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 | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 176 | 177 | 200 | 277 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.87 | 1.88 | 2.13 | 2.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 0.321 | 1.174 | 0.332 | 0.270 | 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 | 228 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 11.40 | 1.10 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.527 | 9.746 | 0.776 | 0.489 | 0.252 | 0.464 | 0.516 | 23.173 |
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 | 340 | 33 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 17.00 | 1.65 | 1.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.667 | 4.660 | 0.828 | 0.887 | 0.254 | 0.711 | 2.962 | 22.990 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.201 | 1.293 | 0.285 | 0.574 | 0.256 | 1.544 | 0.308 | 22.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 210 | 833 | 921 | 3242 | 856 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 5.37 | 5.94 | 20.92 | 5.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.876 | 6.651 | 1.648 | 0.675 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 164 | 520 | 581 | 1953 | 599 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 4.09 | 4.57 | 15.38 | 4.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.692 | 6.548 | 1.631 | 0.461 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 120 | 268 | 305 | 645 | 384 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 2.76 | 3.14 | 6.65 | 3.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.491 | 6.528 | 1.580 | 0.451 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 45 | 82 | 64 | 292 | 97 | 104 | 1151 | 67 |
N.S. |
1 | 1.10 | 2.00 | 1.56 | 7.12 | 2.37 | 2.54 | 28.07 | 1.63 |
time (sec) |
N/A | 0.255 | 0.587 | 1.260 | 0.361 | 0.250 | 0.218 | 0.552 | 22.928 |
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 | 16 | 16 | 18 | 16 | 581 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 36.31 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.203 | 6.458 | 0.655 | 0.573 | 0.243 | 0.412 | 0.361 | 22.934 |
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 | 16 | 16 | 18 | 16 | 813 | 29 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 50.81 | 1.81 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.207 | 2.788 | 0.651 | 1.299 | 0.236 | 0.643 | 2.334 | 22.766 |
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 | 22 | 24 | 24 | 22 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.293 | 41.082 | 0.279 | 1.130 | 0.242 | 7.042 | 0.324 | 23.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 416 | 742 | 966 | 1673 | 7004 | 2770 | 0 | 0 | 0 |
N.S. |
1 | 1.78 | 2.32 | 4.02 | 16.84 | 6.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.954 | 8.092 | 1.494 | 3.264 | 0.354 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 308 | 532 | 528 | 1056 | 3887 | 1742 | 0 | 0 | 0 |
N.S. |
1 | 1.73 | 1.71 | 3.43 | 12.62 | 5.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.947 | 5.417 | 1.324 | 1.369 | 0.319 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 324 | 471 | 546 | 1938 | 970 | 0 | 0 | 0 |
N.S. |
1 | 1.81 | 2.63 | 3.05 | 10.83 | 5.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.347 | 7.512 | 1.200 | 0.532 | 0.306 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 176 | 260 | 246 | 762 | 454 | 0 | 0 | 0 |
N.S. |
1 | 1.63 | 2.41 | 2.28 | 7.06 | 4.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.685 | 1.944 | 0.879 | 0.353 | 0.266 | 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 | 22 | 22 | 24 | 22 | 1793 | 24 | 20 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 81.50 | 1.09 | 0.91 | 1.09 | 1.18 |
time (sec) |
N/A | 0.296 | 40.315 | 0.519 | 2.819 | 0.251 | 1.034 | 4.946 | 24.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 2289 | 35 | 22 | 0 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 104.05 | 1.59 | 1.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.291 | 45.766 | 0.500 | 9.880 | 0.259 | 3.860 | 0.000 | 24.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 406 | 406 | 1445 | 476 | 547 | 341 | 0 | 2468 | 0 |
