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 | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 457 | 478 | 498 | 1170 | 0 | 750 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.09 | 2.56 | 0.00 | 1.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.740 | 24.489 | 2.088 | 0.000 | 0.144 | 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 | 401 | 421 | 442 | 1135 | 0 | 806 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.10 | 2.83 | 0.00 | 2.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.656 | 24.325 | 2.348 | 0.000 | 0.167 | 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 | 392 | 409 | 401 | 912 | 0 | 813 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.02 | 2.33 | 0.00 | 2.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.625 | 23.678 | 2.032 | 0.000 | 0.359 | 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 | 474 | 490 | 500 | 894 | 0 | 1184 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.05 | 1.89 | 0.00 | 2.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.725 | 13.579 | 3.037 | 0.000 | 0.367 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 570 | 600 | 610 | 995 | 0 | 1675 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.07 | 1.75 | 0.00 | 2.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.852 | 25.797 | 4.195 | 0.000 | 0.255 | 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 | 379 | 399 | 388 | 697 | 0 | 467 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.02 | 1.84 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.701 | 20.218 | 2.051 | 0.000 | 0.120 | 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 | 303 | 315 | 314 | 505 | 0 | 401 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.04 | 1.67 | 0.00 | 1.32 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.527 | 18.644 | 1.901 | 0.000 | 0.192 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 245 | 246 | 381 | 0 | 351 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.02 | 1.58 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.398 | 14.389 | 2.083 | 0.000 | 0.160 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 94 | 121 | 121 | 0 | 299 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 1.29 | 0.00 | 3.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.207 | 5.592 | 1.941 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 94 | 94 | 113 | 0 | 108 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.20 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.207 | 4.457 | 1.957 | 0.000 | 0.084 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 146 | 146 | 127 | 216 | 0 | 385 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 1.48 | 0.00 | 2.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 5.384 | 2.325 | 0.000 | 0.089 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 328 | 290 | 511 | 0 | 606 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.91 | 1.61 | 0.00 | 1.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.514 | 16.632 | 2.220 | 0.000 | 0.183 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 403 | 432 | 381 | 639 | 0 | 950 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.95 | 1.59 | 0.00 | 2.36 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.684 | 9.119 | 2.536 | 0.000 | 0.197 | 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 | 395 | 414 | 360 | 700 | 0 | 609 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.91 | 1.77 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.660 | 12.887 | 2.008 | 0.000 | 0.140 | 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 | 310 | 329 | 262 | 557 | 0 | 519 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.85 | 1.80 | 0.00 | 1.