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 | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 360 | 360 | 371 | 335 | 0 | 3449 | 0 | 3656 | 8768 |
N.S. |
1 | 1.00 | 1.03 | 0.93 | 0.00 | 9.58 | 0.00 | 10.16 | 24.36 |
time (sec) |
N/A | 2.270 | 1.803 | 0.297 | 0.000 | 2.327 | 0.000 | 0.653 | 12.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 751 | 751 | 720 | 785 | 0 | 8780 | 0 | 3037 | 20000 |
N.S. |
1 | 1.00 | 0.96 | 1.05 | 0.00 | 11.69 | 0.00 | 4.04 | 26.63 |
time (sec) |
N/A | 10.316 | 15.346 | 3.078 | 0.000 | 2.184 | 0.000 | 2.000 | 35.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 577 | 577 | 506 | 639 | 0 | 5124 | 0 | 2512 | 13637 |
N.S. |
1 | 1.00 | 0.88 | 1.11 | 0.00 | 8.88 | 0.00 | 4.35 | 23.63 |
time (sec) |
N/A | 3.187 | 13.143 | 1.099 | 0.000 | 0.558 | 0.000 | 1.263 | 27.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 441 | 441 | 817 | 530 | 0 | 11128 | 0 | 2116 | 13764 |
N.S. |
1 | 1.00 | 1.85 | 1.20 | 0.00 | 25.23 | 0.00 | 4.80 | 31.21 |
time (sec) |
N/A | 1.215 | 15.795 | 0.727 | 0.000 | 0.727 | 0.000 | 1.290 | 32.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 634 | 634 | 580 | 778 | 0 | 30962 | 0 | 5171 | 23750 |
N.S. |
1 | 1.00 | 0.91 | 1.23 | 0.00 | 48.84 | 0.00 | 8.16 | 37.46 |
time (sec) |
N/A | 3.676 | 12.277 | 1.714 | 0.000 | 23.161 | 0.000 | 2.146 | 87.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 835 | 834 | 799 | 1027 | 0 | 55168 | 0 | 9101 | 132771 |
N.S. |
1 | 1.00 | 0.96 | 1.23 | 0.00 | 66.07 | 0.00 | 10.90 | 159.01 |
time (sec) |
N/A | 11.140 | 13.357 | 46.461 | 0.000 | 135.890 | 0.000 | 2.429 | 26.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 629 | 629 | 232 | 691 | 0 | 753 | 0 | 0 | 711 |
N.S. |
1 | 1.00 | 0.37 | 1.10 | 0.00 | 1.20 | 0.00 | 0.00 | 1.13 |
time (sec) |
N/A | 0.876 | 0.674 | 1.680 | 0.000 | 0.285 | 0.000 | 0.000 | 10.630 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 705 | 705 | 188 | 714 | 0 | 2759 | 0 | 0 | 4530 |
N.S. |
1 | 1.00 | 0.27 | 1.01 | 0.00 | 3.91 | 0.00 | 0.00 | 6.43 |
time (sec) |
N/A | 0.584 | 0.754 | 0.452 | 0.000 | 0.312 | 0.000 | 0.000 | 12.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 124 | 281 | 0 | 200 | 0 | 614 | 200 |
N.S. |
1 | 1.00 | 0.44 | 1.01 | 0.00 | 0.72 | 0.00 | 2.20 | 0.72 |
time (sec) |
N/A | 0.428 | 0.698 | 1.349 | 0.000 | 0.302 | 0.000 | 0.702 | 9.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 266 | 266 | 119 | 276 | 0 | 195 | 0 | 605 | 191 |
N.S. |
1 | 1.00 | 0.45 | 1.04 | 0.00 | 0.73 | 0.00 | 2.27 | 0.72 |
time (sec) |
N/A | 0.313 | 0.441 | 0.556 | 0.000 | 0.282 | 0.000 | 0.706 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 253 | 253 | 114 | 273 | 0 | 190 | 0 | 594 | 182 |
N.S. |
1 | 1.00 | 0.45 | 1.08 | 0.00 | 0.75 | 0.00 | 2.35 | 0.72 |
time (sec) |
N/A | 0.258 | 0.395 | 0.600 | 0.000 | 0.292 | 0.000 | 0.724 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 222 | 100 | 241 | 0 | 169 | 0 | 461 | 116 |
N.S. |
1 | 1.00 | 0.45 | 1.09 | 0.00 | 0.76 | 0.00 | 2.08 | 0.52 |
time (sec) |