N.S. |
1 | 1.00 | 3.56 | 1.17 | 1.35 | 0.84 | 0.00 | 6.08 | 0.00 |
time (sec) |
N/A | 1.177 | 12.760 | 1.435 | 0.375 | 0.272 | 0.000 | 0.966 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 751 | 384 | 499 | 280 | 0 | 1540 | 0 |
N.S. |
1 | 1.00 | 2.13 | 1.09 | 1.41 | 0.79 | 0.00 | 4.36 | 0.00 |
time (sec) |
N/A | 0.885 | 1.747 | 0.720 | 0.376 | 0.269 | 0.000 | 0.812 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 251 | 296 | 424 | 235 | 0 | 844 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.97 | 1.39 | 0.77 | 0.00 | 2.78 | 0.00 |
time (sec) |
N/A | 0.741 | 0.242 | 0.700 | 0.348 | 0.272 | 0.000 | 0.586 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 251 | 296 | 424 | 235 | 0 | 844 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.97 | 1.39 | 0.77 | 0.00 | 2.78 | 0.00 |
time (sec) |
N/A | 0.716 | 0.049 | 0.494 | 0.386 | 0.262 | 0.000 | 0.610 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 751 | 384 | 499 | 280 | 0 | 1540 | 0 |
N.S. |
1 | 1.00 | 2.13 | 1.09 | 1.41 | 0.79 | 0.00 | 4.36 | 0.00 |
time (sec) |
N/A | 0.841 | 1.346 | 0.484 | 0.368 | 0.265 | 0.000 | 0.825 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 406 | 406 | 1445 | 476 | 547 | 341 | 0 | 2468 | 0 |
N.S. |
1 | 1.00 | 3.56 | 1.17 | 1.35 | 0.84 | 0.00 | 6.08 | 0.00 |
time (sec) |
N/A | 0.971 | 6.015 | 1.187 | 0.395 | 0.295 | 0.000 | 0.975 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 140 | 251 | 285 | 347 | 0 | 1379 | 0 |
N.S. |
1 | 1.00 | 0.61 | 1.10 | 1.25 | 1.52 | 0.00 | 6.05 | 0.00 |
time (sec) |
N/A | 0.732 | 1.384 | 3.809 | 0.339 | 0.265 | 0.000 | 1.049 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 140 | 206 | 264 | 249 | 0 | 857 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.03 | 1.32 | 1.24 | 0.00 | 4.28 | 0.00 |
time (sec) |
N/A | 0.615 | 0.993 | 0.691 | 0.332 | 0.274 | 0.000 | 0.842 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 120 | 159 | 219 | 175 | 0 | 460 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.91 | 1.26 | 1.01 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.506 | 0.868 | 0.697 | 0.335 | 0.260 | 0.000 | 0.553 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 120 | 159 | 219 | 175 | 0 | 460 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.91 | 1.26 | 1.01 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.488 | 0.019 | 0.474 | 0.320 | 0.261 | 0.000 | 0.569 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 140 | 206 | 264 | 249 | 0 | 857 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.03 | 1.32 | 1.24 | 0.00 | 4.28 | 0.00 |
time (sec) |
N/A | 0.548 | 0.047 | 0.570 | 0.336 | 0.274 | 0.000 | 0.791 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 140 | 251 | 285 | 347 | 0 | 1379 | 0 |
N.S. |
1 | 1.00 | 0.61 | 1.10 | 1.25 | 1.52 | 0.00 | 6.05 | 0.00 |
time (sec) |
N/A | 0.615 | 0.141 | 3.529 | 0.340 | 0.281 | 0.000 | 1.068 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2177 | 719 | 826 | 521 | 0 | 3706 | 0 |
N.S. |
1 | 1.00 | 3.54 | 1.17 | 1.34 | 0.85 | 0.00 | 6.03 | 0.00 |
time (sec) |
N/A | 1.587 | 17.080 | 12.006 | 0.400 | 0.310 | 0.000 | 1.741 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1126 | 580 | 760 | 427 | 0 | 2314 | 0 |
N.S. |
1 | 1.00 | 2.11 | 1.09 | 1.42 | 0.80 | 0.00 | 4.33 | 0.00 |
time (sec) |
N/A | 1.252 | 3.535 | 0.806 | 0.371 | 0.296 | 0.000 | 1.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 372 | 447 | 680 | 356 | 0 | 1270 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.78 | 0.00 | 2.77 | 0.00 |
time (sec) |
N/A | 1.019 | 0.353 | 0.846 | 0.379 | 0.319 | 0.000 | 0.821 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 372 | 447 | 680 | 356 | 0 | 1270 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.78 | 0.00 | 2.77 | 0.00 |
time (sec) |
N/A | 0.980 | 0.275 | 0.484 | 0.386 | 0.274 | 0.000 | 0.837 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1126 | 580 | 760 | 427 | 0 | 2314 | 0 |
