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 | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 444 | 444 | 182 | 859 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.41 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.622 | 11.149 | 3.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 355 | 355 | 181 | 784 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.51 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.439 | 11.182 | 3.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 429 | 233 | 1326 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.54 | 3.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.677 | 11.217 | 5.856 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 485 | 485 | 196 | 1338 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.40 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.736 | 11.177 | 5.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 381 | 381 | 195 | 1194 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.51 | 3.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.538 | 11.177 | 4.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 474 | 474 | 189 | 1298 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.40 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.604 | 11.176 | 3.219 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 366 | 366 | 187 | 851 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.51 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.411 | 11.164 | 3.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 519 | 519 | 197 | 1345 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.38 | 2.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.746 | 11.190 | 3.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 412 | 412 | 199 | 1191 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.48 | 2.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.557 | 11.184 | 3.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 484 | 484 | 184 | 1080 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.38 | 2.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.582 | 11.228 | 3.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 376 | 376 | 184 | 923 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.49 | 2.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.387 | 11.169 | 3.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 460 | 460 | 168 | 893 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.37 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.547 | 11.121 | 3.181 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 363 | 363 | 169 | 813 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.47 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.366 | 11.120 | 3.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 464 | 464 | 181 | 880 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.39 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.577 | 11.180 | 3.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 367 | 367 | 180 | 798 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.49 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.366 | 11.150 | 3.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 535 | 535 | 235 | 1100 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.44 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.783 | 11.202 | 3.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 429 | 234 | 948 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.55 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.572 | 11.219 | 3.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 529 | 529 | 189 | 1130 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.36 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.754 | 11.190 | 3.190 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 420 | 420 | 191 | 956 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.45 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.526 | 11.190 | 3.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 485 | 485 | 185 | 917 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.38 | 1.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.719 | 11.169 | 3.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 391 | 391 | 186 | 840 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.48 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.445 | 11.229 | 3.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 531 | 531 | 230 | 1097 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.43 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.768 | 11.236 | 3.