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.523 | 11.618 | 2.146 | 0.000 | 0.149 | 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 | 249 | 261 | 210 | 451 | 0 | 452 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.84 | 1.81 | 0.00 | 1.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.400 | 10.767 | 1.939 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 243 | 186 | 352 | 0 | 379 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.81 | 1.52 | 0.00 | 1.64 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.377 | 6.193 | 2.005 | 0.000 | 0.153 | 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 | 274 | 296 | 220 | 471 | 0 | 493 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.80 | 1.72 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.433 | 7.390 | 1.963 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 370 | 392 | 266 | 649 | 0 | 797 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.72 | 1.75 | 0.00 | 2.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.596 | 11.756 | 2.140 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 478 | 508 | 420 | 692 | 0 | 1277 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.88 | 1.45 | 0.00 | 2.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.763 | 12.320 | 2.717 | 0.000 | 0.141 | 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 | 470 | 492 | 451 | 895 | 0 | 933 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.96 | 1.90 | 0.00 | 1.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.812 | 24.925 | 2.548 | 0.000 | 0.314 | 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 | 383 | 400 | 405 | 792 | 0 | 816 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.06 | 2.07 | 0.00 | 2.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.625 | 13.349 | 2.339 | 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 | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 357 | 353 | 659 | 0 | 700 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.03 | 1.92 | 0.00 | 2.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.561 | 12.377 | 2.373 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 344 | 384 | 290 | 569 | 0 | 581 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 0.84 | 1.65 | 0.00 | 1.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.618 | 20.490 | 2.265 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 359 | 383 | 375 | 596 | 0 | 767 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.04 | 1.66 | 0.00 | 2.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.568 | 9.434 | 2.014 | 0.000 | 0.168 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 451 | 475 | 429 | 653 | 0 | 953 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.95 | 1.45 | 0.00 | 2.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.690 | 10.151 | 2.501 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 567 | 602 | 504 | 762 | 0 | 1510 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.89 | 1.34 | 0.00 | 2.66 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.897 | 14.065 | 2.725 | 0.000 | 0.170 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 117 | 215 | 0 | 211 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.29 | 4.22 | 0.00 | 4.