N.S. |
1 | 1.00 | 2.11 | 1.09 | 1.42 | 0.80 | 0.00 | 4.33 | 0.00 |
time (sec) |
N/A | 1.169 | 2.460 | 0.534 | 0.378 | 0.300 | 0.000 | 1.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2177 | 719 | 826 | 521 | 0 | 3706 | 0 |
N.S. |
1 | 1.00 | 3.54 | 1.17 | 1.34 | 0.85 | 0.00 | 6.03 | 0.00 |
time (sec) |
N/A | 1.373 | 6.019 | 11.522 | 0.385 | 0.292 | 0.000 | 1.708 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 273 | 273 | 245 | 0 | 0 | 188 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.506 | 0.278 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 260 | 325 | 158 | 187 | 967 | 378 | 935 | 361 | 576 |
N.S. |
1 | 1.25 | 0.61 | 0.72 | 3.72 | 1.45 | 3.60 | 1.39 | 2.22 |
time (sec) |
N/A | 0.964 | 1.806 | 2.129 | 0.272 | 0.267 | 0.875 | 0.361 | 1.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 243 | 135 | 148 | 549 | 238 | 602 | 241 | 366 |
N.S. |
1 | 1.24 | 0.69 | 0.76 | 2.80 | 1.21 | 3.07 | 1.23 | 1.87 |
time (sec) |
N/A | 0.818 | 0.895 | 1.588 | 0.249 | 0.264 | 0.627 | 0.326 | 25.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 133 | 89 | 109 | 263 | 130 | 320 | 145 | 202 |
N.S. |
1 | 0.99 | 0.66 | 0.81 | 1.96 | 0.97 | 2.39 | 1.08 | 1.51 |
time (sec) |
N/A | 0.405 | 0.467 | 1.359 | 0.239 | 0.250 | 0.432 | 0.333 | 23.746 |
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 | 72 | 80 | 75 | 68 | 92 | 58 | 138 | 75 | 94 |
N.S. |
1 | 1.11 | 1.04 | 0.94 | 1.28 | 0.81 | 1.92 | 1.04 | 1.31 |
time (sec) |
N/A | 0.311 | 0.144 | 1.003 | 0.226 | 0.239 | 0.318 | 0.323 | 0.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 110 | 178 | 281 | 124 | 0 | 6046 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.38 | 2.18 | 0.96 | 0.00 | 46.87 | 0.00 |
time (sec) |
N/A | 0.425 | 0.246 | 0.969 | 0.307 | 0.242 | 0.000 | 0.537 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 151 | 256 | 308 | 183 | 0 | 63510 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.43 | 1.72 | 1.02 | 0.00 | 354.80 | 0.00 |
time (sec) |
N/A | 0.483 | 1.715 | 1.325 | 0.361 | 0.256 | 0.000 | 2.633 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 197 | 329 | 343 | 309 | 0 | 111694 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.42 | 1.48 | 1.34 | 0.00 | 483.52 | 0.00 |
time (sec) |
N/A | 0.570 | 4.011 | 1.694 | 0.461 | 0.270 | 0.000 | 3.423 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 316 | 404 | 393 | 455 | 0 | 157526 | 0 |
N.S. |
1 | 1.00 | 1.10 | 1.41 | 1.37 | 1.59 | 0.00 | 548.87 | 0.00 |
time (sec) |
N/A | 0.622 | 2.303 | 2.200 | 0.645 | 0.283 | 0.000 | 4.641 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 419 | 419 | 409 | 0 | 0 | 280 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.685 | 0.956 | 0.000 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 330 | 330 | 563 | 253 | 1339 | 527 | 1098 | 531 | 816 |
N.S. |
1 | 1.00 | 1.71 | 0.77 | 4.06 | 1.60 | 3.33 | 1.61 | 2.47 |
time (sec) |
N/A | 0.648 | 3.710 | 3.183 | 0.321 | 0.269 | 1.155 | 0.390 | 28.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 259 | 259 | 195 | 205 | 766 | 342 | 690 | 351 | 516 |
N.S. |
1 | 1.00 | 0.75 | 0.79 | 2.96 | 1.32 | 2.66 | 1.36 | 1.99 |
time (sec) |
N/A | 0.515 | 2.246 | 2.440 | 0.274 | 0.259 | 0.827 | 0.344 | 2.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 252 | 144 | 375 | 193 | 382 | 209 | 295 |
N.S. |
1 | 1.00 | 1.37 | 0.78 | 2.04 | 1.05 | 2.08 | 1.14 | 1.60 |
time (sec) |
N/A | 0.402 | 0.915 | 2.375 | 0.246 | 0.247 | 0.573 | 0.347 | 0.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 110 | 91 | 139 | 91 | 163 | 106 | 119 |
N.S. |
1 | 1.00 | 1.01 | 0.83 | 1.28 | 0.83 | 1.50 | 0.97 | 1.09 |
time (sec) |
N/A | 0.289 | 0.355 | 1.817 | 0.232 | 0.248 | 0.401 | 0.327 | 0.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 154 | 257 | 413 | 182 | 0 | 44961 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.39 | 2.23 | 0.98 | 0.00 | 243.03 | 0.00 |
time (sec) |