N/A | 0.164 | 0.319 | 0.516 | 0.000 | 0.322 | 0.000 | 0.704 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 100 | 249 | 0 | 181 | 0 | 279 | 167 |
N.S. |
1 | 1.00 | 0.46 | 1.14 | 0.00 | 0.83 | 0.00 | 1.28 | 0.77 |
time (sec) |
N/A | 0.185 | 0.221 | 0.484 | 0.000 | 0.283 | 0.000 | 0.494 | 9.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 253 | 253 | 114 | 294 | 0 | 217 | 0 | 594 | 182 |
N.S. |
1 | 1.00 | 0.45 | 1.16 | 0.00 | 0.86 | 0.00 | 2.35 | 0.72 |
time (sec) |
N/A | 0.280 | 0.558 | 0.575 | 0.000 | 0.334 | 0.000 | 0.489 | 10.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 266 | 266 | 119 | 307 | 0 | 249 | 0 | 599 | 187 |
N.S. |
1 | 1.00 | 0.45 | 1.15 | 0.00 | 0.94 | 0.00 | 2.25 | 0.70 |
time (sec) |
N/A | 0.270 | 0.695 | 0.564 | 0.000 | 0.415 | 0.000 | 0.509 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 296 | 296 | 136 | 317 | 0 | 252 | 0 | 633 | 216 |
N.S. |
1 | 1.00 | 0.46 | 1.07 | 0.00 | 0.85 | 0.00 | 2.14 | 0.73 |
time (sec) |
N/A | 0.322 | 1.182 | 0.603 | 0.000 | 0.399 | 0.000 | 0.677 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 129 | 312 | 0 | 247 | 0 | 624 | 208 |
N.S. |
1 | 1.00 | 0.46 | 1.10 | 0.00 | 0.87 | 0.00 | 2.20 | 0.73 |
time (sec) |
N/A | 0.293 | 1.031 | 0.626 | 0.000 | 0.451 | 0.000 | 0.677 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 129 | 312 | 0 | 247 | 0 | 622 | 208 |
N.S. |
1 | 1.00 | 0.48 | 1.16 | 0.00 | 0.91 | 0.00 | 2.30 | 0.77 |
time (sec) |
N/A | 0.261 | 0.841 | 0.560 | 0.000 | 0.381 | 0.000 | 0.673 | 9.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 129 | 243 | 0 | 247 | 0 | 622 | 208 |
N.S. |
1 | 1.00 | 0.48 | 0.90 | 0.00 | 0.91 | 0.00 | 2.30 | 0.77 |
time (sec) |
N/A | 0.245 | 0.582 | 1.092 | 0.000 | 0.301 | 0.000 | 0.668 | 9.952 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 129 | 249 | 0 | 247 | 0 | 622 | 207 |
N.S. |
1 | 1.00 | 0.48 | 0.92 | 0.00 | 0.91 | 0.00 | 2.30 | 0.77 |
time (sec) |
N/A | 0.243 | 0.592 | 0.907 | 0.000 | 0.278 | 0.000 | 0.495 | 9.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 138 | 338 | 0 | 277 | 0 | 633 | 217 |
N.S. |
1 | 1.00 | 0.49 | 1.19 | 0.00 | 0.98 | 0.00 | 2.24 | 0.77 |
time (sec) |
N/A | 0.257 | 1.202 | 0.704 | 0.000 | 0.285 | 0.000 | 0.538 | 9.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 296 | 296 | 143 | 352 | 0 | 309 | 0 | 638 | 226 |
N.S. |
1 | 1.00 | 0.48 | 1.19 | 0.00 | 1.04 | 0.00 | 2.16 | 0.76 |
time (sec) |
N/A | 0.328 | 1.351 | 0.799 | 0.000 | 0.292 | 0.000 | 0.529 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 313 | 143 | 328 | 0 | 307 | 0 | 642 | 245 |
N.S. |
1 | 1.00 | 0.46 | 1.05 | 0.00 | 0.98 | 0.00 | 2.05 | 0.78 |
time (sec) |
N/A | 0.366 | 1.871 | 0.780 | 0.000 | 0.297 | 0.000 | 0.700 | 10.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 141 | 328 | 0 | 307 | 0 | 642 | 245 |
N.S. |
1 | 1.00 | 0.47 | 1.09 | 0.00 | 1.02 | 0.00 | 2.14 | 0.82 |
time (sec) |
N/A | 0.307 | 1.627 | 0.726 | 0.000 | 0.283 | 0.000 | 0.711 | 10.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 143 | 328 | 0 | 307 | 0 | 642 | 245 |
N.S. |