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 4.851 | 1.963 | 0.000 | 0.170 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 76 | 115 | 0 | 78 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.49 | 2.25 | 0.00 | 1.53 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.191 | 4.036 | 2.118 | 0.000 | 0.168 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 117 | 215 | 0 | 213 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.21 | 4.06 | 0.00 | 4.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.187 | 4.751 | 2.323 | 0.000 | 0.088 | 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 | 53 | 53 | 82 | 115 | 0 | 78 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.55 | 2.17 | 0.00 | 1.47 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.180 | 4.037 | 1.942 | 0.000 | 0.078 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 66 | 17 | 0 | 16 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 5.50 | 1.42 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.135 | 0.043 | 1.931 | 0.000 | 0.087 | 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 | 12 | 12 | 66 | 50 | 0 | 16 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 5.50 | 4.17 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.144 | 0.003 | 2.016 | 0.000 | 0.083 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 70 | 129 | 674 | 343 | 2218 | 530 | 333 |
| N.S. |
1 | 1.00 | 0.74 | 1.36 | 7.09 | 3.61 | 23.35 | 5.58 | 3.51 |
| time (sec) |
N/A | 0.256 | 0.106 | 2.041 | 0.212 | 0.501 | 1.552 | 0.304 | 9.849 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 60 | 76 | 323 | 201 | 993 | 293 | 197 |
| N.S. |
1 | 1.00 | 0.87 | 1.10 | 4.68 | 2.91 | 14.39 | 4.25 | 2.86 |
| time (sec) |
N/A | 0.234 | 0.074 | 2.095 | 0.211 | 0.457 | 0.817 | 0.269 | 9.749 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 41 | 34 | 37 | 114 | 81 | 299 | 118 | 88 |
| N.S. |
1 | 1.00 | 0.83 | 0.90 | 2.78 | 1.98 | 7.29 | 2.88 | 2.15 |
| time (sec) |
N/A | 0.196 | 0.049 | 1.912 | 0.208 | 0.273 | 0.413 | 0.281 | 9.540 |
| 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 | 18 | 18 | 18 | 19 | 18 | 20 | 20 | 18 | 18 |
| N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.11 | 1.11 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.143 | 0.005 | 1.854 | 0.205 | 0.281 | 0.020 | 0.271 | 9.617 |
| 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 | 32 | 32 | 32 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.164 | 0.050 | 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 | 39 | 39 | 36 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.170 | 0.052 | 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 | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 267 | 267 | 236 | 904 | 669 | 1449 | 21005 | 2539 | 1085 |
| N.S. |
1 | 1.00 | 0.88 | 3.39 | 2.51 | 5.43 | 78.67 | 9.51 | 4.06 |
| time (sec) |
N/A | 0.445 | 0.301 | 2.109 | 0.222 | 0.442 | 4.416 | 0.296 | 10.363 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 159 | 138 | 419 | 318 | 584 | 6418 | 1001 | 464 |
| N.S. |
1 | 1.00 | 0.87 | 2.64 | 2.00 | 3.67 | 40.36 | 6.30 | 2.92 |
| time (sec) |
N/A | 0.320 | 0.173 | 2.208 | 0.205 | 0.490 | 1.537 | 0.273 | 9.929 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 75 | 116 | 113 | 160 | 1095 | 260 | 146 |
| N.S. |
1 | 1.00 | 1.00 | 1.55 | 1.51 | 2.13 | 14.60 | 3.47 | 1.95 |
| time (sec) |
N/A | 0.222 | 0.101 | 2.135 | 0.197 | 0.259 | 0.536 | 0.283 | 9.634 |