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 426 | 426 | 229 | 939 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.54 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.552 | 11.210 | 3.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 628 | 628 | 319 | 1349 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.51 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.992 | 11.315 | 3.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 512 | 512 | 318 | 1094 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.765 | 11.406 | 3.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 568 | 568 | 256 | 1409 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.45 | 2.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.953 | 11.303 | 3.106 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 454 | 454 | 252 | 1193 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.56 | 2.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.640 | 11.302 | 2.911 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 551 | 551 | 278 | 1393 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.50 | 2.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.967 | 11.326 | 3.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 447 | 447 | 275 | 1192 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.639 | 11.336 | 3.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 625 | 625 | 327 | 1518 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.52 | 2.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.998 | 11.394 | 3.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 514 | 514 | 328 | 1311 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.64 | 2.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.733 | 11.372 | 2.987 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 735 | 735 | 407 | 1888 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.55 | 2.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.232 | 11.821 | 3.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 606 | 606 | 427 | 1464 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.001 | 11.911 | 3.164 | 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(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 209 | 187 | 211 | 0 | 442 | 0 | 226 | 993 |
| N.S. |
1 | 1.00 | 0.89 | 1.01 | 0.00 | 2.11 | 0.00 | 1.08 | 4.75 |
| time (sec) |
N/A | 0.177 | 1.493 | 2.132 | 0.000 | 0.301 | 0.000 | 0.320 | 67.877 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 119 | 159 | 0 | 334 | 0 | 159 | 639 |
| N.S. |
1 | 1.00 | 0.87 | 1.16 | 0.00 | 2.44 | 0.00 | 1.16 | 4.66 |
| time (sec) |
N/A | 0.092 | 0.859 | 3.062 | 0.000 | 0.297 | 0.000 | 0.322 | 30.482 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 86 | 124 | 0 | 259 | 0 | 106 | 280 |
| N.S. |
1 | 1.00 | 1.00 | 1.44 | 0.00 | 3.01 | 0.00 | 1.23 | 3.26 |
| time (sec) |
N/A | 0.057 | 0.337 | 3.123 | 0.000 | 0.342 | 0.000 | 0.311 | 9.515 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 92 | 92 | 151 | 0 | 777 | 0 | 0 | 4638 |
| N.S. |
1 | 1.00 | 1.00 | 1.64 | 0.00 | 8.45 | 0.00 | 0.00 | 50.41 |
| time (sec) |
N/A | 0.066 | 0.405 | 3.068 | 0.000 | 0.392 | 0.000 | 0.000 | 23.876 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 89 | 132 | 0 | 280 | 0 | 434 | 477 |
| N.S. |
1 | 1.00 | 1.00 | 1.48 | 0.00 | 3.15 | 0.00 | 4.88 | 5.36 |
| time (sec) |
N/A | 0.050 | 0.591 | 3.088 | 0.000 | 0.316 | 0.000 | 0.559 | 10.968 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 125 | 171 | 0 | 358 | 0 | 1107 | 955 |
| N.S. |
1 | 1.00 | 0.87 | 1.20 | 0.00 | 2.50 | 0.00 | 7.74 | 6.68 |
| time (sec) |
N/A | 0.082 | 1.091 | 3.149 | 0.000 | 0.388 | 0.000 | 0.568 | 28.147 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 343 | 343 | 246 | 394 | 0 | 233 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 1.15 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.212 | 1.500 | 5.093 | 0.000 | 0.086 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 259 | 259 | 199 | 285 | 0 | 156 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 1.10 | 0.00 | 0.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.123 | 0.981 | 5.892 | 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 | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 232 | 111 | 168 | 0 | 109 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.48 | 0.72 | 0.00 | 0.47 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.104 | 1.045 | 4.890 | 0.000 | 0.086 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 307 | 228 | 314 | 0 | 158 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 1.02 | 0.00 | 0.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.194 | 1.631 | 5.690 | 0.000 | 0.085 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 276 | 276 | 231 | 282 | 0 | 574 | 0 | 305 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 1.02 | 0.00 | 2.08 | 0.00 | 1.11 | 0.00 |