1 | 1.00 | 0.48 | 1.09 | 0.00 | 1.02 | 0.00 | 2.14 | 0.82 |
time (sec) |
N/A | 0.308 | 1.412 | 0.684 | 0.000 | 0.277 | 0.000 | 0.724 | 10.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 143 | 328 | 0 | 307 | 0 | 640 | 245 |
N.S. |
1 | 1.00 | 0.48 | 1.09 | 0.00 | 1.02 | 0.00 | 2.13 | 0.82 |
time (sec) |
N/A | 0.304 | 1.402 | 0.691 | 0.000 | 0.283 | 0.000 | 0.699 | 10.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 141 | 324 | 0 | 307 | 0 | 642 | 245 |
N.S. |
1 | 1.00 | 0.47 | 1.08 | 0.00 | 1.02 | 0.00 | 2.14 | 0.82 |
time (sec) |
N/A | 0.265 | 0.693 | 1.514 | 0.000 | 0.276 | 0.000 | 0.713 | 10.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 314 | 314 | 143 | 324 | 0 | 307 | 0 | 642 | 246 |
N.S. |
1 | 1.00 | 0.46 | 1.03 | 0.00 | 0.98 | 0.00 | 2.04 | 0.78 |
time (sec) |
N/A | 0.282 | 0.715 | 1.697 | 0.000 | 0.276 | 0.000 | 0.529 | 10.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 313 | 148 | 354 | 0 | 337 | 0 | 651 | 252 |
N.S. |
1 | 1.00 | 0.47 | 1.13 | 0.00 | 1.08 | 0.00 | 2.08 | 0.81 |
time (sec) |
N/A | 0.305 | 1.840 | 0.950 | 0.000 | 0.279 | 0.000 | 0.550 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 389 | 389 | 432 | 501 | 0 | 4275 | 0 | 2436 | 10944 |
N.S. |
1 | 1.00 | 1.11 | 1.29 | 0.00 | 10.99 | 0.00 | 6.26 | 28.13 |
time (sec) |
N/A | 1.366 | 3.785 | 0.451 | 0.000 | 0.917 | 0.000 | 2.080 | 14.855 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 458 | 437 | 480 | 521 | 0 | 4933 | 0 | 5281 | 12164 |
N.S. |
1 | 0.95 | 1.05 | 1.14 | 0.00 | 10.77 | 0.00 | 11.53 | 26.56 |
time (sec) |
N/A | 5.181 | 5.433 | 0.291 | 0.000 | 2.947 | 0.000 | 0.703 | 15.084 |
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 | 28 | 28 | 19 | 15 | 16 | 15 | 24 | 16 | 15 |
N.S. |
1 | 1.00 | 0.68 | 0.54 | 0.57 | 0.54 | 0.86 | 0.57 | 0.54 |
time (sec) |
N/A | 0.003 | 0.012 | 0.020 | 0.208 | 0.270 | 0.412 | 0.283 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 295 | 391 | 0 | 787 | 887 | 393 | 632 |
N.S. |
1 | 1.00 | 1.19 | 1.58 | 0.00 | 3.17 | 3.58 | 1.58 | 2.55 |
time (sec) |
N/A | 0.169 | 1.930 | 0.410 | 0.000 | 0.361 | 0.740 | 0.299 | 11.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 191 | 195 | 229 | 0 | 505 | 473 | 236 | 332 |
N.S. |
1 | 1.00 | 1.02 | 1.20 | 0.00 | 2.64 | 2.48 | 1.24 | 1.74 |
time (sec) |
N/A | 0.154 | 1.224 | 0.362 | 0.000 | 0.329 | 0.638 | 0.298 | 10.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 115 | 115 | 0 | 297 | 224 | 121 | 145 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 2.58 | 1.95 | 1.05 | 1.26 |
time (sec) |
N/A | 0.032 | 0.539 | 0.299 | 0.000 | 0.304 | 0.522 | 0.299 | 10.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 75 | 65 | 0 | 177 | 119 | 66 | 63 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.00 | 2.36 | 1.59 | 0.88 | 0.84 |
time (sec) |