| 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 | 93 | 93 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.241 | 0.105 | 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 | 180 | 208 | 174 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.16 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.398 | 0.210 | 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 | 350 | 396 | 337 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.687 | 0.612 | 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 | 105 | 105 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.225 | 1.563 | 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 | 105 | 105 | 76 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.214 | 0.935 | 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 | 105 | 105 | 74 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.217 | 1.033 | 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 | 105 | 105 | 138 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.208 | 1.747 | 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 | 103 | 103 | 76 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.219 | 0.224 | 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 | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 101 | 94 | 93 | 93 | 100 | 96 | 93 |
| N.S. |
1 | 1.00 | 1.77 | 1.65 | 1.63 | 1.63 | 1.75 | 1.68 | 1.63 |
| time (sec) |
N/A | 0.231 | 0.020 | 2.157 | 0.197 | 0.270 | 0.027 | 0.284 | 0.047 |
| 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 | 57 | 57 | 74 | 72 | 72 | 72 | 80 | 73 | 71 |
| N.S. |
1 | 1.00 | 1.30 | 1.26 | 1.26 | 1.26 | 1.40 | 1.28 | 1.25 |
| time (sec) |
N/A | 0.213 | 0.015 | 2.127 | 0.200 | 0.264 | 0.024 | 0.266 | 0.033 |
| 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 | 57 | 57 | 53 | 48 | 47 | 47 | 51 | 49 | 48 |
| N.S. |
1 | 1.00 | 0.93 | 0.84 | 0.82 | 0.82 | 0.89 | 0.86 | 0.84 |
| time (sec) |
N/A | 0.205 | 0.010 | 2.235 | 0.205 | 0.568 | 0.022 | 0.269 | 0.026 |
| 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 | 31 | 32 | 32 | 27 | 26 | 26 | 29 | 26 | 26 |
| N.S. |
1 | 1.03 | 1.03 | 0.87 | 0.84 | 0.84 | 0.94 | 0.84 | 0.84 |
| time (sec) |
N/A | 0.166 | 0.003 | 0.176 | 0.230 | 0.388 | 0.019 | 0.304 | 0.044 |
| 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 | 41 | 41 | 38 | 39 | 39 | 39 | 36 | 40 | 39 |
| N.S. |
1 | 1.00 | 0.93 | 0.95 | 0.95 | 0.95 | 0.88 | 0.98 | 0.95 |
| time (sec) |
N/A | 0.190 | 0.015 | 2.125 | 0.209 | 0.380 | 0.078 | 0.279 | 0.055 |
| 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 | 43 | 43 | 39 | 44 | 46 | 59 | 42 | 66 | 49 |
| N.S. |
1 | 1.00 | 0.91 | 1.02 | 1.07 | 1.37 | 0.98 | 1.53 | 1.14 |
| time (sec) |
N/A | 0.197 | 0.024 | 2.074 | 0.216 | 0.291 | 0.116 | 0.263 | 0.063 |
| 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 | 53 | 51 | 48 | 47 | 57 | 73 | 56 | 48 | 58 |
| N.S. |
1 | 0.96 | 0.91 | 0.89 | 1.08 | 1.38 | 1.06 | 0.91 | 1.09 |
| time (sec) |
N/A | 0.197 | 0.018 | 2.042 | 0.220 | 0.276 | 0.169 | 0.279 | 9.529 |
| 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 | 54 | 52 | 39 | 39 | 63 | 63 | 66 | 38 | 63 |
| N.S. |
1 | 0.96 | 0.72 | 0.72 | 1.17 | 1.17 | 1.22 | 0.70 | 1.17 |
| time (sec) |
N/A | 0.203 | 0.018 | 2.058 | 0.199 | 0.266 | 0.233 | 0.272 | 0.042 |
| 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 | 59 | 57 | 40 | 40 | 75 | 75 | 80 | 59 | 77 |
| N.S. |
1 | 0.97 | 0.68 | 0.68 | 1.27 | 1.27 | 1.36 | 1.00 | 1.31 |
| time (sec) |
N/A | 0.202 | 0.018 | 2.073 | 0.193 | 0.273 | 0.276 | 0.275 | 9.370 |
| 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 | 117 | 117 | 167 | 165 | 163 | 163 | 182 | 172 | 160 |
| N.S. |
1 | 1.00 | 1.43 | 1.41 | 1.39 | 1.39 | 1.56 | 1.47 | 1.37 |
| time (sec) |
N/A | 0.328 | 0.023 | 2.270 | 0.197 | 0.259 | 0.032 | 0.265 | 9.489 |