| time (sec) |
N/A | 0.235 | 2.900 | 3.171 | 0.000 | 0.295 | 0.000 | 0.326 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 148 | 212 | 0 | 440 | 0 | 225 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 1.13 | 0.00 | 2.35 | 0.00 | 1.20 | 0.00 |
| time (sec) |
N/A | 0.138 | 1.583 | 3.202 | 0.000 | 0.272 | 0.000 | 0.327 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 125 | 104 | 153 | 0 | 334 | 0 | 149 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 1.22 | 0.00 | 2.67 | 0.00 | 1.19 | 0.00 |
| time (sec) |
N/A | 0.075 | 0.920 | 3.120 | 0.000 | 0.268 | 0.000 | 0.312 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 133 | 132 | 243 | 0 | 918 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.99 | 1.83 | 0.00 | 6.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.104 | 1.108 | 3.082 | 0.000 | 0.718 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 135 | 194 | 0 | 958 | 0 | 498 | 0 |
| N.S. |
1 | 1.00 | 0.99 | 1.43 | 0.00 | 7.04 | 0.00 | 3.66 | 0.00 |
| time (sec) |
N/A | 0.099 | 1.243 | 3.189 | 0.000 | 0.573 | 0.000 | 0.346 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 110 | 164 | 0 | 360 | 0 | 1101 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 1.25 | 0.00 | 2.75 | 0.00 | 8.40 | 0.00 |
| time (sec) |
N/A | 0.077 | 1.309 | 3.165 | 0.000 | 0.403 | 0.000 | 0.591 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 429 | 305 | 568 | 0 | 320 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 1.32 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.376 | 2.834 | 7.495 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 335 | 335 | 245 | 411 | 0 | 234 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 1.23 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.262 | 2.175 | 7.642 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 244 | 206 | 289 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.111 | 2.118 | 4.903 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 311 | 311 | 227 | 340 | 0 | 169 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 1.09 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.202 | 2.456 | 5.752 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 340 | 340 | 271 | 368 | 0 | 734 | 0 | 398 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 1.08 | 0.00 | 2.16 | 0.00 | 1.17 | 0.00 |
| time (sec) |
N/A | 0.281 | 3.840 | 3.222 | 0.000 | 0.340 | 0.000 | 0.331 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 237 | 214 | 281 | 0 | 574 | 0 | 304 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 1.19 | 0.00 | 2.42 | 0.00 | 1.28 | 0.00 |
| time (sec) |
N/A | 0.163 | 3.218 | 3.151 | 0.000 | 0.315 | 0.000 | 0.321 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 164 | 137 | 206 | 0 | 440 | 0 | 210 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 1.26 | 0.00 | 2.68 | 0.00 | 1.28 | 0.00 |
| time (sec) |
N/A | 0.106 | 1.590 | 3.171 | 0.000 | 0.296 | 0.000 | 0.325 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 162 | 375 | 0 | 1075 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 2.01 | 0.00 | 5.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.179 | 1.942 | 3.037 | 0.000 | 1.676 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 166 | 303 | 0 | 1097 | 0 | 558 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 1.62 | 0.00 | 5.87 | 0.00 | 2.98 | 0.00 |
| time (sec) |
N/A | 0.167 | 2.079 | 3.402 | 0.000 | 1.288 | 0.000 | 0.359 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 192 | 206 | 230 | 0 | 1123 | 0 | 1175 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 1.20 | 0.00 | 5.85 | 0.00 | 6.12 | 0.00 |
| time (sec) |
