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 | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 109 | 107 | 127 | 149 | 219 | 0 | 568 | 286 |
N.S. |
1 | 0.90 | 0.88 | 1.05 | 1.23 | 1.81 | 0.00 | 4.69 | 2.36 |
time (sec) |
N/A | 0.316 | 0.338 | 1.268 | 0.201 | 0.319 | 0.000 | 1.557 | 14.901 |
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 | 74 | 74 | 62 | 72 | 74 | 102 | 0 | 313 | 124 |
N.S. |
1 | 1.00 | 0.84 | 0.97 | 1.00 | 1.38 | 0.00 | 4.23 | 1.68 |
time (sec) |
N/A | 0.293 | 0.183 | 0.836 | 0.209 | 0.295 | 0.000 | 0.649 | 14.307 |
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 | 54 | 50 | 54 | 49 | 41 | 46 | 0 | 238 | 257 |
N.S. |
1 | 0.93 | 1.00 | 0.91 | 0.76 | 0.85 | 0.00 | 4.41 | 4.76 |
time (sec) |
N/A | 0.250 | 0.030 | 0.496 | 0.200 | 0.289 | 0.000 | 0.368 | 14.368 |
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 | 138 | 139 | 136 | 114 | 142 | 234 | 0 | 303 | 160 |
N.S. |
1 | 1.01 | 0.99 | 0.83 | 1.03 | 1.70 | 0.00 | 2.20 | 1.16 |
time (sec) |
N/A | 0.367 | 0.431 | 1.048 | 0.204 | 0.345 | 0.000 | 0.321 | 14.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 199 | 187 | 164 | 303 | 693 | 0 | 656 | 313 |
N.S. |
1 | 1.01 | 0.95 | 0.83 | 1.54 | 3.52 | 0.00 | 3.33 | 1.59 |
time (sec) |
N/A | 0.465 | 1.770 | 1.468 | 0.217 | 0.411 | 0.000 | 0.379 | 14.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 278 | 285 | 283 | 230 | 558 | 1378 | 0 | 795 | 471 |
N.S. |
1 | 1.03 | 1.02 | 0.83 | 2.01 | 4.96 | 0.00 | 2.86 | 1.69 |
time (sec) |
N/A | 0.603 | 6.451 | 2.361 | 0.214 | 0.618 | 0.000 | 0.434 | 15.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 283 | 559 | 365 | 0 | 843 | 0 | 411 | 9452 |
N.S. |
1 | 1.42 | 2.80 | 1.82 | 0.00 | 4.22 | 0.00 | 2.06 | 47.26 |
time (sec) |
N/A | 0.781 | 6.180 | 2.076 | 0.000 | 0.560 | 0.000 | 2.113 | 17.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 174 | 327 | 219 | 0 | 584 | 0 | 294 | 7044 |
N.S. |
1 | 1.16 | 2.18 | 1.46 | 0.00 | 3.89 | 0.00 | 1.96 | 46.96 |
time (sec) |
N/A | 0.824 | 1.534 | 1.152 | 0.000 | 0.343 | 0.000 | 0.936 | 16.187 |
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 | 85 | 90 | 80 | 115 | 0 | 383 | 0 | 144 | 551 |
N.S. |
1 | 1.06 | 0.94 | 1.35 | 0.00 | 4.51 | 0.00 | 1.69 | 6.48 |
time (sec) |
N/A | 0.485 | 0.311 | 0.789 | 0.000 | 0.301 | 0.000 | 0.535 | 14.685 |
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 | 227 | 227 | 209 | 184 | 0 | 705 | 0 | 332 | 6093 |
N.S. |
1 | 1.00 | 0.92 | 0.81 | 0.00 | 3.11 | 0.00 | 1.46 | 26.84 |
time (sec) |
N/A | 0.712 | 1.625 | 1.440 | 0.000 | 0.324 | 0.000 | 0.335 | 18.955 |
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 | 360 | 360 | 303 | 260 | 0 | 1481 | 0 | 487 | 8348 |
N.S. |
1 | 1.00 | 0.84 | 0.72 | 0.00 | 4.11 | 0.00 | 1.35 | 23.19 |
time (sec) |
N/A | 0.914 | 2.111 | 1.815 | 0.000 | 0.358 | 0.000 | 0.383 | 19.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
size | 761 | 0 | 1846 | 2967 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 2.43 | 3.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 52.967 | 3.689 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
size | 740 | 0 | 548 | 1651 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.74 | 2.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 21.452 | 3.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
size | 415 | 352 | 646 | 820 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 1.56 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.353 | 5.978 | 2.538 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD |
size | 422 | 412 | 1475 | 1919 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 3.50 | 4.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.237 | 38.297 | 3.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
size | 863 | 0 | 1571 | 4016 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.82 | 4.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 23.898 | 3.274 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD |
size | 836 | 0 | 2169 | 7581 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 2.59 | 9.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 33.622 | 4.790 | 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 | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 132 | 152 | 883 | 191 | 425 | 0 | 966 | 0 |
N.S. |
1 | 0.78 | 0.90 | 5.22 | 1.13 | 2.51 | 0.00 | 5.72 | 0.00 |
time (sec) |
N/A | 0.363 | 1.908 | 16.530 | 0.284 | 0.438 | 0.000 | 1.758 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 81 | 87 | 465 | 108 | 311 | 0 | 539 | 0 |
N.S. |
1 | 0.81 | 0.87 | 4.65 | 1.08 | 3.11 | 0.00 | 5.39 | 0.00 |
time (sec) |
N/A | 0.299 | 0.700 | 10.670 | 0.303 | 0.441 | 0.000 | 0.705 | 0.000 |
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 | 51 | 49 | 49 | 42 | 67 | 192 | 0 | 185 | 47 |
