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 | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 360 | 667 | 570 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.94 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.908 | 5.770 | 0.442 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 187 | 192 | 386 | 0 | 198 | 0 | 318 | 0 |
| N.S. |
1 | 1.09 | 1.12 | 2.24 | 0.00 | 1.15 | 0.00 | 1.85 | 0.00 |
| time (sec) |
N/A | 0.764 | 0.485 | 0.243 | 0.000 | 0.285 | 0.000 | 0.410 | 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 | 341 | 326 | 670 | 568 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.96 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.741 | 5.334 | 0.404 | 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 | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 140 | 162 | 270 | 0 | 165 | 0 | 395 | 0 |
| N.S. |
1 | 0.93 | 1.08 | 1.80 | 0.00 | 1.10 | 0.00 | 2.63 | 0.00 |
| time (sec) |
N/A | 0.453 | 0.940 | 0.132 | 0.000 | 0.273 | 0.000 | 0.358 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 318 | 660 | 570 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.99 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.654 | 4.055 | 0.421 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 296 | 337 | 756 | 759 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.14 | 2.55 | 2.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.838 | 4.556 | 0.440 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 504 | 1400 | 730 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.17 | 3.26 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.901 | 11.770 | 0.570 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 403 | 498 | 1003 | 921 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.24 | 2.49 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.030 | 7.922 | 0.509 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 572 | 775 | 1657 | 821 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.35 | 2.90 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.808 | 12.708 | 0.679 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 374 | 364 | 242 | 1165 | 311 | 277 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.65 | 3.11 | 0.83 | 0.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.385 | 0.228 | 0.639 | 0.312 | 0.286 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 303 | 246 | 678 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.122 | 0.266 | 0.197 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 149 | 120 | 700 | 188 | 208 | 0 | 0 | 0 |
| N.S. |
1 | 0.79 | 0.64 | 3.72 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.433 | 0.210 | 0.207 | 0.308 | 0.267 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 169 | 128 | 531 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.67 | 2.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.506 | 0.168 | 0.175 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 378 | 234 | 391 | 659 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.62 | 1.03 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.966 | 1.230 | 0.213 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 182 | 257 | 565 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.80 | 1.13 | 2.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.000 | 1.041 | 0.233 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 398 | 248 | 480 | 589 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.62 | 1.21 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.197 | 4.000 | 0.279 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 206 | 248 | 2041 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 0.79 | 6.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.822 | 1.181 | 0.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 503 | 561 | 244 | 1678 | 356 | 360 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.49 | 3.34 | 0.71 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.345 | 0.289 | 0.398 | 0.305 | 0.282 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 421 | 509 | 297 | 1320 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.21 | 0.71 | 3.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.030 | 0.237 | 0.292 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 279 | 189 | 159 | 1151 | 236 | 295 | 0 | 0 | 0 |
| N.S. |
1 | 0.68 | 0.57 | 4.13 | 0.85 | 1.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.517 | 0.143 | 0.486 | 0.303 | 0.271 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 332 | 247 | 929 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.81 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.937 | 0.667 | 0.234 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 545 | 378 | 576 | 1072 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.69 | 1.06 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.772 | 2.138 | 0.276 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 424 | 370 | 396 | 709 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.93 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.616 | 3.112 | 0.272 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 590 | 376 | 854 | 884 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.64 | 1.45 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.800 | 7.187 | 0.290 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 400 | 392 | 493 | 2250 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.23 | 5.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.951 | 1.707 | 0.329 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 651 | 799 | 270 | 2146 | 401 | 486 | 0 | 0 | 0 |
| N.S. |
1 | 1.23 | 0.41 | 3.30 | 0.62 | 0.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.647 | 0.272 | 0.422 | 0.300 | 0.295 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 556 | 764 | 348 | 1939 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.37 | 0.63 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.267 | 0.283 | 0.348 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 382 | 228 | 176 | 1611 | 281 | 405 | 0 | 0 | 0 |
| N.S. |
1 | 0.60 | 0.46 | 4.22 | 0.74 | 1.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.656 | 0.210 | 0.427 | 0.296 | 0.277 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 438 | 521 | 299 | 1349 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.19 | 0.68 | 3.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.505 | 0.795 | 0.272 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 687 | 563 | 775 | 1490 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.82 | 1.13 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.893 | 3.628 | 0.342 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 561 | 620 | 586 | 972 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.04 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.915 | 2.313 | 0.325 | 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(-2) | F(-1) |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 740 | 558 | 1073 | 1326 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 1.45 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.151 | 7.482 | 0.342 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | B | F | F | F | F(-2) | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 591 | 0 | 690 | 2650 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.17 | 4.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 3.113 | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 400 | 412 | 230 | 1020 | 365 | 276 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.58 | 2.55 | 0.91 | 0.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.536 | 0.124 | 0.332 | 0.306 | 0.285 | 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 | 337 | 347 | 283 | 722 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.84 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.224 | 1.700 | 0.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 245 | 176 | 812 | 251 | 210 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.64 | 2.93 | 0.91 | 0.76 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.824 | 0.091 | 0.355 | 0.295 | 0.269 | 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 | 206 | 176 | 210 | 517 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 1.02 | 2.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.581 | 1.768 | 0.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 146 | 99 | 86 | 316 | 130 | 147 | 0 | 0 | 0 |
