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 | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 189 | 210 | 1588 | 0 | 1178 | 0 | 1238 | 1308 | 0 |
N.S. |
1 | 1.07 | 1.19 | 8.97 | 0.00 | 6.66 | 0.00 | 6.99 | 7.39 | 0.00 |
time (sec) |
N/A | 0.301 | 0.936 | 0.336 | 0.000 | 9.910 | 0.000 | 0.368 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 209 | 261 | 1417 | 0 | 1267 | 0 | 2589 | 1567 | 0 |
N.S. |
1 | 1.01 | 1.27 | 6.88 | 0.00 | 6.15 | 0.00 | 12.57 | 7.61 | 0.00 |
time (sec) |
N/A | 0.333 | 0.342 | 0.332 | 0.000 | 29.931 | 0.000 | 0.514 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 247 | 223 | 302 | 0 | 656 | 0 | 3978 | 1732 | 528 |
N.S. |
1 | 1.06 | 0.96 | 1.30 | 0.00 | 2.83 | 0.00 | 17.15 | 7.47 | 2.28 |
time (sec) |
N/A | 0.427 | 0.240 | 0.342 | 0.000 | 74.326 | 0.000 | 0.531 | 3.189 | 3.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 294 | 381 | 614 | 0 | 0 | 0 | 5705 | 2628 | 846 |
N.S. |
1 | 0.89 | 1.15 | 1.86 | 0.00 | 0.00 | 0.00 | 17.29 | 7.96 | 2.56 |
time (sec) |
N/A | 0.469 | 0.380 | 0.348 | 0.000 | 0.000 | 0.000 | 0.685 | 0.364 | 3.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 432 | 343 | 581 | 1010 | 0 | 0 | 0 | 7493 | 3656 | 1177 |
N.S. |
1 | 0.79 | 1.34 | 2.34 | 0.00 | 0.00 | 0.00 | 17.34 | 8.46 | 2.72 |
time (sec) |
N/A | 0.489 | 0.574 | 0.335 | 0.000 | 0.000 | 0.000 | 0.907 | 0.444 | 4.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 284 | 319 | 498 | 0 | 671 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.75 | 0.00 | 2.36 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.408 | 19.158 | 3.335 | 0.000 | 0.128 | 0.000 | 0.000 | 8.750 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 210 | 214 | 219 | 0 | 310 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.92 | 0.93 | 0.96 | 0.00 | 1.35 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.305 | 12.162 | 1.166 | 0.000 | 0.113 | 0.000 | 0.000 | 0.562 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 221 | 214 | 0 | 313 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.06 | 1.03 | 0.00 | 1.50 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.302 | 12.186 | 1.305 | 0.000 | 0.115 | 0.000 | 0.000 | 0.578 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 219 | 214 | 0 | 312 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.03 | 0.00 | 1.50 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.307 | 12.232 | 1.286 | 0.000 | 0.108 | 0.000 | 0.000 | 0.906 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 209 | 221 | 227 | 0 | 315 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.01 | 1.07 | 1.10 | 0.00 | 1.53 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.293 | 12.279 | 1.342 | 0.000 | 0.116 | 0.000 | 0.000 | 0.888 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 139 | 309 | 604 | 0 | 1228 | 0 | 0 | 99 | 0 |
N.S. |
1 | 0.96 | 2.13 | 4.17 | 0.00 | 8.47 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.296 | 16.270 | 12.842 | 0.000 | 0.104 | 0.000 | 0.000 | 9.839 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 222 | 312 | 729 | 0 | 1126 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.07 | 1.50 | 3.50 | 0.00 | 5.41 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.369 | 18.370 | 4.535 | 0.000 | 0.114 | 0.000 | 0.000 | 13.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 289 | 288 | 0 | 194 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 3.14 | 3.13 | 0.00 | 2.11 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.225 | 21.673 | 1.454 | 0.000 | 0.074 | 0.000 | 0.000 | 1.603 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 434 | 502 | 432 | 0 | 0 | 0 | 1026 | 4185 | 0 |
N.S. |
1 | 0.97 | 1.12 | 0.96 | 0.00 | 0.00 | 0.00 | 2.29 | 9.34 | 0.00 |
time (sec) |
N/A | 0.521 | 2.235 | 1.776 | 0.000 | 0.000 | 0.000 | 0.418 | 0.839 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 376 | 472 | 372 | 0 | 696 | 0 | 735 | 2549 | 9140 |
N.S. |
1 | 0.93 | 1.16 | 0.92 | 0.00 | 1.71 | 0.00 | 1.81 | 6.28 | 22.51 |
time (sec) |
N/A | 0.445 | 1.107 | 0.740 | 0.000 | 57.632 | 0.000 | 0.275 | 0.790 | 40.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 318 | 466 | 364 | 0 | 3716 | 0 | 599 | 1207 | 16501 |
N.S. |
1 | 0.82 | 1.21 | 0.94 | 0.00 | 9.63 | 0.00 | 1.55 | 3.13 | 42.75 |
time (sec) |
N/A | 0.397 | 0.890 | 0.672 | 0.000 | 5.251 | 0.000 | 0.518 | 0.632 | 0.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 386 | 519 | 423 | 0 | 0 | 0 | 912 | 2870 | 373297 |
N.S. |
1 | 0.91 | 1.22 | 1.00 | 0.00 | 0.00 | 0.00 | 2.15 | 6.75 | 878.35 |
time (sec) |
N/A | 0.445 | 3.567 | 0.724 | 0.000 | 0.000 | 0.000 | 0.804 | 0.843 | 17.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 493 | 458 | 112 | 495 | 0 | 0 | 0 | 1277 | 9649 | 0 |