N.S. |
1 | 0.96 | 0.96 | 0.82 | 1.31 | 3.76 | 0.00 | 3.63 | 0.92 |
time (sec) |
N/A | 0.239 | 0.136 | 0.659 | 0.282 | 0.427 | 0.000 | 0.405 | 13.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 118 | 100 | 543 | 0 | 2132 | 0 | 293 | 0 |
N.S. |
1 | 1.11 | 0.94 | 5.12 | 0.00 | 20.11 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.365 | 0.234 | 2.245 | 0.000 | 0.604 | 0.000 | 0.630 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 215 | 268 | 212 | 2072 | 0 | 3523 | 0 | 514 | 0 |
N.S. |
1 | 1.25 | 0.99 | 9.64 | 0.00 | 16.39 | 0.00 | 2.39 | 0.00 |
time (sec) |
N/A | 0.552 | 2.452 | 2.199 | 0.000 | 1.810 | 0.000 | 0.837 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 344 | 345 | 376 | 1380 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.09 | 4.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.252 | 11.573 | 11.952 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 151 | 182 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.21 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 0.133 | 6.573 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 246 | 154 | 546 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.63 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.485 | 3.607 | 5.809 | 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 | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 123 | 131 | 646 | 175 | 381 | 0 | 699 | 0 |
N.S. |
1 | 0.83 | 0.89 | 4.36 | 1.18 | 2.57 | 0.00 | 4.72 | 0.00 |
time (sec) |
N/A | 0.337 | 0.871 | 16.651 | 0.278 | 0.426 | 0.000 | 1.807 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 71 | 66 | 312 | 92 | 273 | 0 | 265 | 0 |
N.S. |
1 | 0.90 | 0.84 | 3.95 | 1.16 | 3.46 | 0.00 | 3.35 | 0.00 |
time (sec) |
N/A | 0.301 | 0.412 | 11.293 | 0.273 | 0.406 | 0.000 | 0.819 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 26 | 49 | 145 | 0 | 102 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 1.58 | 4.68 | 0.00 | 3.29 | 0.87 |
time (sec) |
N/A | 0.235 | 0.091 | 0.742 | 0.269 | 0.392 | 0.000 | 0.493 | 14.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 106 | 118 | 100 | 658 | 0 | 2420 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.94 | 6.21 | 0.00 | 22.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.361 | 0.292 | 2.292 | 0.000 | 1.423 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 260 | 272 | 280 | 3107 | 0 | 4336 | 0 | 533 | 0 |
N.S. |
1 | 1.05 | 1.08 | 11.95 | 0.00 | 16.68 | 0.00 | 2.05 | 0.00 |
time (sec) |
N/A | 0.473 | 2.382 | 2.011 | 0.000 | 25.895 | 0.000 | 0.920 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 404 | 610 | 446 | 2243 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.51 | 1.10 | 5.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.227 | 15.799 | 15.874 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 310 | 310 | 382 | 1069 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 3.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.013 | 12.550 | 10.915 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 138 | 147 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.124 | 5.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 361 | 361 | 366 | 1374 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 3.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.759 | 13.148 | 7.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | A | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 119 | 117 | 1234 | 194 | 467 | 0 | 0 | 0 |
N.S. |
1 | 0.80 | 0.79 | 8.34 | 1.31 | 3.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 0.560 | 15.602 | 0.286 | 0.503 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 79 | 66 | 731 | 110 | 317 | 0 | 258 | 0 |
N.S. |
1 | 0.90 | 0.75 | 8.31 | 1.25 | 3.60 | 0.00 | 2.93 | 0.00 |
time (sec) |
N/A | 0.329 | 0.258 | 9.564 | 0.277 | 0.443 | 0.000 | 1.105 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 52 | 43 | 45 | 70 | 260 | 0 | 214 | 50 |
N.S. |
1 | 0.96 | 0.80 | 0.83 | 1.30 | 4.81 | 0.00 | 3.96 | 0.93 |
time (sec) |
N/A | 0.249 | 0.104 | 0.789 | 0.263 | 0.421 | 0.000 | 0.778 | 15.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 142 | 143 | 212 | 2692 | 0 | 3924 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.49 | 18.96 | 0.00 | 27.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.416 | 0.672 | 2.217 | 0.000 | 24.540 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 236 | 310 | 315 | 6367 | 0 | 8098 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 1.33 | 26.98 | 0.00 | 34.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.593 | 1.092 | 2.335 | 0.000 | 48.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 530 | 907 | 531 | 1965 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.71 | 1.00 | 3.