Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 95 | 127 | 296 | 125 | 179 | 0 | 0 | 94 | 0 |
N.S. |
1 | 0.96 | 1.28 | 2.99 | 1.26 | 1.81 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.335 | 0.524 | 0.961 | 0.043 | 0.097 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 115 | 120 | 47 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 2.45 | 2.55 | 1.00 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.240 | 0.057 | 0.493 | 0.038 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 125 | 266 | 546 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.56 | 1.19 | 2.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.649 | 0.699 | 1.149 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 150 | 168 | 478 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.90 | 1.01 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.768 | 0.617 | 1.150 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 227 | 455 | 780 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.63 | 1.26 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 1.588 | 3.673 | 1.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 263 | 278 | 1505 | 0 | 0 | 0 | 0 | 118 | 0 |
N.S. |
1 | 0.90 | 0.95 | 5.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.456 | 0.573 | 1.270 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 412 | 477 | 427 | 663 | 0 | 0 | 0 | 0 | 280 | 0 |
N.S. |
1 | 1.16 | 1.04 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 2.965 | 0.731 | 1.499 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 383 | 288 | 579 | 0 | 0 | 0 | 0 | 324 | 0 |
N.S. |
1 | 0.98 | 0.74 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 3.346 | 1.562 | 1.456 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 265 | 318 | 412 | 0 | 0 | 0 | 0 | 256 | 0 |
N.S. |
1 | 0.90 | 1.09 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.393 | 0.626 | 1.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 187 | 215 | 478 | 0 | 0 | 0 | 0 | 298 | 0 |
N.S. |
1 | 0.80 | 0.92 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.999 | 1.234 | 1.148 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 121 | 217 | 318 | 0 | 0 | 0 | 0 | 228 | 0 |
N.S. |
1 | 0.64 | 1.15 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.605 | 0.798 | 1.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 133 | 152 | 343 | 0 | 0 | 0 | 0 | 234 | 0 |
N.S. |
1 | 0.74 | 0.85 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.642 | 0.279 | 1.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 412 | 242 | 568 | 0 | 0 | 0 | 0 | 0 | 316 | 0 |
N.S. |
1 | 0.59 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 2.550 | 1.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 265 | 296 | 1087 | 0 | 0 | 0 | 0 | 275 | 0 |
N.S. |
1 | 0.87 | 0.97 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 2.415 | 1.172 | 1.415 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 573 | 404 | 884 | 0 | 0 | 0 | 0 | 0 | 372 | 0 |
N.S. |
1 | 0.71 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 5.018 | 7.301 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 443 | 446 | 438 | 2608 | 0 | 0 | 0 | 0 | 307 | 0 |
N.S. |
1 | 1.01 | 0.99 | 5.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 3.470 | 0.869 | 1.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 418 | 523 | 333 | 1042 | 0 | 0 | 0 | 0 | 500 | 0 |
N.S. |
1 | 1.25 | 0.80 | 2.49 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 3.178 | 1.455 | 1.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 408 | 359 | 766 | 0 | 0 | 0 | 0 | 553 | 0 |
N.S. |
1 | 1.03 | 0.90 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 2.259 | 1.106 | 1.339 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 315 | 301 | 704 | 0 | 0 | 0 | 0 | 479 | 0 |
N.S. |
1 | 1.03 | 0.98 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 2.105 | 1.028 | 1.181 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 209 | 280 | 2207 | 0 | 0 | 0 | 0 | 487 | 0 |
N.S. |
1 | 0.67 | 0.90 | 7.07 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 1.183 | 1.298 | 1.323 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 178 | 254 | 591 | 0 | 0 | 0 | 0 | 446 | 0 |
N.S. |
1 | 0.66 | 0.94 | 2.19 | 0.00 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 1.231 | 1.205 | 1.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 258 | 236 | 2131 | 0 | 0 | 0 | 0 | 486 | 0 |
N.S. |
1 | 0.88 | 0.81 | 7.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 1.844 | 0.838 | 1.190 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 518 | 419 | 547 | 0 | 0 | 0 | 0 | 0 | 614 | 0 |
N.S. |
1 | 0.81 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 4.252 | 2.936 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 436 | 408 | 3513 | 0 | 0 | 0 | 0 | 531 | 0 |
N.S. |
1 | 1.04 | 0.97 | 8.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 4.176 | 1.951 | 1.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 687 | 0 | 983 | 0 | 0 | 0 | 0 | 0 | 668 | 0 |
N.S. |
1 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.000 | 7.607 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 508 | 694 | 417 | 3506 | 0 | 0 | 0 | 0 | 560 | 0 |
N.S. |
1 | 1.37 | 0.82 | 6.90 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 6.859 | 2.397 | 1.413 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1311 | 1028 | 546 | 0 | 0 | 0 | 0 | 0 | 1133 | 0 |
N.S. |
1 | 0.78 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 3.643 | 0.576 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 757 | 650 | 409 | 0 | 0 | 0 | 0 | 0 | 649 | 0 |