N.S. |
1 | 0.93 | 0.23 | 1.00 | 0.00 | 0.00 | 0.00 | 2.59 | 19.57 | 0.00 |
time (sec) |
N/A | 0.509 | 10.053 | 1.182 | 0.000 | 0.000 | 0.000 | 1.539 | 2.808 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 432 | 501 | 432 | 0 | 0 | 0 | 857 | 4185 | 0 |
N.S. |
1 | 0.97 | 1.12 | 0.97 | 0.00 | 0.00 | 0.00 | 1.92 | 9.38 | 0.00 |
time (sec) |
N/A | 0.532 | 2.033 | 1.291 | 0.000 | 0.000 | 0.000 | 0.404 | 0.697 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 374 | 472 | 369 | 0 | 451 | 0 | 623 | 2549 | 7103 |
N.S. |
1 | 0.93 | 1.17 | 0.91 | 0.00 | 1.12 | 0.00 | 1.54 | 6.31 | 17.58 |
time (sec) |
N/A | 0.442 | 0.958 | 1.460 | 0.000 | 35.700 | 0.000 | 0.286 | 0.635 | 25.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 320 | 466 | 364 | 0 | 6174 | 0 | 644 | 1207 | 13287 |
N.S. |
1 | 0.83 | 1.21 | 0.94 | 0.00 | 15.99 | 0.00 | 1.67 | 3.13 | 34.42 |
time (sec) |
N/A | 0.404 | 1.879 | 0.647 | 0.000 | 49.491 | 0.000 | 0.401 | 0.553 | 4.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 392 | 520 | 423 | 0 | 0 | 0 | 838 | 4618 | 413671 |
N.S. |
1 | 0.92 | 1.22 | 0.99 | 0.00 | 0.00 | 0.00 | 1.96 | 10.81 | 968.78 |
time (sec) |
N/A | 0.456 | 10.343 | 0.779 | 0.000 | 0.000 | 0.000 | 0.787 | 0.835 | 18.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 464 | 112 | 495 | 0 | 0 | 0 | 1239 | 13315 | 0 |
N.S. |
1 | 0.94 | 0.23 | 1.00 | 0.00 | 0.00 | 0.00 | 2.50 | 26.90 | 0.00 |
time (sec) |
N/A | 0.497 | 10.057 | 1.145 | 0.000 | 0.000 | 0.000 | 3.489 | 2.116 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 528 | 421 | 565 | 415 | 0 | 0 | 0 | 888 | 6541 | 0 |
N.S. |
1 | 0.80 | 1.07 | 0.79 | 0.00 | 0.00 | 0.00 | 1.68 | 12.39 | 0.00 |
time (sec) |
N/A | 0.587 | 3.333 | 0.904 | 0.000 | 0.000 | 0.000 | 0.661 | 1.419 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 49 | 0 | 0 | 0 | 144 | 0 | 129 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 2.06 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.209 | 0.109 | 0.000 | 0.000 | 0.000 | 0.516 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 49 | 0 | 0 | 0 | 379 | 0 | 129 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 5.41 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.226 | 0.002 | 0.000 | 0.000 | 0.000 | 2.874 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 70 | 49 | 0 | 0 | 0 | 379 | 0 | 129 | 0 |
N.S. |
1 | 0.70 | 0.49 | 0.00 | 0.00 | 0.00 | 3.79 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.199 | 0.099 | 0.000 | 0.000 | 0.000 | 2.982 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 86 | 0 | 0 | 0 | 379 | 0 | 129 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 3.79 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.221 | 0.208 | 0.000 | 0.000 | 0.000 | 2.766 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 223 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.367 | 0.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.705 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 266 | 195 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.378 | 0.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 260 | 205 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.98 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.440 | 0.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 268 | 0 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.446 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 208 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.418 | 0.294 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 277 | 215 | 0 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.402 | 0.343 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 261 | 223 | 0 | 0 | 0 | 0 | 0 | 172 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.406 | 0.241 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 558 | 577 | 508 | 0 | 0 | 0 | 0 | 0 | 212 | 0 |
N.S. |
1 | 1.03 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.947 | 1.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 213 | 121 | 0 | 0 | 0 | 1647 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 0.70 | 0.00 | 0.00 | 0.00 | 9.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.342 | 0.205 | 0.000 | 0.000 | 0.000 | 49.657 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 368 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.443 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.658 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 339 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.509 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.723 | 0.000 |