| 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 | 117 | 117 | 117 | 128 | 130 | 130 | 141 | 131 | 127 |
| N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.11 | 1.11 | 1.21 | 1.12 | 1.09 |
| time (sec) |
N/A | 0.295 | 0.021 | 2.150 | 0.194 | 0.247 | 0.030 | 0.268 | 0.054 |
| 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 | 80 | 80 | 91 | 88 | 87 | 87 | 95 | 89 | 87 |
| N.S. |
1 | 1.00 | 1.14 | 1.10 | 1.09 | 1.09 | 1.19 | 1.11 | 1.09 |
| time (sec) |
N/A | 0.215 | 0.013 | 2.157 | 0.192 | 0.243 | 0.026 | 0.279 | 9.323 |
| 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 | 45 | 45 | 60 | 51 | 50 | 50 | 58 | 50 | 50 |
| N.S. |
1 | 1.00 | 1.33 | 1.13 | 1.11 | 1.11 | 1.29 | 1.11 | 1.11 |
| time (sec) |
N/A | 0.178 | 0.004 | 2.412 | 0.187 | 0.265 | 0.022 | 0.271 | 0.026 |
| 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 | 94 | 94 | 79 | 96 | 105 | 105 | 88 | 106 | 106 |
| N.S. |
1 | 1.00 | 0.84 | 1.02 | 1.12 | 1.12 | 0.94 | 1.13 | 1.13 |
| time (sec) |
N/A | 0.257 | 0.032 | 2.255 | 0.195 | 0.455 | 0.143 | 0.281 | 0.045 |
| 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 | 94 | 94 | 91 | 100 | 112 | 150 | 107 | 153 | 116 |
| N.S. |
1 | 1.00 | 0.97 | 1.06 | 1.19 | 1.60 | 1.14 | 1.63 | 1.23 |
| time (sec) |
N/A | 0.255 | 0.059 | 2.079 | 0.196 | 0.471 | 0.238 | 0.286 | 0.058 |
| 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 | 100 | 100 | 111 | 107 | 120 | 177 | 122 | 112 | 125 |
| N.S. |
1 | 1.00 | 1.11 | 1.07 | 1.20 | 1.77 | 1.22 | 1.12 | 1.25 |
| time (sec) |
N/A | 0.273 | 0.039 | 2.134 | 0.209 | 0.397 | 0.399 | 0.270 | 0.067 |
| 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 | 101 | 101 | 110 | 106 | 130 | 183 | 138 | 106 | 133 |
| N.S. |
1 | 1.00 | 1.09 | 1.05 | 1.29 | 1.81 | 1.37 | 1.05 | 1.32 |
| time (sec) |
N/A | 0.266 | 0.057 | 2.115 | 0.205 | 0.532 | 0.578 | 0.277 | 9.516 |
| 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 | 109 | 109 | 100 | 109 | 146 | 194 | 150 | 165 | 144 |
| N.S. |
1 | 1.00 | 0.92 | 1.00 | 1.34 | 1.78 | 1.38 | 1.51 | 1.32 |
| time (sec) |
N/A | 0.277 | 0.036 | 2.109 | 0.219 | 0.246 | 0.742 | 0.274 | 9.480 |
| 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 | 110 | 110 | 90 | 105 | 151 | 151 | 162 | 104 | 148 |
| N.S. |
1 | 1.00 | 0.82 | 0.95 | 1.37 | 1.37 | 1.47 | 0.95 | 1.35 |
| time (sec) |
N/A | 0.267 | 0.039 | 2.134 | 0.193 | 0.267 | 0.993 | 0.270 | 0.073 |
| 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 | 117 | 117 | 89 | 102 | 159 | 159 | 172 | 103 | 157 |
| N.S. |
1 | 1.00 | 0.76 | 0.87 | 1.36 | 1.36 | 1.47 | 0.88 | 1.34 |
| time (sec) |
N/A | 0.264 | 0.035 | 2.136 | 0.214 | 0.252 | 1.264 | 0.276 | 9.416 |
| 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 | 114 | 114 | 90 | 105 | 173 | 173 | 185 | 104 | 171 |
| N.S. |
1 | 1.00 | 0.79 | 0.92 | 1.52 | 1.52 | 1.62 | 0.91 | 1.50 |
| time (sec) |
N/A | 0.270 | 0.038 | 2.156 | 0.212 | 0.236 | 1.719 | 0.275 | 0.074 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 190 | 338 | 336 | 336 | 336 | 371 | 362 | 329 |
| N.S. |
1 | 1.00 | 1.78 | 1.77 | 1.77 | 1.77 | 1.95 | 1.91 | 1.73 |
| time (sec) |
N/A | 0.515 | 0.055 | 2.512 | 0.200 | 0.260 | 0.046 | 0.276 | 0.177 |
| 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 | 190 | 190 | 252 | 284 | 292 | 292 | 321 | 303 | 281 |
| N.S. |
1 | 1.00 | 1.33 | 1.49 | 1.54 | 1.54 | 1.69 | 1.59 | 1.48 |
| time (sec) |
N/A | 0.470 | 0.060 | 2.334 | 0.200 | 0.257 | 0.042 | 0.269 | 9.481 |