N.S. |
1 | 0.86 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 2.881 | 0.413 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 356 | 270 | 0 | 0 | 0 | 0 | 0 | 294 | 0 |
N.S. |
1 | 0.95 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 1.100 | 0.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 26 | 26 | 28 | 26 | 28 | 40 | 65 | 28 | 78 | 28 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.54 | 2.50 | 1.08 | 3.00 | 1.08 |
time (sec) |
N/A | 0.286 | 5.401 | 1.370 | 0.136 | 0.114 | 3.525 | 0.152 | 0.178 | 3.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 26 | 26 | 28 | 26 | 28 | 55 | 92 | 28 | 102 | 28 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 2.12 | 3.54 | 1.08 | 3.92 | 1.08 |
time (sec) |
N/A | 1.166 | 6.220 | 1.437 | 0.152 | 0.098 | 17.267 | 0.153 | 0.196 | 3.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 26 | 28 | 66 | 0 | 28 | 126 | 28 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 2.54 | 0.00 | 1.08 | 4.85 | 1.08 |
time (sec) |
N/A | 2.225 | 6.663 | 1.461 | 0.141 | 0.092 | 0.000 | 0.167 | 0.220 | 3.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 133 | 0 | 0 | 255 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 4.75 | 0.00 | 0.00 | 9.11 | 1.00 |
time (sec) |
N/A | 4.202 | 3.397 | 2.372 | 0.182 | 0.096 | 0.000 | 0.000 | 0.310 | 3.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 80 | 0 | 0 | 163 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.86 | 0.00 | 0.00 | 5.82 | 1.00 |
time (sec) |
N/A | 1.730 | 0.840 | 2.111 | 0.165 | 0.110 | 0.000 | 0.000 | 0.249 | 3.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 40 | 27 | 0 | 74 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.43 | 0.96 | 0.00 | 2.64 | 1.00 |
time (sec) |
N/A | 1.336 | 0.607 | 1.932 | 0.149 | 0.092 | 21.797 | 0.000 | 0.203 | 3.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 40 | 27 | 28 | 82 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.43 | 0.96 | 1.00 | 2.93 | 1.00 |
time (sec) |
N/A | 0.523 | 3.107 | 0.923 | 0.144 | 0.103 | 10.944 | 0.183 | 0.211 | 3.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 26 | 28 | 67 | 27 | 28 | 139 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.39 | 0.96 | 1.00 | 4.96 | 1.00 |
time (sec) |
N/A | 0.552 | 4.064 | 1.787 | 0.193 | 0.111 | 10.209 | 0.193 | 0.203 | 3.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 78 | 0 | 28 | 193 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.79 | 0.00 | 1.00 | 6.89 | 1.00 |
time (sec) |
N/A | 0.537 | 4.341 | 1.825 | 0.186 | 0.096 | 0.000 | 0.216 | 0.219 | 3.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.405 | 0.452 | 1.029 | 0.132 | 0.093 | 1.243 | 0.154 | 0.186 | 3.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.281 | 0.423 | 1.028 | 0.134 | 0.097 | 3.556 | 0.196 | 0.188 | 3.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 271 | 121 | 156 | 0 | 166 | 185 | 0 | 24 | 0 |
N.S. |
1 | 1.45 | 0.65 | 0.83 | 0.00 | 0.89 | 0.99 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.631 | 0.058 | 1.717 | 0.000 | 0.106 | 0.837 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 203 | 98 | 164 | 127 | 128 | 148 | 0 | 24 | 0 |
N.S. |
1 | 1.33 | 0.64 | 1.07 | 0.83 | 0.84 | 0.97 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.325 | 0.050 | 1.854 | 0.036 | 0.101 | 0.635 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 114 | 83 | 84 | 0 | 128 | 100 | 0 | 24 | 0 |
N.S. |
1 | 1.09 | 0.79 | 0.80 | 0.00 | 1.22 | 0.95 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.780 | 0.047 | 1.293 | 0.000 | 0.092 | 0.430 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 69 | 58 | 90 | 61 | 92 | 61 | 101 | 52 | 0 |
N.S. |
1 | 1.08 | 0.91 | 1.41 | 0.95 | 1.44 | 0.95 | 1.58 | 0.81 | 0.00 |
time (sec) |
N/A | 0.400 | 0.025 | 1.160 | 0.027 | 0.096 | 0.348 | 0.162 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 23 | 10 | 23 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.77 | 0.77 | 1.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.248 | 0.006 | 0.428 | 0.031 | 0.098 | 0.282 | 0.114 | 0.190 | 3.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 122 | 146 | 197 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.20 | 1.43 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.968 | 0.128 | 1.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 103 | 97 | 187 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.17 | 1.10 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.149 | 0.188 | 1.613 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 218 | 304 | 377 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.04 | 1.45 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.652 | 3.004 | 1.692 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 171 | 152 | 163 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.83 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.686 | 0.262 | 4.898 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 154 | 135 | 148 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.84 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.652 | 0.216 | 1.760 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 71 | 65 | 67 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.87 | 0.79 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.477 | 0.165 | 2.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 104 | 91 | 100 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.86 | 0.75 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.498 | 0.183 | 1.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 71 | 63 | 67 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.87 | 0.77 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.388 | 0.196 | 1.709 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 27 | 22 | 0 | 26 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.81 | 0.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.844 | 2.129 | 0.775 | 0.103 | 0.082 | 0.802 | 0.000 | 0.181 | 3.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 27 | 30 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 1.00 | 1.11 | 1.00 |
