599 | 1.598 | 8.956 | 0.000 | 0.098 | 0.000 | 0.000 | 0.674 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 64 | 244 | 0 | 185 | 0 | 0 | 96 |
| N.S. |
1 | 1.00 | 0.90 | 3.44 | 0.00 | 2.61 | 0.00 | 0.00 | 1.35 |
| time (sec) |
N/A | 0.603 | 0.979 | 8.279 | 0.000 | 0.107 | 0.000 | 0.000 | 16.084 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 102 | 107 | 401 | 0 | 213 | 0 | 0 | 150 |
| N.S. |
1 | 0.99 | 1.04 | 3.89 | 0.00 | 2.07 | 0.00 | 0.00 | 1.46 |
| time (sec) |
N/A | 0.720 | 0.888 | 14.942 | 0.000 | 0.109 | 0.000 | 0.000 | 16.465 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 130 | 134 | 636 | 0 | 235 | 0 | 0 | 177 |
| N.S. |
1 | 0.93 | 0.96 | 4.54 | 0.00 | 1.68 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 0.737 | 1.259 | 19.604 | 0.000 | 0.117 | 0.000 | 0.000 | 16.918 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 175 | 139 | 548 | 0 | 243 | 0 | 0 | 229 |
| N.S. |
1 | 0.96 | 0.76 | 3.01 | 0.00 | 1.34 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 0.993 | 2.517 | 174.398 | 0.000 | 0.122 | 0.000 | 0.000 | 16.305 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 146 | 106 | 487 | 0 | 216 | 0 | 0 | 177 |
| N.S. |
1 | 1.04 | 0.76 | 3.48 | 0.00 | 1.54 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 0.877 | 2.546 | 172.277 | 0.000 | 0.103 | 0.000 | 0.000 | 16.112 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 124 | 102 | 404 | 0 | 240 | 0 | 0 | 158 |
| N.S. |
1 | 1.02 | 0.84 | 3.34 | 0.00 | 1.98 | 0.00 | 0.00 | 1.31 |
| time (sec) |
N/A | 0.801 | 2.138 | 10.358 | 0.000 | 0.105 | 0.000 | 0.000 | 16.654 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 129 | 105 | 650 | 0 | 255 | 0 | 0 | 194 |
| N.S. |
1 | 1.02 | 0.83 | 5.16 | 0.00 | 2.02 | 0.00 | 0.00 | 1.54 |
| time (sec) |
N/A | 0.826 | 2.701 | 15.062 | 0.000 | 0.119 | 0.000 | 0.000 | 17.212 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 161 | 175 | 723 | 0 | 286 | 0 | 0 | 227 |
| N.S. |
1 | 0.94 | 1.02 | 4.20 | 0.00 | 1.66 | 0.00 | 0.00 | 1.32 |
| time (sec) |
N/A | 0.945 | 2.257 | 21.692 | 0.000 | 0.116 | 0.000 | 0.000 | 17.882 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 190 | 191 | 832 | 0 | 314 | 0 | 0 | 233 |
| N.S. |
1 | 0.89 | 0.89 | 3.89 | 0.00 | 1.47 | 0.00 | 0.00 | 1.09 |
| time (sec) |
N/A | 0.988 | 6.093 | 27.595 | 0.000 | 0.119 | 0.000 | 0.000 | 18.061 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 200 | 260 | 1074 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 1.43 | 5.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.627 | 2.879 | 12.502 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 147 | 207 | 822 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.52 | 6.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.146 | 1.792 | 9.564 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 87 | 128 | 295 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.44 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.664 | 1.249 | 8.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 58 | 217 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.528 | 0.565 | 6.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 85 | 206 | 298 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 2.40 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.774 | 2.787 | 9.328 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 162 | 260 | 439 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.73 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.532 | 2.504 | 15.710 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 232 | 326 | 758 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.50 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.074 | 4.820 | 25.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 295 | 318 | 1059 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.04 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.990 | 3.862 | 20.870 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 220 | 281 | 843 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.26 | 3.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.398 | 3.266 | 17.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 197 | 260 | 802 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.28 | 3.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.280 | 2.872 | 14.837 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 182 | 273 | 715 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.39 | 3.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.388 | 3.037 | 14.708 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 255 | 242 | 317 | 850 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.24 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.903 | 4.677 | 17.729 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 327 | 427 | 997 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.23 | 2.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.626 | 7.319 | 31.829 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 461 | 463 | 461 | 2216 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 4.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.019 | 6.683 | 38.748 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 367 | 372 | 390 | 2000 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.06 | 5.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.278 | 5.645 | 33.447 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 352 | 361 | 1959 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.04 | 5.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.237 | 4.997 | 30.689 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 338 | 336 | 364 | 1872 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.08 | 5.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.096 | 5.356 | 29.475 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 342 | 334 | 383 | 1768 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.12 | 5.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.245 | 5.382 | 29.881 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 420 | 413 | 458 | 1997 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.09 | 4.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.116 | 5.968 | 36.683 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 523 | 514 | 570 | 2151 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.09 | 4.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.993 | 7.759 | 64.239 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 381 | 455 | 3535 | 0 | 578 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.33 | 10.31 | 0.00 | 1.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.183 | 21.963 | 11.860 | 0.000 | 0.152 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 267 | 297 | 353 | 2460 | 0 | 509 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.32 | 9.21 | 0.00 | 1.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.285 | 18.006 | 10.808 | 0.000 | 0.132 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 223 | 305 | 1643 | 0 | 452 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.52 | 8.17 | 0.00 | 2.25 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.694 | 12.213 | 8.337 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 230 | 25347 | 1337 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 121.86 | 6.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.299 | 34.477 | 10.945 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 281 | 53253 | 1196 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 210.49 | 4.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.793 | 35.939 | 12.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 356 | 78854 | 2162 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 234.68 | 6.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.560 | 37.011 | 14.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 427 | 456 | 540 | 4705 | 0 | 656 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.26 | 11.02 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.847 | 21.921 | 13.191 | 0.000 | 0.171 | 0.000 | 0.000 | 0.000 |