| 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 | 188 | 188 | 206 | 234 | 232 | 232 | 255 | 246 | 224 |
| N.S. |
1 | 1.00 | 1.10 | 1.24 | 1.23 | 1.23 | 1.36 | 1.31 | 1.19 |
| time (sec) |
N/A | 0.444 | 0.055 | 2.316 | 0.197 | 0.281 | 0.037 | 0.273 | 9.482 |
| 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 | 161 | 161 | 155 | 183 | 181 | 181 | 202 | 188 | 174 |
| N.S. |
1 | 1.00 | 0.96 | 1.14 | 1.12 | 1.12 | 1.25 | 1.17 | 1.08 |
| time (sec) |
N/A | 0.336 | 0.047 | 2.168 | 0.212 | 0.422 | 0.037 | 0.271 | 0.090 |
| 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 | 104 | 104 | 116 | 127 | 126 | 126 | 139 | 129 | 121 |
| N.S. |
1 | 1.00 | 1.12 | 1.22 | 1.21 | 1.21 | 1.34 | 1.24 | 1.16 |
| time (sec) |
N/A | 0.244 | 0.025 | 2.121 | 0.190 | 0.426 | 0.029 | 0.273 | 9.413 |
| 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 | 56 | 55 | 85 | 74 | 73 | 73 | 85 | 73 | 73 |
| N.S. |
1 | 0.98 | 1.52 | 1.32 | 1.30 | 1.30 | 1.52 | 1.30 | 1.30 |
| time (sec) |
N/A | 0.187 | 0.004 | 2.095 | 0.205 | 0.374 | 0.023 | 0.274 | 0.034 |
| 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 | 173 | 173 | 142 | 190 | 198 | 198 | 177 | 205 | 213 |
| N.S. |
1 | 1.00 | 0.82 | 1.10 | 1.14 | 1.14 | 1.02 | 1.18 | 1.23 |
| time (sec) |
N/A | 0.346 | 0.052 | 2.180 | 0.208 | 0.717 | 0.207 | 0.269 | 9.434 |
| 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 | 158 | 158 | 193 | 194 | 206 | 272 | 192 | 270 | 274 |
| N.S. |
1 | 1.00 | 1.22 | 1.23 | 1.30 | 1.72 | 1.22 | 1.71 | 1.73 |
| time (sec) |
N/A | 0.354 | 0.061 | 2.126 | 0.202 | 0.284 | 0.385 | 0.277 | 9.397 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 198 | 191 | 214 | 315 | 218 | 205 | 235 |
| N.S. |
1 | 1.00 | 1.21 | 1.17 | 1.31 | 1.93 | 1.34 | 1.26 | 1.44 |
| time (sec) |
N/A | 0.353 | 0.066 | 2.112 | 0.197 | 0.254 | 0.645 | 0.287 | 0.081 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 165 | 197 | 198 | 226 | 334 | 238 | 205 | 228 |
| N.S. |
1 | 1.00 | 1.19 | 1.20 | 1.37 | 2.02 | 1.44 | 1.24 | 1.38 |
| time (sec) |
N/A | 0.360 | 0.070 | 2.357 | 0.217 | 0.252 | 1.062 | 0.263 | 9.349 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 185 | 203 | 239 | 356 | 243 | 290 | 236 |
| N.S. |
1 | 1.00 | 1.08 | 1.19 | 1.40 | 2.08 | 1.42 | 1.70 | 1.38 |
| time (sec) |
N/A | 0.359 | 0.066 | 2.447 | 0.199 | 0.284 | 1.893 | 0.276 | 9.480 |
| 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 | 172 | 172 | 182 | 198 | 246 | 326 | 264 | 200 | 247 |
| N.S. |
1 | 1.00 | 1.06 | 1.15 | 1.43 | 1.90 | 1.53 | 1.16 | 1.44 |
| time (sec) |
N/A | 0.361 | 0.085 | 2.149 | 0.224 | 0.293 | 5.093 | 0.275 | 9.459 |
| 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 | 184 | 184 | 172 | 201 | 263 | 339 | 272 | 208 | 262 |
| N.S. |
1 | 1.00 | 0.93 | 1.09 | 1.43 | 1.84 | 1.48 | 1.13 | 1.42 |
| time (sec) |
N/A | 0.356 | 0.062 | 2.153 | 0.200 | 0.275 | 24.868 | 0.262 | 9.582 |
| 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 | 178 | 178 | 161 | 191 | 263 | 263 | 286 | 202 | 254 |
| N.S. |
1 | 1.00 | 0.90 | 1.07 | 1.48 | 1.48 | 1.61 | 1.13 | 1.43 |
| time (sec) |
N/A | 0.349 | 0.055 | 2.119 | 0.206 | 0.272 | 125.018 | 0.280 | 0.086 |
| 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 | 188 | 188 | 163 | 199 | 282 | 282 | 0 | 204 | 275 |
| N.S. |
1 | 1.00 | 0.87 | 1.06 | 1.50 | 1.50 | 0.00 | 1.09 | 1.46 |
| time (sec) |
N/A | 0.338 | 0.062 | 2.105 | 0.219 | 0.427 | 0.000 | 0.289 | 9.402 |
| 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 | 190 | 190 | 163 | 199 | 293 | 293 | 0 | 204 | 287 |
| N.S. |
1 | 1.00 | 0.86 | 1.05 | 1.54 | 1.54 | 0.00 | 1.07 | 1.51 |