N/A | 0.013 | 0.281 | 0.331 | 0.000 | 0.297 | 0.266 | 0.287 | 10.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 175 | 238 | 0 | 992 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 1.57 | 0.00 | 6.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.120 | 0.879 | 0.361 | 0.000 | 0.942 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 151 | 675 | 0 | 1456 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 4.22 | 0.00 | 9.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.089 | 1.239 | 0.376 | 0.000 | 1.314 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 149 | 1138 | 0 | 918 | 0 | 693 | 0 |
N.S. |
1 | 1.00 | 0.97 | 7.44 | 0.00 | 6.00 | 0.00 | 4.53 | 0.00 |
time (sec) |
N/A | 0.066 | 10.116 | 0.455 | 0.000 | 0.714 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 206 | 1253 | 0 | 1950 | 0 | 1992 | 0 |
N.S. |
1 | 1.00 | 0.96 | 5.83 | 0.00 | 9.07 | 0.00 | 9.27 | 0.00 |
time (sec) |
N/A | 0.100 | 10.264 | 0.506 | 0.000 | 2.137 | 0.000 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 308 | 308 | 276 | 2525 | 0 | 3780 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 8.20 | 0.00 | 12.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.268 | 10.514 | 0.560 | 0.000 | 12.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 402 | 402 | 367 | 3912 | 0 | 6374 | 0 | 8697 | 0 |
N.S. |
1 | 1.00 | 0.91 | 9.73 | 0.00 | 15.86 | 0.00 | 21.63 | 0.00 |
time (sec) |
N/A | 0.330 | 11.651 | 0.693 | 0.000 | 58.981 | 0.000 | 0.689 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 321 | 321 | 509 | 754 | 0 | 1359 | 3259 | 737 | 0 |
N.S. |
1 | 1.00 | 1.59 | 2.35 | 0.00 | 4.23 | 10.15 | 2.30 | 0.00 |
time (sec) |
N/A | 0.228 | 4.493 | 0.338 | 0.000 | 0.385 | 0.836 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 337 | 460 | 0 | 899 | 1656 | 465 | 0 |
N.S. |
1 | 1.00 | 1.31 | 1.79 | 0.00 | 3.50 | 6.44 | 1.81 | 0.00 |
time (sec) |
N/A | 0.217 | 2.680 | 0.296 | 0.000 | 0.355 | 0.704 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 192 | 233 | 0 | 529 | 711 | 250 | 305 |
N.S. |
1 | 1.00 | 1.19 | 1.45 | 0.00 | 3.29 | 4.42 | 1.55 | 1.89 |
time (sec) |
N/A | 0.046 | 1.430 | 0.275 | 0.000 | 0.313 | 0.559 | 0.291 | 10.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 104 | 104 | 0 | 277 | 539 | 121 | 103 |
N.S. |
1 | 1.00 | 0.93 | 0.93 | 0.00 | 2.47 | 4.81 | 1.08 | 0.92 |
time (sec) |
N/A | 0.022 | 0.611 | 0.327 | 0.000 | 0.368 | 0.670 | 0.279 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 247 | 383 | 0 | 1523 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.52 | 0.00 | 6.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 1.535 | 0.353 | 0.000 | 132.302 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 214 | 622 | 0 | 1583 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 2.74 | 0.00 | 6.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.173 | 10.301 | 0.396 | 0.000 | 9.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 236 | 311 | 1177 | 0 | 2711 | 0 | 794 | 0 |
N.S. |
1 | 1.00 | 1.32 | 4.99 | 0.00 | 11.49 | 0.00 | 3.36 | 0.00 |
time (sec) |
N/A | 0.166 | 10.573 | 0.438 | 0.000 | 15.091 | 0.000 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 307 | 421 | 3085 | 0 | 4911 | 0 | 2059 | 0 |
N.S. |
1 | 1.00 | 1.37 | 10.05 | 0.00 | 16.00 | 0.00 | 6.71 | 0.00 |
time (sec) |