N/A | 0.149 | 3.625 | 3.210 | 0.000 | 1.328 | 0.000 | 0.397 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 553 | 553 | 379 | 738 | 0 | 429 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.33 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.494 | 4.167 | 8.348 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 436 | 436 | 306 | 563 | 0 | 323 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 1.29 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.333 | 2.973 | 8.787 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 330 | 330 | 254 | 365 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.203 | 2.844 | 5.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 261 | 362 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.202 | 3.040 | 5.733 | 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 | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 92 | 135 | 0 | 84 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 1.36 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.066 | 0.492 | 4.803 | 0.000 | 0.084 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 66 | 81 | 46 | 72 | 0 | 40 | 414 |
| N.S. |
1 | 1.00 | 1.02 | 1.25 | 0.71 | 1.11 | 0.00 | 0.62 | 6.37 |
| time (sec) |
N/A | 0.034 | 0.453 | 3.141 | 0.281 | 0.249 | 0.000 | 0.285 | 16.953 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 87 | 129 | 0 | 77 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 1.84 | 0.00 | 1.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.032 | 0.305 | 3.961 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 39 | 53 | 60 | 27 | 65 | 34 | 33 | 206 |
| N.S. |
1 | 1.00 | 1.36 | 1.54 | 0.69 | 1.67 | 0.87 | 0.85 | 5.28 |
| time (sec) |
N/A | 0.022 | 0.122 | 3.135 | 0.291 | 0.274 | 1.505 | 0.290 | 7.199 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 241 | 127 | 259 | 0 | 146 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.53 | 1.07 | 0.00 | 0.61 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.102 | 0.755 | 4.158 | 0.000 | 0.085 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 120 | 161 | 0 | 336 | 0 | 160 | 550 |
| N.S. |
1 | 1.00 | 0.85 | 1.14 | 0.00 | 2.38 | 0.00 | 1.13 | 3.90 |
| time (sec) |
N/A | 0.120 | 1.154 | 3.185 | 0.000 | 0.357 | 0.000 | 0.302 | 28.278 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 88 | 129 | 0 | 256 | 0 | 104 | 279 |
| N.S. |
1 | 1.00 | 1.00 | 1.47 | 0.00 | 2.91 | 0.00 | 1.18 | 3.17 |
| time (sec) |
N/A | 0.065 | 0.792 | 3.114 | 0.000 | 0.269 | 0.000 | 0.306 | 10.116 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 45 | 89 | 0 | 194 | 0 | 54 | 49 |
| N.S. |
1 | 1.00 | 1.00 | 1.98 | 0.00 | 4.31 | 0.00 | 1.20 | 1.09 |
| time (sec) |
N/A | 0.044 | 0.324 | 3.130 | 0.000 | 0.290 | 0.000 | 0.294 | 6.032 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 46 | 89 | 0 | 204 | 0 | 89 | 136 |
| N.S. |
1 | 1.00 | 1.00 | 1.93 | 0.00 | 4.43 | 0.00 | 1.93 | 2.96 |
| time (sec) |
N/A | 0.033 | 0.475 | 3.212 | 0.000 | 0.263 | 0.000 | 0.321 | 8.291 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 91 | 137 | 0 | 278 | 0 | 413 | 481 |
| N.S. |
1 | 1.00 | 1.00 | 1.51 | 0.00 | 3.05 | 0.00 | 4.54 | 5.29 |
| time (sec) |
N/A | 0.055 | 0.715 | 3.164 | 0.000 | 0.317 | 0.000 | 0.321 | 11.492 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 126 | 172 | 0 | 360 | 0 | 1015 | 962 |
| N.S. |
1 | 1.00 | 0.85 | 1.15 | 0.00 | 2.42 | 0.00 | 6.81 | 6.46 |
| time (sec) |
N/A | 0.099 | 1.289 | 3.160 | 0.000 | 0.368 | 0.000 | 0.575 | 28.093 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 342 | 342 | 249 | 379 | 0 | 232 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 1.11 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.211 | 1.998 | 7.165 | 0.000 | 0.084 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 261 | 201 | 293 | 0 | 156 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 1.12 | 0.00 | 0.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.115 | 1.465 | 5.508 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 122 | 129 | 0 | 112 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.05 | 1.11 | 0.00 | 0.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.033 | 0.657 | 3.052 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 146 | 189 | 0 | 107 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 1.24 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.078 | 1.067 | 4.770 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 307 | 229 | 315 | 0 | 157 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 1.03 | 0.00 | 0.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.177 | 1.723 | 6.281 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 153 | 180 | 0 | 498 | 0 | 185 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 1.40 | 0.00 | 3.86 | 0.00 | 1.43 | 0.00 |
| time (sec) |
N/A | 0.120 | 1.767 | 3.140 | 0.000 | 0.317 | 0.000 | 0.340 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 83 | 83 | 155 | 0 | 367 | 0 | 135 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.87 | 0.00 | 4.42 | 0.00 | 1.63 | 0.00 |
| time (sec) |