N/A | 0.521 | 0.412 | 1.282 | 0.361 | 0.245 | 0.000 | 1.724 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 212 | 372 | 446 | 264 | 0 | 1022022 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.45 | 1.74 | 1.03 | 0.00 | 3976.74 | 0.00 |
time (sec) |
N/A | 0.623 | 2.005 | 1.612 | 0.435 | 0.256 | 0.000 | 49.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 338 | 338 | 283 | 478 | 481 | 438 | 0 | 1708998 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.41 | 1.42 | 1.30 | 0.00 | 5056.21 | 0.00 |
time (sec) |
N/A | 0.733 | 2.962 | 2.207 | 0.583 | 0.296 | 0.000 | 98.985 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 413 | 413 | 451 | 588 | 531 | 640 | 0 | 2478918 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.42 | 1.29 | 1.55 | 0.00 | 6002.22 | 0.00 |
time (sec) |
N/A | 0.861 | 2.488 | 2.901 | 0.830 | 0.309 | 0.000 | 198.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 255 | 0 | 0 | 190 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.536 | 2.274 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 233 | 153 | 185 | 1033 | 546 | 1334 | 359 | 576 |
N.S. |
1 | 1.00 | 0.66 | 0.79 | 4.43 | 2.34 | 5.73 | 1.54 | 2.47 |
time (sec) |
N/A | 0.509 | 1.374 | 3.443 | 0.298 | 0.270 | 1.522 | 0.422 | 26.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 132 | 148 | 602 | 349 | 857 | 241 | 366 |
N.S. |
1 | 1.00 | 0.73 | 0.82 | 3.33 | 1.93 | 4.73 | 1.33 | 2.02 |
time (sec) |
N/A | 0.432 | 2.449 | 2.541 | 0.262 | 0.253 | 1.126 | 0.381 | 1.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 91 | 111 | 303 | 194 | 461 | 145 | 202 |
N.S. |
1 | 1.00 | 0.71 | 0.86 | 2.35 | 1.50 | 3.57 | 1.12 | 1.57 |
time (sec) |
N/A | 0.334 | 0.545 | 2.213 | 0.260 | 0.265 | 0.812 | 0.349 | 1.023 |
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 | 77 | 77 | 63 | 69 | 119 | 87 | 201 | 75 | 84 |
N.S. |
1 | 1.00 | 0.82 | 0.90 | 1.55 | 1.13 | 2.61 | 0.97 | 1.09 |
time (sec) |
N/A | 0.250 | 0.509 | 1.674 | 0.235 | 0.252 | 0.551 | 0.321 | 0.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 110 | 178 | 281 | 126 | 0 | 6046 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.38 | 2.18 | 0.98 | 0.00 | 46.87 | 0.00 |
time (sec) |
N/A | 0.435 | 0.296 | 1.548 | 0.331 | 0.249 | 0.000 | 0.575 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 189 | 256 | 308 | 198 | 0 | 63798 | 0 |
N.S. |
1 | 1.00 | 1.06 | 1.43 | 1.72 | 1.11 | 0.00 | 356.41 | 0.00 |
time (sec) |
N/A | 0.503 | 1.001 | 1.960 | 0.369 | 0.255 | 0.000 | 3.428 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 235 | 239 | 329 | 343 | 348 | 0 | 111694 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.40 | 1.46 | 1.48 | 0.00 | 475.29 | 0.00 |
time (sec) |
N/A | 0.576 | 1.109 | 2.724 | 0.459 | 0.266 | 0.000 | 3.469 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 554 | 404 | 393 | 524 | 0 | 157526 | 0 |
N.S. |
1 | 1.00 | 1.93 | 1.41 | 1.37 | 1.83 | 0.00 | 548.87 | 0.00 |
time (sec) |
N/A | 0.653 | 5.301 | 3.589 | 0.670 | 0.290 | 0.000 | 4.836 | 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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.566 | 12.321 | 0.336 | 0.767 | 0.247 | 24.325 | 0.315 | 25.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 372 | 2918 | 1335 | 1654 | 1453 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 9.50 | 4.35 | 5.39 | 4.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.755 | 6.448 | 3.237 | 0.546 | 0.353 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 298 | 1956 | 908 | 979 | 984 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 7.95 | 3.69 | 3.98 | 4.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.346 | 6.407 | 2.372 | 0.422 | 0.327 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 207 | 564 | 544 | 529 | 594 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 3.12 | 3.01 | 2.92 | 3.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.990 | 3.184 | 1.872 | 0.358 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 134 | 139 | 249 | 223 | 292 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 1.22 | 2.18 | 1.96 | 2.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.623 | 0.795 | 1.680 | 0.297 | 0.274 | 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 | 22 | 22 | 24 | 22 | 231 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 10.50 | 1.09 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.639 | 0.893 | 0.871 | 0.538 | 0.240 | 0.962 | 0.330 | 26.137 |