N/A | 0.237 | 11.035 | 0.454 | 0.000 | 186.224 | 0.000 | 4.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 222 | 5074 | 0 | 2570 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 22.55 | 0.00 | 11.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.111 | 10.452 | 0.583 | 0.000 | 10.785 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 296 | 296 | 275 | 5189 | 0 | 4830 | 0 | 8409 | 0 |
N.S. |
1 | 1.00 | 0.93 | 17.53 | 0.00 | 16.32 | 0.00 | 28.41 | 0.00 |
time (sec) |
N/A | 0.138 | 10.937 | 0.701 | 0.000 | 44.813 | 0.000 | 0.979 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 409 | 409 | 349 | 10397 | 0 | 8058 | 0 | 14486 | 0 |
N.S. |
1 | 1.00 | 0.85 | 25.42 | 0.00 | 19.70 | 0.00 | 35.42 | 0.00 |
time (sec) |
N/A | 0.375 | 11.397 | 1.038 | 0.000 | 116.606 | 0.000 | 7.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 510 | 510 | 430 | 15720 | 0 | 0 | 0 | 22933 | 0 |
N.S. |
1 | 1.00 | 0.84 | 30.82 | 0.00 | 0.00 | 0.00 | 44.97 | 0.00 |
time (sec) |
N/A | 0.499 | 14.797 | 1.205 | 0.000 | 0.000 | 0.000 | 1.890 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 400 | 400 | 280 | 1207 | 0 | 2119 | 11123 | 1193 | 0 |
N.S. |
1 | 1.00 | 0.70 | 3.02 | 0.00 | 5.30 | 27.81 | 2.98 | 0.00 |
time (sec) |
N/A | 0.291 | 10.504 | 0.390 | 0.000 | 0.571 | 0.948 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 323 | 323 | 541 | 661 | 0 | 1425 | 5671 | 770 | 0 |
N.S. |
1 | 1.00 | 1.67 | 2.05 | 0.00 | 4.41 | 17.56 | 2.38 | 0.00 |
time (sec) |
N/A | 0.269 | 6.127 | 0.388 | 0.000 | 0.490 | 0.824 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 207 | 311 | 314 | 0 | 857 | 2428 | 423 | 0 |
N.S. |
1 | 1.00 | 1.50 | 1.52 | 0.00 | 4.14 | 11.73 | 2.04 | 0.00 |
time (sec) |
N/A | 0.066 | 2.798 | 0.365 | 0.000 | 0.389 | 0.674 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 149 | 150 | 143 | 0 | 425 | 1732 | 206 | 143 |
N.S. |
1 | 1.00 | 1.01 | 0.96 | 0.00 | 2.85 | 11.62 | 1.38 | 0.96 |
time (sec) |
N/A | 0.033 | 1.331 | 0.325 | 0.000 | 0.382 | 1.387 | 0.278 | 10.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 443 | 715 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.482 | 3.062 | 0.363 | 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(-2) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 388 | 388 | 370 | 916 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.434 | 10.733 | 0.365 | 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(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 331 | 445 | 1435 | 0 | 3019 | 0 | 1500 | 0 |
N.S. |
1 | 1.00 | 1.34 | 4.34 | 0.00 | 9.12 | 0.00 | 4.53 | 0.00 |
time (sec) |
N/A | 0.370 | 11.114 | 0.455 | 0.000 | 73.706 | 0.000 | 0.508 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 337 | 337 | 559 | 2389 | 0 | 5131 | 0 | 2152 | 0 |
N.S. |
1 | 1.00 | 1.66 | 7.09 | 0.00 | 15.23 | 0.00 | 6.39 | 0.00 |
time (sec) |