N/A | 0.063 | 1.281 | 3.107 | 0.000 | 0.298 | 0.000 | 0.323 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 34 | 30 | 0 | 48 | 0 | 70 | 45 |
| N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 1.41 | 0.00 | 2.06 | 1.32 |
| time (sec) |
N/A | 0.023 | 0.071 | 3.087 | 0.000 | 0.259 | 0.000 | 0.322 | 5.808 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 114 | 285 | 0 | 706 | 0 | 312 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 2.08 | 0.00 | 5.15 | 0.00 | 2.28 | 0.00 |
| time (sec) |
N/A | 0.104 | 2.207 | 3.312 | 0.000 | 0.371 | 0.000 | 0.373 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 54 | 50 | 0 | 128 | 0 | 214 | 139 |
| N.S. |
1 | 1.00 | 0.61 | 0.56 | 0.00 | 1.44 | 0.00 | 2.40 | 1.56 |
| time (sec) |
N/A | 0.056 | 1.849 | 3.059 | 0.000 | 0.301 | 0.000 | 0.332 | 6.163 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 52 | 47 | 0 | 126 | 0 | 129 | 137 |
| N.S. |
1 | 1.00 | 0.70 | 0.64 | 0.00 | 1.70 | 0.00 | 1.74 | 1.85 |
| time (sec) |
N/A | 0.036 | 1.498 | 3.080 | 0.000 | 0.306 | 0.000 | 0.306 | 5.916 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 91 | 114 | 0 | 262 | 0 | 597 | 220 |
| N.S. |
1 | 1.00 | 0.59 | 0.74 | 0.00 | 1.70 | 0.00 | 3.88 | 1.43 |
| time (sec) |
N/A | 0.136 | 2.397 | 3.122 | 0.000 | 0.408 | 0.000 | 0.362 | 6.215 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 91 | 120 | 0 | 269 | 0 | 472 | 227 |
| N.S. |
1 | 1.00 | 0.66 | 0.87 | 0.00 | 1.95 | 0.00 | 3.42 | 1.64 |
| time (sec) |
N/A | 0.076 | 1.997 | 3.151 | 0.000 | 0.443 | 0.000 | 0.360 | 6.113 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 83 | 108 | 0 | 259 | 0 | 243 | 216 |
| N.S. |
1 | 1.00 | 0.73 | 0.96 | 0.00 | 2.29 | 0.00 | 2.15 | 1.91 |
| time (sec) |
N/A | 0.056 | 1.662 | 3.108 | 0.000 | 0.422 | 0.000 | 0.310 | 6.096 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 217 | 151 | 205 | 0 | 451 | 0 | 1036 | 336 |
| N.S. |
1 | 1.00 | 0.70 | 0.94 | 0.00 | 2.08 | 0.00 | 4.77 | 1.55 |
| time (sec) |
N/A | 0.179 | 3.493 | 3.132 | 0.000 | 0.691 | 0.000 | 0.421 | 6.456 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 46 | 92 | 0 | 201 | 0 | 57 | 48 |
| N.S. |
1 | 1.00 | 0.98 | 1.96 | 0.00 | 4.28 | 0.00 | 1.21 | 1.02 |
| time (sec) |
N/A | 0.041 | 0.347 | 3.086 | 0.000 | 0.304 | 0.000 | 0.308 | 5.683 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 48 | 95 | 0 | 203 | 0 | 57 | 51 |
| N.S. |
1 | 1.00 | 1.00 | 1.98 | 0.00 | 4.23 | 0.00 | 1.19 | 1.06 |
| time (sec) |
N/A | 0.040 | 0.350 | 3.109 | 0.000 | 0.286 | 0.000 | 0.302 | 5.433 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 110 | 72 | 70 | 0 | 113 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 0.64 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.030 | 0.529 | 3.062 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 59 | 59 | 0 | 67 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.68 | 0.00 | 0.77 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.050 | 0.486 | 3.703 | 0.000 | 0.080 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 70 | 76 | 0 | 97 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.86 | 0.00 | 1.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.037 | 0.474 | 2.809 | 0.000 | 0.087 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 48 | 25 | 0 | 48 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.55 | 0.81 | 0.00 | 1.55 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.020 | 0.267 | 3.428 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 37 | 23 | 0 | 48 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 0.74 | 0.00 | 1.55 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.020 | 0.253 | 3.166 | 0.000 | 0.090 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 48 | 29 | 0 | 53 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.37 | 0.83 | 0.00 | 1.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.033 | 0.263 | 3.442 | 0.000 | 0.083 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 38 | 33 | 0 | 53 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.09 | 0.94 | 0.00 | 1.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.026 | 0.240 | 3.177 | 0.000 | 0.089 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 28 | 29 | 0 | 53 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.83 | 0.00 | 1.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.030 | 0.249 | 3.482 | 0.000 | 0.090 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 28 | 27 | 0 | 66 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.77 | 0.00 | 1.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.022 | 0.235 | 3.113 | 0.000 | 0.089 | 0.000 | 0.000 | 0.000 |