| N.S. |
1 | 0.68 | 0.59 | 2.16 | 0.89 | 1.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.304 | 0.072 | 0.142 | 0.296 | 0.273 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 49 | 64 | 143 | 47 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 2.92 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.209 | 0.445 | 0.151 | 0.278 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 144 | 301 | 387 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.56 | 1.17 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.611 | 0.635 | 0.161 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 138 | 159 | 427 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 0.87 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.611 | 0.690 | 0.213 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 402 | 251 | 487 | 585 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.62 | 1.21 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.243 | 4.395 | 0.246 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 319 | 255 | 269 | 2319 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.80 | 0.84 | 7.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.199 | 0.760 | 0.259 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 549 | 504 | 453 | 1087 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.83 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.504 | 0.853 | 0.536 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 424 | 394 | 312 | 807 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.74 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.824 | 2.205 | 0.262 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 412 | 286 | 369 | 668 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.69 | 0.90 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.255 | 0.694 | 0.398 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 195 | 295 | 504 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.78 | 1.18 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.886 | 1.015 | 0.203 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 137 | 276 | 401 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 1.33 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.549 | 1.580 | 0.138 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 140 | 165 | 354 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.72 | 0.85 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.561 | 0.828 | 0.175 | 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 | 467 | 278 | 667 | 591 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.60 | 1.43 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.846 | 1.891 | 0.260 | 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 | 333 | 277 | 322 | 513 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.97 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.825 | 1.177 | 0.244 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 634 | 457 | 844 | 869 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.72 | 1.33 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.098 | 7.957 | 0.343 | 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 | 483 | 464 | 462 | 2844 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.96 | 5.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.061 | 1.080 | 0.316 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 546 | 565 | 594 | 815 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.09 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.301 | 1.517 | 0.583 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 421 | 426 | 374 | 801 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.89 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.720 | 1.380 | 0.338 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 350 | 511 | 505 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.54 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.860 | 0.833 | 0.209 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 332 | 218 | 303 | 3298 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 0.91 | 9.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.919 | 1.165 | 0.273 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 197 | 461 | 468 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.67 | 1.57 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.726 | 1.795 | 0.319 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 311 | 270 | 320 | 2895 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 1.03 | 9.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.227 | 1.172 | 0.243 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 577 | 474 | 935 | 924 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.82 | 1.62 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.916 | 8.740 | 0.384 | 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 | 452 | 455 | 352 | 3773 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.78 | 8.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.002 | 2.980 | 0.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | A | F | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 752 | 0 | 1090 | 1121 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.45 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 9.806 | 0.421 | 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 | 538 | 723 | 441 | 5225 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.34 | 0.82 | 9.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.667 | 3.374 | 0.335 | 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 | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 225 | 100 | 129 | 0 | 84 | 146 | 143 | 0 |
| N.S. |
1 | 1.43 | 0.64 | 0.82 | 0.00 | 0.54 | 0.93 | 0.91 | 0.00 |
| time (sec) |
N/A | 0.905 | 0.051 | 0.115 | 0.000 | 0.252 | 0.515 | 0.315 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 159 | 81 | 127 | 105 | 64 | 121 | 0 | 0 |
| N.S. |
1 | 1.26 | 0.64 | 1.01 | 0.83 | 0.51 | 0.96 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.641 | 0.043 | 0.152 | 0.295 | 0.266 | 0.404 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 97 | 73 | 71 | 0 | 59 | 78 | 81 | 0 |
| N.S. |
1 | 1.09 | 0.82 | 0.80 | 0.00 | 0.66 | 0.88 | 0.91 | 0.00 |
| time (sec) |
N/A | 0.423 | 0.027 | 0.171 | 0.000 | 0.253 | 0.322 | 0.330 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 56 | 51 | 80 | 49 | 35 | 49 | 49 | 0 |
| N.S. |
1 | 1.02 | 0.93 | 1.45 | 0.89 | 0.64 | 0.89 | 0.89 | 0.00 |
| time (sec) |
N/A | 0.255 | 0.017 | 0.143 | 0.280 | 0.257 | 0.244 | 0.301 | 0.000 |
| 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 | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 11 | 11 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.85 | 0.85 |