N/A | 0.276 | 11.889 | 0.557 | 0.000 | 123.005 | 0.000 | 4.466 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 492 | 492 | 593 | 4043 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.21 | 8.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.482 | 12.395 | 0.652 | 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 | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 83 | 71 | 60 | 78 | 0 | 77 | 77 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.68 | 0.89 | 0.00 | 0.88 | 0.88 |
time (sec) |
N/A | 0.034 | 0.131 | 0.248 | 0.282 | 0.375 | 0.000 | 0.349 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 76 | 60 | 59 | 92 | 0 | 168 | 73 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 0.87 | 1.35 | 0.00 | 2.47 | 1.07 |
time (sec) |
N/A | 0.027 | 0.020 | 0.203 | 0.305 | 0.423 | 0.000 | 0.367 | 10.008 |
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 | 38 | 38 | 36 | 23 | 41 | 32 | 85 | 25 | 22 |
N.S. |
1 | 1.00 | 0.95 | 0.61 | 1.08 | 0.84 | 2.24 | 0.66 | 0.58 |
time (sec) |
N/A | 0.007 | 0.107 | 0.259 | 0.289 | 0.697 | 0.095 | 0.273 | 10.400 |
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 | 54 | 53 | 34 | 52 | 45 | 36 | 45 | 84 |
N.S. |
1 | 1.00 | 0.98 | 0.63 | 0.96 | 0.83 | 0.67 | 0.83 | 1.56 |
time (sec) |
N/A | 0.011 | 0.066 | 0.267 | 0.435 | 0.315 | 0.453 | 0.267 | 11.252 |
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 | 56 | 56 | 43 | 52 | 47 | 41 | 32 | 74 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.93 | 0.84 | 0.73 | 0.57 | 1.32 |
time (sec) |
N/A | 0.013 | 0.101 | 0.264 | 0.390 | 0.269 | 0.449 | 0.279 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 57 | 50 | 62 | 64 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.82 | 1.02 | 1.05 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.028 | 0.100 | 0.269 | 0.205 | 0.295 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 59 | 46 | 58 | 51 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.71 | 0.89 | 0.78 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.029 | 0.083 | 0.263 | 0.291 | 0.289 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 261 | 193 | 187 | 0 | 431 | 656 | 206 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.72 | 0.00 | 1.65 | 2.51 | 0.79 | 0.00 |
time (sec) |
N/A | 0.259 | 0.520 | 0.402 | 0.000 | 0.346 | 0.460 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 153 | 144 | 0 | 347 | 439 | 159 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.00 | 1.72 | 2.17 | 0.79 | 0.00 |
time (sec) |
N/A | 0.141 | 0.432 | 0.348 | 0.000 | 0.340 | 0.410 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 296 | 296 | 247 | 276 | 0 | 599 | 622 | 291 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.93 | 0.00 | 2.02 | 2.10 | 0.98 | 0.00 |
time (sec) |
N/A | 0.261 | 0.750 | 0.443 | 0.000 | 0.357 | 0.797 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 150 | 162 | 0 | 391 | 393 | 176 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.93 | 0.00 | 2.25 | 2.26 | 1.01 | 0.00 |
time (sec) |
N/A | 0.100 | 0.518 | 0.368 | 0.000 | 0.306 | 0.688 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 106 | 94 | 0 | 247 | 243 | 105 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.74 | 0.00 | 1.94 | 1.91 | 0.83 | 0.00 |
time (sec) |