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.898 | 17.412 | 14.836 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 344 | 382 | 329 | 828 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.96 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.379 | 11.177 | 9.790 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 347 | 376 | 972 | 1799 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.80 | 5.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.259 | 6.080 | 7.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 449 | 664 | 469 | 2062 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.48 | 1.04 | 4.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.434 | 10.812 | 8.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 238 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.524 | 3.161 | 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 | 160 | 160 | 178 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.400 | 1.013 | 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 | 129 | 129 | 106 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.381 | 0.584 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 266 | 0 | 786 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 2.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 4.223 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 25 | 24 | 25 | 27 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.96 | 1.00 | 1.08 |
time (sec) |
N/A | 0.242 | 29.433 | 1.182 | 1.427 | 0.387 | 69.961 | 1.874 | 18.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 25 | 24 | 25 | 27 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.96 | 1.00 | 1.08 |
time (sec) |
N/A | 0.236 | 0.888 | 1.102 | 1.331 | 0.378 | 1.412 | 1.040 | 14.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 25 | 24 | 25 | 27 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.00 | 0.96 | 1.00 | 1.08 |
time (sec) |
N/A | 0.239 | 15.729 | 1.148 | 1.334 | 0.385 | 0.719 | 0.836 | 20.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 53 | 24 | 25 | 27 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.12 | 0.96 | 1.00 | 1.08 |
time (sec) |
N/A | 0.246 | 19.967 | 1.130 | 1.255 | 0.538 | 4.317 | 1.425 | 28.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 22 | 25 | 27 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.96 | 1.09 | 1.17 |
time (sec) |
N/A | 0.221 | 7.759 | 1.869 | 1.886 | 0.464 | 33.982 | 0.829 | 15.760 |
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 | 177 | 160 | 137 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.347 | 1.374 | 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 | 102 | 99 | 80 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.289 | 0.562 | 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 | 48 | 48 | 48 | 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 | 0.220 | 0.171 | 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 | 162 | 171 | 132 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.370 | 0.386 | 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 | 279 | 284 | 186 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.444 | 0.709 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 20 | 23 | 25 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.19 |
time (sec) |
N/A | 0.212 | 13.790 | 1.375 | 19.761 | 0.300 | 29.679 | 1.547 | 17.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 20 | 23 | 25 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.19 |
time (sec) |
N/A | 0.960 | 12.262 | 0.983 | 5.804 | 0.274 | 3.984 | 0.710 | 15.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 20 | 23 | 25 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.19 |
time (sec) |
N/A | 0.211 | 8.653 | 1.199 | 5.851 | 0.317 | 19.226 | 0.568 | 18.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 0 | 23 | 25 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.00 | 1.10 | 1.19 |
time (sec) |
N/A | 0.223 | 13.642 | 1.167 | 18.680 | 0.606 | 0.000 | 0.679 | 28.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 0 | 23 | 25 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.00 | 1.00 | 1.09 |
time (sec) |
N/A | 0.226 | 7.605 | 1.146 | 1.918 | 0.355 | 0.000 | 0.429 | 19.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 25 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.09 |
time (sec) |
N/A | 0.221 | 10.142 | 1.515 | 1.747 | 0.350 | 6.022 | 0.583 | 14.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 25 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.09 |
time (sec) |
N/A | 0.218 | 23.219 | 1.334 | 1.934 | 0.354 | 2.489 | 0.752 | 18.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 25 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.09 |
time (sec) |
N/A | 0.224 | 10.638 | 1.118 | 1.969 | 0.439 | 52.603 | 0.565 | 20.456 |