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 | 22 | 343 | 35 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 15.59 | 1.59 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.755 | 2.878 | 1.000 | 0.884 | 0.250 | 1.261 | 2.356 | 26.525 |
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 | 22 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.642 | 13.473 | 0.286 | 1.180 | 0.247 | 22.089 | 0.337 | 25.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 329 | 798 | 1056 | 17589 | 1233 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 2.67 | 3.53 | 58.83 | 4.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.707 | 1.935 | 4.395 | 4.509 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 216 | 232 | 539 | 649 | 10994 | 797 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 2.50 | 3.00 | 50.90 | 3.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.173 | 1.487 | 2.565 | 1.309 | 0.317 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 144 | 310 | 332 | 3199 | 448 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 2.23 | 2.39 | 23.01 | 3.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.772 | 4.431 | 1.780 | 1.141 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 104 | 124 | 2110 | 95 | 0 | 1759 | 162 |
N.S. |
1 | 1.00 | 1.79 | 2.14 | 36.38 | 1.64 | 0.00 | 30.33 | 2.79 |
time (sec) |
N/A | 0.440 | 1.089 | 1.309 | 0.301 | 0.261 | 0.000 | 0.862 | 26.264 |
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 | 22 | 1438 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 65.36 | 1.09 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.680 | 3.793 | 0.409 | 0.658 | 0.264 | 0.629 | 1.332 | 26.129 |
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 | 22 | 1678 | 35 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 76.27 | 1.59 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.841 | 4.046 | 0.436 | 1.431 | 0.249 | 0.960 | 6.955 | 25.787 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.212 | 14.811 | 0.299 | 0.764 | 0.235 | 2.200 | 0.343 | 25.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 302 | 407 | 1632 | 1877 | 7158 | 1751 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 5.40 | 6.22 | 23.70 | 5.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.195 | 7.087 | 1.376 | 3.676 | 0.299 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 256 | 321 | 1032 | 1203 | 3958 | 1139 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 4.03 | 4.70 | 15.46 | 4.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.576 | 6.996 | 1.334 | 1.224 | 0.274 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 197 | 548 | 644 | 1966 | 657 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 3.26 | 3.83 | 11.70 | 3.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.953 | 6.834 | 1.184 | 0.542 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 124 | 240 | 281 | 830 | 339 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 2.20 | 2.58 | 7.61 | 3.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.518 | 6.253 | 0.836 | 0.384 | 0.262 | 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 | 16 | 16 | 18 | 16 | 1636 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 102.25 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.208 | 9.055 | 0.464 | 2.644 | 0.249 | 0.441 | 0.390 | 24.340 |
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 | 16 | 16 | 18 | 16 | 2124 | 29 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 132.75 | 1.81 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.213 | 11.518 | 0.469 | 10.314 | 0.245 | 0.695 | 2.389 | 24.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 1332 | 470 | 551 | 376 | 0 | 2435 | 0 |
N.S. |
1 | 1.00 | 3.27 | 1.15 | 1.35 | 0.92 | 0.00 | 5.98 | 0.00 |