N/A | 0.075 | 0.384 | 0.296 | 0.000 | 0.280 | 0.608 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 66 | 57 | 0 | 165 | 146 | 61 | 80 |
N.S. |
1 | 1.00 | 0.97 | 0.84 | 0.00 | 2.43 | 2.15 | 0.90 | 1.18 |
time (sec) |
N/A | 0.017 | 0.280 | 0.328 | 0.000 | 0.299 | 0.419 | 0.296 | 10.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 35 | 30 | 0 | 106 | 85 | 66 | 29 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.00 | 2.94 | 2.36 | 1.83 | 0.81 |
time (sec) |
N/A | 0.008 | 0.071 | 0.311 | 0.000 | 0.290 | 0.370 | 0.270 | 10.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 92 | 157 | 0 | 343 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.99 | 0.00 | 4.34 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.027 | 0.319 | 0.345 | 0.000 | 0.324 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 125 | 271 | 0 | 652 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 2.02 | 0.00 | 4.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.052 | 0.595 | 0.368 | 0.000 | 0.421 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 205 | 561 | 0 | 1362 | 0 | 795 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.68 | 0.00 | 6.52 | 0.00 | 3.80 | 0.00 |
time (sec) |
N/A | 0.150 | 10.186 | 0.358 | 0.000 | 1.169 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 293 | 293 | 288 | 966 | 0 | 2688 | 0 | 2133 | 0 |
N.S. |
1 | 1.00 | 0.98 | 3.30 | 0.00 | 9.17 | 0.00 | 7.28 | 0.00 |
time (sec) |
N/A | 0.230 | 10.393 | 0.403 | 0.000 | 5.310 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 286 | 286 | 317 | 447 | 0 | 1173 | 0 | 395 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.56 | 0.00 | 4.10 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.209 | 1.506 | 0.500 | 0.000 | 0.477 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 177 | 194 | 307 | 0 | 755 | 0 | 240 | 0 |
N.S. |
1 | 1.00 | 1.10 | 1.73 | 0.00 | 4.27 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.120 | 0.845 | 0.408 | 0.000 | 0.430 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 118 | 207 | 0 | 461 | 0 | 132 | 150 |
N.S. |
1 | 1.00 | 0.91 | 1.60 | 0.00 | 3.57 | 0.00 | 1.02 | 1.16 |
time (sec) |
N/A | 0.058 | 0.670 | 0.380 | 0.000 | 0.391 | 0.000 | 0.292 | 10.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 43 | 45 | 0 | 74 | 0 | 55 | 45 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 0.00 | 1.64 | 0.00 | 1.22 | 1.00 |
time (sec) |
N/A | 0.007 | 0.356 | 0.346 | 0.000 | 0.344 | 0.000 | 0.290 | 10.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 33 | 0 | 61 | 0 | 41 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.91 | 0.00 | 1.28 | 0.97 |
time (sec) |
N/A | 0.004 | 0.248 | 0.332 | 0.000 | 0.301 | 0.000 | 0.290 | 9.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 190 | 400 | 0 | 1349 | 0 | 461 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.58 | 0.00 | 8.70 | 0.00 | 2.97 | 0.00 |
time (sec) |