time (sec) |
N/A | 0.772 | 1.873 | 0.769 | 0.126 | 0.081 | 0.664 | 0.130 | 0.191 | 2.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 0 | 30 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 0.00 | 1.11 | 1.00 |
time (sec) |
N/A | 0.490 | 3.811 | 0.925 | 0.110 | 0.074 | 0.742 | 0.000 | 0.198 | 2.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 204 | 179 | 196 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.83 | 0.73 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.147 | 0.479 | 1.913 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 171 | 152 | 163 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.83 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.893 | 0.381 | 5.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 154 | 136 | 149 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.84 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.603 | 0.358 | 1.756 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 121 | 109 | 115 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.84 | 0.76 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.454 | 0.298 | 3.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 27 | 22 | 0 | 55 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.81 | 0.00 | 2.04 | 1.00 |
time (sec) |
N/A | 0.945 | 2.112 | 0.664 | 0.119 | 0.093 | 2.371 | 0.000 | 0.197 | 3.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 27 | 58 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 1.00 | 2.15 | 1.00 |
time (sec) |
N/A | 0.759 | 2.276 | 0.632 | 0.120 | 0.086 | 1.991 | 0.138 | 0.202 | 3.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 0 | 61 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 0.00 | 2.26 | 1.00 |
time (sec) |
N/A | 0.308 | 3.770 | 0.685 | 0.116 | 0.079 | 2.317 | 0.000 | 0.221 | 2.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 204 | 180 | 197 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.83 | 0.73 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.734 | 0.716 | 2.003 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 221 | 197 | 211 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.82 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.020 | 0.657 | 8.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 204 | 180 | 197 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 0.83 | 0.73 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.055 | 0.617 | 1.982 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 171 | 153 | 163 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 0.83 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.883 | 0.498 | 3.933 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 44 | 22 | 0 | 86 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.63 | 0.81 | 0.00 | 3.19 | 1.00 |
time (sec) |
N/A | 1.383 | 2.115 | 0.691 | 0.107 | 0.085 | 5.293 | 0.000 | 0.188 | 2.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 27 | 27 | 29 | 25 | 27 | 48 | 24 | 27 | 89 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.78 | 0.89 | 1.00 | 3.30 | 1.00 |
time (sec) |
N/A | 1.146 | 2.297 | 0.694 | 0.117 | 0.075 | 4.077 | 0.152 | 0.230 | 2.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 48 | 24 | 0 | 90 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.78 | 0.89 | 0.00 | 3.33 | 1.00 |
time (sec) |
N/A | 0.319 | 3.783 | 0.721 | 0.115 | 0.080 | 4.433 | 0.000 | 0.212 | 2.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 36 | 31 | 30 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.88 | 0.76 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.397 | 0.063 | 1.376 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 32 | 22 | 23 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.19 | 0.81 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.373 | 0.127 | 1.322 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 21 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.360 | 0.078 | 1.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 21 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.346 | 0.007 | 0.661 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 2.44 | 0.00 |
time (sec) |
N/A | 0.276 | 0.089 | 0.980 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 21 | 7 | 22 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 2.33 | 0.78 | 2.44 | 1.00 | 1.00 |
time (sec) |
