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 | B | F | F(-1) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 584 | 291 | 1617 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.50 | 2.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.374 | 17.776 | 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(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 522 | 271 | 788 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.327 | 10.072 | 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(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 942 | 442 | 528 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.47 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.467 | 6.957 | 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(-2) | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 743 | 365 | 757 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.49 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.121 | 10.009 | 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(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 386 | 227 | 642 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.59 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.531 | 8.665 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 312 | 312 | 260 | 425 | 415 | 333 | 593 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.36 | 1.33 | 1.07 | 1.90 | 0.00 | 0.00 |
time (sec) |
N/A | 0.701 | 0.213 | 0.295 | 0.199 | 0.270 | 1.202 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 222 | 187 | 295 | 287 | 241 | 389 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.33 | 1.30 | 1.09 | 1.76 | 0.00 | 0.00 |
time (sec) |
N/A | 0.581 | 0.179 | 0.290 | 0.189 | 0.260 | 0.632 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 149 | 125 | 188 | 180 | 163 | 240 | 0 | 0 |
N.S. |
1 | 1.01 | 0.85 | 1.28 | 1.22 | 1.11 | 1.63 | 0.00 | 0.00 |
time (sec) |
N/A | 0.392 | 0.118 | 0.366 | 0.186 | 0.266 | 0.370 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 84 | 71 | 97 | 91 | 94 | 109 | 0 | 0 |
N.S. |
1 | 1.04 | 0.88 | 1.20 | 1.12 | 1.16 | 1.35 | 0.00 | 0.00 |
time (sec) |
N/A | 0.282 | 0.046 | 0.015 | 0.184 | 0.260 | 0.222 | 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 | 30 | 30 | 30 | 31 | 30 | 43 | 26 | 41 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.43 | 0.87 | 1.37 | 0.93 |
time (sec) |
N/A | 0.160 | 0.008 | 0.051 | 0.177 | 0.253 | 0.070 | 0.271 | 2.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 485 | 485 | 434 | 224 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.202 | 0.333 | 7.909 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 707 | 707 | 622 | 848 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.485 | 1.317 | 7.960 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 559 | 559 | 443 | 683 | 684 | 586 | 989 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 1.22 | 1.22 | 1.05 | 1.77 | 0.00 | 0.00 |
time (sec) |
N/A | 1.235 | 0.336 | 0.617 | 0.201 | 0.272 | 1.024 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 329 | 329 | 289 | 431 | 429 | 380 | 595 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.31 | 1.30 | 1.16 | 1.81 | 0.00 | 0.00 |
time (sec) |
N/A | 0.832 | 0.238 | 0.439 | 0.206 | 0.261 | 0.587 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 164 | 215 | 218 | 209 | 279 | 0 | 0 |
N.S. |
1 | 1.00 | 1.07 | 1.41 | 1.42 | 1.37 | 1.82 | 0.00 | 0.00 |
time (sec) |
N/A | 0.474 | 0.144 | 0.221 | 0.198 | 0.276 | 0.315 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 74 | 72 | 72 | 96 | 82 | 111 | 0 |
N.S. |
1 | 1.09 | 1.61 | 1.57 | 1.57 | 2.09 | 1.78 | 2.41 | 0.00 |
time (sec) |
N/A | 0.281 | 0.087 | 0.112 | 0.182 | 0.260 | 0.108 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 739 | 739 | 985 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.705 | 0.551 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 670 | 670 | 444 | 654 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.66 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.484 | 0.754 | 1.757 | 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 | 388 | 388 | 253 | 380 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.929 | 0.431 | 0.824 | 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 | 180 | 180 | 126 | 178 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.548 | 0.185 | 0.584 | 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 | 54 | 49 | 45 | 56 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.83 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.394 | 0.057 | 0.082 | 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 | 20 | 20 | 22 | 20 | 22 | 29 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.45 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.205 | 0.689 | 0.477 | 0.245 | 0.265 | 3.577 | 0.290 | 2.619 |
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 | 20 | 20 | 22 | 20 | 22 | 53 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 2.65 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.213 | 2.876 | 0.499 | 0.257 | 0.242 | 65.608 | 0.293 | 2.553 |
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 | 495 | 495 | 356 | 1036 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.075 | 2.179 | 0.971 | 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 | 247 | 247 | 190 | 438 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.672 | 0.913 | 0.651 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 71 | 118 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.84 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.602 | 0.190 | 0.095 | 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 | 20 | 20 | 22 | 20 | 766 | 57 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 38.30 | 2.85 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.213 | 12.000 | 0.480 | 0.906 | 0.255 | 33.777 | 0.291 | 2.663 |