N/A | 0.082 | 0.994 | 0.322 | 0.000 | 0.588 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 255 | 255 | 250 | 655 | 0 | 3004 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.57 | 0.00 | 11.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.184 | 10.259 | 0.368 | 0.000 | 1.175 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 371 | 371 | 353 | 1189 | 0 | 5732 | 0 | 2718 | 0 |
N.S. |
1 | 1.00 | 0.95 | 3.20 | 0.00 | 15.45 | 0.00 | 7.33 | 0.00 |
time (sec) |
N/A | 0.317 | 10.789 | 0.444 | 0.000 | 4.642 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 519 | 519 | 486 | 1978 | 0 | 9408 | 0 | 5445 | 0 |
N.S. |
1 | 1.00 | 0.94 | 3.81 | 0.00 | 18.13 | 0.00 | 10.49 | 0.00 |
time (sec) |
N/A | 0.557 | 11.366 | 0.554 | 0.000 | 28.620 | 0.000 | 0.599 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 389 | 389 | 566 | 1931 | 0 | 2249 | 0 | 820 | 0 |
N.S. |
1 | 1.00 | 1.46 | 4.96 | 0.00 | 5.78 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.303 | 2.949 | 0.650 | 0.000 | 1.497 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 295 | 401 | 1132 | 0 | 1515 | 0 | 564 | 0 |
N.S. |
1 | 1.00 | 1.36 | 3.84 | 0.00 | 5.14 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.236 | 2.131 | 0.447 | 0.000 | 1.448 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 190 | 287 | 0 | 366 | 0 | 333 | 528 |
N.S. |
1 | 1.00 | 1.61 | 2.43 | 0.00 | 3.10 | 0.00 | 2.82 | 4.47 |
time (sec) |
N/A | 0.033 | 1.168 | 0.422 | 0.000 | 1.235 | 0.000 | 0.292 | 10.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 167 | 206 | 0 | 305 | 0 | 263 | 321 |
N.S. |
1 | 1.00 | 1.70 | 2.10 | 0.00 | 3.11 | 0.00 | 2.68 | 3.28 |
time (sec) |
N/A | 0.023 | 1.008 | 0.316 | 0.000 | 0.788 | 0.000 | 0.305 | 10.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 110 | 122 | 0 | 247 | 0 | 197 | 121 |
N.S. |
1 | 1.00 | 1.21 | 1.34 | 0.00 | 2.71 | 0.00 | 2.16 | 1.33 |
time (sec) |
N/A | 0.018 | 0.808 | 0.296 | 0.000 | 0.724 | 0.000 | 0.293 | 10.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 55 | 67 | 0 | 192 | 0 | 144 | 57 |
N.S. |
1 | 1.00 | 0.79 | 0.96 | 0.00 | 2.74 | 0.00 | 2.06 | 0.81 |
time (sec) |
N/A | 0.008 | 0.623 | 0.302 | 0.000 | 0.343 | 0.000 | 0.282 | 9.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 310 | 310 | 309 | 766 | 0 | 4612 | 0 | 8447 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.47 | 0.00 | 14.88 | 0.00 | 27.25 | 0.00 |
time (sec) |
N/A | 0.196 | 10.334 | 0.345 | 0.000 | 2.152 | 0.000 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 473 | 473 | 482 | 1143 | 0 | 8874 | 0 | 5572 | 0 |
N.S. |
1 | 1.00 | 1.02 | 2.42 | 0.00 | 18.76 | 0.00 | 11.78 | 0.00 |
time (sec) |
N/A | 0.406 | 11.103 | 0.392 | 0.000 | 7.451 | 0.000 | 0.841 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 621 | 621 | 626 | 2043 | 0 | 14440 | 0 | 26254 | 0 |
N.S. |
1 | 1.00 | 1.01 | 3.29 | 0.00 | 23.25 | 0.00 | 42.28 | 0.00 |
time (sec) |
N/A | 0.652 | 11.594 | 0.490 | 0.000 | 37.630 | 0.000 | 1.002 | 0.000 |
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 | 29 | 29 | 40 | 22 | 23 | 44 | 19 | 21 | 46 |
N.S. |
1 | 1.00 | 1.38 | 0.76 | 0.79 | 1.52 | 0.66 | 0.72 | 1.59 |
time (sec) |
N/A | 0.008 | 0.093 | 0.241 | 0.282 | 0.295 | 0.426 | 0.264 | 10.143 |