time (sec) |
N/A | 1.044 | 8.890 | 3.804 | 0.357 | 0.284 | 0.000 | 1.093 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 693 | 376 | 503 | 294 | 0 | 1515 | 0 |
N.S. |
1 | 1.00 | 1.97 | 1.07 | 1.43 | 0.84 | 0.00 | 4.32 | 0.00 |
time (sec) |
N/A | 0.831 | 1.515 | 0.722 | 0.335 | 0.276 | 0.000 | 0.824 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 252 | 286 | 429 | 233 | 0 | 826 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 1.43 | 0.78 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.654 | 0.385 | 0.730 | 0.344 | 0.253 | 0.000 | 0.575 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 252 | 286 | 429 | 233 | 0 | 826 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 1.43 | 0.78 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.640 | 0.086 | 0.505 | 0.347 | 0.262 | 0.000 | 0.601 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 693 | 376 | 503 | 294 | 0 | 1515 | 0 |
N.S. |
1 | 1.00 | 1.97 | 1.07 | 1.43 | 0.84 | 0.00 | 4.32 | 0.00 |
time (sec) |
N/A | 0.773 | 1.044 | 0.553 | 0.366 | 0.272 | 0.000 | 0.828 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 1332 | 470 | 551 | 376 | 0 | 2435 | 0 |
N.S. |
1 | 1.00 | 3.27 | 1.15 | 1.35 | 0.92 | 0.00 | 5.98 | 0.00 |
time (sec) |
N/A | 0.878 | 6.021 | 3.579 | 0.378 | 0.275 | 0.000 | 1.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2130 | 716 | 826 | 548 | 0 | 3716 | 0 |
N.S. |
1 | 1.00 | 3.46 | 1.16 | 1.34 | 0.89 | 0.00 | 6.04 | 0.00 |
time (sec) |
N/A | 1.665 | 16.707 | 11.953 | 0.405 | 0.318 | 0.000 | 1.711 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1088 | 583 | 760 | 446 | 0 | 2319 | 0 |
N.S. |
1 | 1.00 | 2.04 | 1.09 | 1.42 | 0.84 | 0.00 | 4.34 | 0.00 |
time (sec) |
N/A | 1.370 | 2.760 | 0.885 | 0.378 | 0.285 | 0.000 | 1.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 374 | 444 | 680 | 365 | 0 | 1270 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.80 | 0.00 | 2.77 | 0.00 |
time (sec) |
N/A | 1.034 | 0.417 | 0.847 | 0.351 | 0.281 | 0.000 | 0.796 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 374 | 444 | 680 | 365 | 0 | 1270 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.80 | 0.00 | 2.77 | 0.00 |
time (sec) |
N/A | 1.006 | 0.208 | 0.505 | 0.351 | 0.273 | 0.000 | 0.804 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1088 | 583 | 760 | 446 | 0 | 2319 | 0 |
N.S. |
1 | 1.00 | 2.04 | 1.09 | 1.42 | 0.84 | 0.00 | 4.34 | 0.00 |
time (sec) |
N/A | 1.187 | 1.888 | 0.519 | 0.375 | 0.283 | 0.000 | 1.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2130 | 716 | 826 | 548 | 0 | 3716 | 0 |
N.S. |
1 | 1.00 | 3.46 | 1.16 | 1.34 | 0.89 | 0.00 | 6.04 | 0.00 |
time (sec) |
N/A | 1.349 | 6.016 | 11.655 | 0.386 | 0.316 | 0.000 | 1.738 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 257 | 477 | 561 | 445 | 0 | 2434 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.17 | 1.38 | 1.09 | 0.00 | 5.98 | 0.00 |
time (sec) |
N/A | 1.060 | 3.418 | 35.515 | 0.361 | 0.298 | 0.000 | 2.644 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 259 | 383 | 511 | 326 | 0 | 1514 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.09 | 1.46 | 0.93 | 0.00 | 4.31 | 0.00 |
time (sec) |
N/A | 0.871 | 2.787 | 0.811 | 0.343 | 0.276 | 0.000 | 1.787 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 256 | 293 | 439 | 242 | 0 | 826 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.98 | 1.47 | 0.81 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.663 | 1.742 | 0.832 | 0.332 | 0.265 | 0.000 | 1.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 256 | 293 | 439 | 242 | 0 | 826 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.98 | 1.47 | 0.81 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.641 | 0.179 | 0.534 | 0.347 | 0.269 | 0.000 | 1.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 259 | 383 | 511 | 326 | 0 | 1514 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.09 | 1.46 | 0.93 | 0.00 | 4.31 | 0.00 |
time (sec) |
N/A | 0.768 | 0.395 | 0.578 | 0.349 | 0.272 | 0.000 | 1.790 | 0.000 |