| time (sec) |
N/A | 0.172 | 0.007 | 0.157 | 0.281 | 0.250 | 0.204 | 0.315 | 0.158 |
| 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 | 92 | 98 | 116 | 161 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.26 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.449 | 0.156 | 0.141 | 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 | 76 | 88 | 72 | 141 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.16 | 0.95 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.482 | 0.273 | 0.143 | 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 | 163 | 163 | 194 | 254 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.916 | 1.161 | 0.194 | 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 | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 42 | 52 | 14 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.24 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.209 | 0.077 | 0.108 | 0.269 | 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 | 179 | 123 | 108 | 169 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.69 | 0.60 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.512 | 0.197 | 0.154 | 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 | 283 | 243 | 149 | 365 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.53 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.021 | 0.496 | 0.187 | 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 | 390 | 387 | 234 | 556 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.60 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.585 | 0.705 | 0.226 | 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 | 1312 | 1031 | 539 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.79 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.113 | 0.804 | 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 | 756 | 650 | 403 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.813 | 0.535 | 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 | 371 | 354 | 267 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.948 | 0.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 29 | 27 | 32 | 43 | 66 | 31 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.19 | 1.59 | 2.44 | 1.15 | 1.07 |
| time (sec) |
N/A | 0.249 | 6.602 | 0.263 | 0.812 | 0.252 | 3.709 | 0.931 | 0.276 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 29 | 27 | 30 | 55 | 92 | 30 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.11 | 2.04 | 3.41 | 1.11 | 1.07 |
| time (sec) |
N/A | 1.009 | 8.428 | 0.283 | 0.772 | 0.264 | 15.094 | 0.904 | 0.173 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 29 | 27 | 32 | 69 | 119 | 31 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.19 | 2.56 | 4.41 | 1.15 | 1.07 |
| time (sec) |
N/A | 1.749 | 9.814 | 0.323 | 0.897 | 0.251 | 117.237 | 0.883 | 0.167 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 31 | 27 | 29 | 134 | 0 | 0 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 4.62 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 2.952 | 9.758 | 5.469 | 0.911 | 0.251 | 0.000 | 0.000 | 0.245 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 31 | 27 | 29 | 85 | 0 | 0 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.93 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 1.522 | 0.604 | 1.994 | 0.760 | 0.254 | 0.000 | 0.000 | 0.234 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 31 | 27 | 29 | 41 | 31 | 0 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.41 | 1.07 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.792 | 0.400 | 0.748 | 0.584 | 0.266 | 20.065 | 0.000 | 0.349 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 31 | 27 | 29 | 56 | 31 | 29 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.93 | 1.07 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.298 | 3.903 | 0.391 | 0.586 | 0.253 | 7.686 | 1.073 | 0.324 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 31 | 27 | 29 | 68 | 31 | 0 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.34 | 1.07 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.307 | 4.394 | 0.338 | 0.635 | 0.257 | 11.902 | 0.000 | 0.247 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 31 | 27 | 29 | 82 | 31 | 0 | 29 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.83 | 1.07 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.310 | 4.562 | 0.366 | 0.657 | 0.265 | 152.970 | 0.000 | 0.239 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 24 | 24 | 26 | 22 | 24 | 36 | 26 | 24 | 24 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.50 | 1.08 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.239 | 0.901 | 0.289 | 0.439 | 0.249 | 1.142 | 0.624 | 0.133 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 370 | 581 | 171 | 278 | 284 | 202 | 355 | 379 | 0 |
| N.S. |
1 | 1.57 | 0.46 | 0.75 | 0.77 | 0.55 | 0.96 | 1.02 | 0.00 |
| time (sec) |
N/A | 2.358 | 0.209 | 0.197 | 0.308 | 0.263 | 1.137 | 0.304 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 378 | 139 | 206 | 216 | 158 | 262 | 267 | 0 |
| N.S. |
1 | 1.38 | 0.51 | 0.75 | 0.79 | 0.58 | 0.96 | 0.98 | 0.00 |
| time (sec) |
N/A | 1.347 | 0.128 | 0.109 | 0.285 | 0.256 | 0.584 | 0.314 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 202 | 101 | 132 | 128 | 95 | 150 | 139 | 0 |
| N.S. |
1 | 1.28 | 0.64 | 0.84 | 0.81 | 0.60 | 0.95 | 0.88 | 0.00 |
| time (sec) |
N/A | 0.724 | 0.063 | 0.066 | 0.291 | 0.254 | 0.292 | 0.310 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 177 | 162 | 0 | 36 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.81 | 0.00 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.580 | 0.237 | 0.000 | 0.435 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 305 | 234 | 438 | 57 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.69 | 1.30 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.631 | 0.398 | 0.234 | 0.546 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 455 | 483 | 1544 | 543 | 78 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 3.39 | 1.19 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.676 | 12.760 | 0.247 | 0.663 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 533 | 611 | 179 | 699 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.15 | 0.34 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.652 | 0.694 | 0.207 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 366 | 138 | 474 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.38 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.927 | 0.323 | 0.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 170 | 114 | 260 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.79 | 0.53 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.721 | 0.044 | 0.138 | 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 | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 42 | 52 | 14 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.24 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.204 | 0.070 | 0.145 | 0.324 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 238 | 154 | 157 | 203 | 49 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.65 | 0.66 | 0.85 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.666 | 0.235 | 0.185 | 0.771 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 388 | 296 | 211 | 535 | 106 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.76 | 0.54 | 1.38 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.498 | 0.491 | 0.234 | 0.516 | 0.000 | 0.000 | 0.000 | 0.000 |