| time (sec) |
N/A | 0.345 | 0.061 | 2.168 | 0.213 | 0.439 | 0.000 | 0.284 | 9.567 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 278 | 423 | 500 | 510 | 510 | 571 | 547 | 495 |
| N.S. |
1 | 1.00 | 1.52 | 1.80 | 1.83 | 1.83 | 2.05 | 1.97 | 1.78 |
| time (sec) |
N/A | 0.722 | 0.090 | 2.135 | 0.204 | 0.354 | 0.056 | 0.282 | 9.569 |
| 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 | 276 | 276 | 361 | 435 | 441 | 441 | 486 | 472 | 425 |
| N.S. |
1 | 1.00 | 1.31 | 1.58 | 1.60 | 1.60 | 1.76 | 1.71 | 1.54 |
| time (sec) |
N/A | 0.671 | 0.128 | 2.147 | 0.201 | 0.668 | 0.050 | 0.279 | 0.240 |
| 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 | 278 | 278 | 307 | 370 | 374 | 374 | 418 | 397 | 357 |
| N.S. |
1 | 1.00 | 1.10 | 1.33 | 1.35 | 1.35 | 1.50 | 1.43 | 1.28 |
| time (sec) |
N/A | 0.639 | 0.099 | 2.270 | 0.203 | 0.277 | 0.046 | 0.266 | 9.639 |
| 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 | 270 | 270 | 300 | 305 | 306 | 306 | 340 | 322 | 288 |
| N.S. |
1 | 1.00 | 1.11 | 1.13 | 1.13 | 1.13 | 1.26 | 1.19 | 1.07 |
| time (sec) |
N/A | 0.486 | 0.046 | 2.500 | 0.227 | 0.235 | 0.041 | 0.281 | 0.159 |
| 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 | 209 | 209 | 197 | 240 | 244 | 244 | 270 | 247 | 225 |
| N.S. |
1 | 1.00 | 0.94 | 1.15 | 1.17 | 1.17 | 1.29 | 1.18 | 1.08 |
| time (sec) |
N/A | 0.406 | 0.070 | 2.178 | 0.199 | 0.267 | 0.038 | 0.281 | 9.488 |
| 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 | 132 | 132 | 148 | 168 | 169 | 169 | 187 | 171 | 161 |
| N.S. |
1 | 1.00 | 1.12 | 1.27 | 1.28 | 1.28 | 1.42 | 1.30 | 1.22 |
| time (sec) |
N/A | 0.288 | 0.033 | 2.211 | 0.236 | 0.265 | 0.032 | 0.280 | 0.094 |
| 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 | 73 | 71 | 110 | 97 | 96 | 96 | 112 | 96 | 96 |
| N.S. |
1 | 0.97 | 1.51 | 1.33 | 1.32 | 1.32 | 1.53 | 1.32 | 1.32 |
| time (sec) |
N/A | 0.208 | 0.004 | 2.111 | 0.194 | 0.244 | 0.026 | 0.268 | 0.068 |
| 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 | 264 | 264 | 227 | 307 | 319 | 319 | 292 | 338 | 357 |
| N.S. |
1 | 1.00 | 0.86 | 1.16 | 1.21 | 1.21 | 1.11 | 1.28 | 1.35 |
| time (sec) |
N/A | 0.515 | 0.106 | 2.339 | 0.196 | 0.255 | 0.292 | 0.291 | 0.068 |
| 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 | 255 | 255 | 289 | 315 | 330 | 421 | 314 | 414 | 701 |
| N.S. |
1 | 1.00 | 1.13 | 1.24 | 1.29 | 1.65 | 1.23 | 1.62 | 2.75 |
| time (sec) |
N/A | 0.501 | 0.100 | 2.204 | 0.189 | 0.539 | 0.557 | 0.285 | 9.402 |
| 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 | 73 | 71 | 110 | 97 | 96 | 96 | 112 | 96 | 96 |
| N.S. |
1 | 0.97 | 1.51 | 1.33 | 1.32 | 1.32 | 1.53 | 1.32 | 1.32 |
| time (sec) |
N/A | 0.206 | 0.006 | 2.127 | 0.216 | 0.401 | 0.033 | 0.262 | 0.072 |
| 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 | 123 | 123 | 111 | 117 | 114 | 283 | 401 | 119 | 127 |
| N.S. |
1 | 1.00 | 0.90 | 0.95 | 0.93 | 2.30 | 3.26 | 0.97 | 1.03 |
| time (sec) |
N/A | 0.279 | 0.097 | 2.282 | 0.276 | 0.405 | 0.529 | 0.307 | 0.111 |
| 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 | 90 | 90 | 80 | 80 | 79 | 187 | 308 | 81 | 91 |
| N.S. |
1 | 1.00 | 0.89 | 0.89 | 0.88 | 2.08 | 3.42 | 0.90 | 1.01 |
| time (sec) |
N/A | 0.237 | 0.055 | 2.257 | 0.277 | 0.355 | 0.415 | 0.294 | 0.129 |
| 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 | 59 | 59 | 56 | 53 | 53 | 137 | 185 | 53 | 62 |
| N.S. |
1 | 1.00 | 0.95 | 0.90 | 0.90 | 2.32 | 3.14 | 0.90 | 1.05 |
| time (sec) |
N/A | 0.205 | 0.043 | 2.560 | 0.274 | 0.287 | 0.250 | 0.280 | 9.561 |