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 | 20 | 20 | 22 | 20 | 1027 | 98 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 51.35 | 4.90 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.217 | 25.139 | 0.750 | 1.177 | 0.252 | 0.000 | 0.298 | 2.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 672 | 672 | 535 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.028 | 4.818 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 322 | 322 | 319 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.098 | 2.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 110 | 101 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.609 | 0.162 | 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 | F(-1) | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 0 | 0 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.229 | 0.000 | 0.632 | 0.000 | 0.000 | 0.822 | 1.022 | 2.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 22 | 0 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.232 | 0.000 | 1.016 | 0.401 | 0.000 | 14.300 | 1.043 | 2.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 770 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.421 | 2.287 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 135 | 140 | 251 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.711 | 0.390 | 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 | F(-1) | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 0 | 0 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.248 | 0.000 | 0.560 | 0.000 | 0.000 | 9.086 | 1.526 | 2.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 20 | 22 | 0 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 0.00 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.243 | 0.000 | 0.837 | 0.497 | 0.000 | 95.972 | 1.533 | 2.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 608 | 608 | 530 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.398 | 0.793 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 218 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.765 | 0.428 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 89 | 101 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.426 | 0.067 | 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 | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.237 | 0.165 | 0.559 | 0.379 | 0.000 | 2.101 | 1.172 | 2.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.228 | 0.216 | 0.895 | 0.396 | 0.000 | 41.199 | 1.130 | 2.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 349 | 349 | 303 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.926 | 0.949 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 116 | 130 | 137 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.631 | 0.181 | 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 | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.233 | 0.172 | 0.581 | 0.376 | 0.000 | 7.802 | 0.395 | 2.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 0 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.238 | 0.227 | 0.796 | 0.403 | 0.000 | 139.898 | 0.409 | 2.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 1.00 |
time (sec) |
N/A | 0.199 | 3.629 | 0.552 | 0.000 | 0.247 | 1.439 | 0.327 | 2.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 1.00 | 1.00 |
time (sec) |
N/A | 0.200 | 2.796 | 0.297 | 0.000 | 0.263 | 0.878 | 0.298 | 2.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 75 | 0 | 0 | 326 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.00 | 4.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 0.084 | 0.000 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 146 | 147 | 139 | 0 | 0 | 738 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.95 | 0.00 | 0.00 | 5.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.358 | 0.244 | 0.000 | 0.000 | 0.318 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 227 | 247 | 191 | 0 | 0 | 1354 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.84 | 0.00 | 0.00 | 5.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.015 | 0.294 | 0.000 | 0.000 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 34 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.215 | 13.099 | 0.178 | 0.000 | 0.254 | 0.998 | 0.374 | 2.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 34 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.55 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.219 | 8.238 | 0.199 | 0.000 | 0.276 | 0.828 | 0.325 | 2.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 0 | 54 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.45 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.227 | 2.760 | 0.683 | 0.000 | 0.267 | 4.451 | 0.330 | 2.641 |
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 | 22 | 22 | 24 | 20 | 99 | 65 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 4.50 | 2.95 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.218 | 5.009 | 0.828 | 0.497 | 0.263 | 59.513 | 0.331 | 2.670 |
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 | 22 | 22 | 24 | 20 | 22 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.217 | 1.017 | 0.595 | 0.253 | 0.248 | 0.368 | 0.297 | 2.612 |
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 | 22 | 22 | 24 | 20 | 22 | 39 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.77 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.220 | 0.809 | 0.645 | 0.284 | 0.244 | 0.619 | 0.300 | 2.729 |
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 | 22 | 22 | 24 | 20 | 22 | 63 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 2.86 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.221 | 1.396 | 0.662 | 0.258 | 0.243 | 1.698 | 0.313 | 2.530 |
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 | 22 | 22 | 24 | 20 | 22 | 87 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 3.95 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.223 | 2.780 | 0.671 | 0.257 | 0.243 | 7.797 | 0.314 | 2.619 |
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 | 22 | 22 | 24 | 20 | 575 | 36 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 26.14 | 1.64 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.216 | 3.566 | 0.654 | 0.660 | 0.274 | 0.649 | 0.353 | 2.653 |
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 | 22 | 22 | 24 | 20 | 591 | 67 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 26.86 | 3.05 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.218 | 6.732 | 0.663 | 0.783 | 0.265 | 1.233 | 0.303 | 2.655 |
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 | 22 | 22 | 24 | 20 | 864 | 108 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 39.27 | 4.91 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.220 | 13.987 | 0.702 | 1.328 | 0.260 | 4.716 | 0.329 | 2.792 |
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 | 22 | 22 | 24 | 20 | 1123 | 149 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 51.05 | 6.77 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.217 | 22.713 | 0.668 | 1.908 | 0.272 | 27.889 | 0.340 | 2.627 |