N/A | 0.263 | 0.031 | 0.296 | 0.031 | 0.088 | 0.247 | 0.109 | 0.203 | 2.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 23 | 23 | 25 | 21 | 23 | 31 | 20 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.35 | 0.87 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.317 | 1.012 | 1.501 | 0.111 | 0.082 | 0.537 | 0.113 | 0.198 | 2.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 23 | 23 | 25 | 21 | 23 | 33 | 22 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.43 | 0.96 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.322 | 0.078 | 0.678 | 0.120 | 0.073 | 0.511 | 0.130 | 0.188 | 2.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 169 | 136 | 149 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.92 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.765 | 0.401 | 1.901 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 121 | 109 | 115 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.84 | 0.76 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.901 | 0.306 | 3.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 115 | 92 | 101 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.95 | 0.76 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.774 | 0.292 | 1.569 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 71 | 65 | 67 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.87 | 0.79 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.516 | 0.272 | 1.866 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 57 | 46 | 53 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.06 | 0.85 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.505 | 0.162 | 1.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 16 | 28 | 26 | 29 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.75 | 1.62 | 1.81 | 1.00 | 1.00 |
time (sec) |
N/A | 0.226 | 0.050 | 0.297 | 0.030 | 0.083 | 1.009 | 0.124 | 0.190 | 3.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 45 | 24 | 0 | 35 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.67 | 0.89 | 0.00 | 1.30 | 1.00 |
time (sec) |
N/A | 0.303 | 1.828 | 0.878 | 0.112 | 0.082 | 1.187 | 0.000 | 0.208 | 3.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 27 | 27 | 29 | 25 | 27 | 49 | 26 | 27 | 39 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.81 | 0.96 | 1.00 | 1.44 | 1.00 |
time (sec) |
N/A | 0.306 | 0.581 | 0.691 | 0.112 | 0.083 | 1.065 | 0.116 | 0.200 | 3.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 27 | 27 | 29 | 25 | 27 | 62 | 24 | 27 | 77 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.30 | 0.89 | 1.00 | 2.85 | 1.00 |
time (sec) |
N/A | 0.316 | 1.266 | 0.620 | 0.110 | 0.090 | 1.175 | 0.121 | 0.193 | 2.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 60 | 22 | 0 | 75 | 25 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.40 | 0.88 | 0.00 | 3.00 | 1.00 |
time (sec) |
N/A | 0.269 | 0.051 | 0.874 | 0.109 | 0.082 | 1.271 | 0.000 | 0.201 | 2.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 24 | 24 | 26 | 22 | 24 | 59 | 22 | 24 | 73 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.46 | 0.92 | 1.00 | 3.04 | 1.00 |
time (sec) |
N/A | 0.229 | 0.089 | 0.670 | 0.097 | 0.094 | 1.329 | 0.116 | 0.186 | 2.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 27 | 63 | 24 | 0 | 75 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.33 | 0.89 | 0.00 | 2.78 | 1.00 |
time (sec) |
N/A | 0.307 | 2.024 | 1.063 | 0.110 | 0.091 | 3.091 | 0.000 | 0.180 | 2.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 27 | 27 | 29 | 25 | 27 | 67 | 26 | 27 | 79 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.48 | 0.96 | 1.00 | 2.93 | 1.00 |
time (sec) |
N/A | 0.306 | 1.706 | 1.061 | 0.119 | 0.080 | 1.801 | 0.123 | 0.191 | 2.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 30 | 27 | 0 | 67 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.90 | 0.00 | 2.23 | 1.00 |
time (sec) |
N/A | 0.342 | 1.760 | 2.016 | 0.128 | 0.087 | 71.477 | 0.000 | 0.196 | 2.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 30 | 27 | 0 | 32 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.90 | 0.00 | 1.07 | 1.00 |
time (sec) |
N/A | 0.318 | 0.483 | 1.858 | 0.120 | 0.091 | 1.296 | 0.000 | 0.192 | 2.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 30 | 30 | 32 | 28 | 30 | 53 | 27 | 30 | 45 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.77 | 0.90 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.329 | 1.259 | 0.876 | 0.119 | 0.092 | 1.647 | 0.172 | 0.195 | 2.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 30 | 30 | 32 | 28 | 30 | 85 | 27 | 30 | 88 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.83 | 0.90 | 1.00 | 2.93 | 1.00 |
time (sec) |
N/A | 0.433 | 1.789 | 1.944 | 0.129 | 0.097 | 9.613 | 0.177 | 0.215 | 2.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 291 | 175 | 633 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.37 | 0.82 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.516 | 0.472 | 2.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 201 | 82 | 144 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 2.16 | 0.88 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 1.783 | 0.265 | 2.586 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 183 | 126 | 364 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.23 | 0.85 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.219 | 0.301 | 1.875 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 73 | 138 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.05 | 0.86 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.693 | 0.147 | 1.838 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 392 | 42 | 24 | 0 | 41 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 14.52 | 1.56 | 0.89 | 0.00 | 1.52 | 1.00 |
time (sec) |
N/A | 0.908 | 9.438 | 1.206 | 0.358 | 0.104 | 1.103 | 0.000 | 0.205 | 3.025 |