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 | C | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 400 | 383 | 288 | 579 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.72 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.986 | 1.702 | 0.286 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 265 | 318 | 412 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.69 | 0.83 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.338 | 0.703 | 0.301 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 187 | 215 | 478 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.80 | 0.92 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.968 | 1.351 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 121 | 217 | 318 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.64 | 1.15 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.602 | 0.906 | 0.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 133 | 152 | 343 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.74 | 0.85 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.621 | 0.749 | 0.282 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 412 | 242 | 568 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.59 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.988 | 1.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 265 | 296 | 1117 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.97 | 3.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.020 | 1.332 | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 573 | 404 | 884 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.71 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.180 | 7.416 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 452 | 446 | 438 | 2608 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.97 | 5.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.260 | 0.940 | 0.368 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 512 | 523 | 333 | 1042 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.65 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.557 | 1.594 | 0.405 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 398 | 408 | 359 | 766 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.90 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.825 | 1.224 | 0.307 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 315 | 301 | 704 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.98 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.995 | 1.124 | 0.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 312 | 209 | 280 | 2352 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.67 | 0.90 | 7.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.985 | 1.399 | 0.287 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 178 | 254 | 591 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 0.94 | 2.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.767 | 1.344 | 0.293 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 258 | 236 | 2131 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.81 | 7.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.359 | 1.449 | 0.279 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 518 | 419 | 547 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.81 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.060 | 3.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 421 | 436 | 408 | 3513 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.97 | 8.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.301 | 2.142 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | F | A | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 687 | 0 | 983 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.000 | 7.775 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 506 | 694 | 417 | 3506 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.37 | 0.82 | 6.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 5.086 | 2.596 | 0.367 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 366 | 369 | 178 | 570 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.49 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.728 | 0.640 | 0.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 30 | 26 | 28 | 133 | 0 | 0 | 28 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 4.75 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 3.274 | 3.615 | 1.048 | 0.356 | 0.266 | 0.000 | 0.000 | 3.121 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 30 | 26 | 28 | 80 | 0 | 0 | 28 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.86 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 1.657 | 0.914 | 0.852 | 0.312 | 0.266 | 0.000 | 0.000 | 3.066 |
| 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 | 28 | 28 | 30 | 26 | 28 | 40 | 27 | 0 | 28 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.43 | 0.96 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.860 | 0.655 | 0.706 | 0.322 | 0.263 | 21.286 | 0.000 | 3.184 |
| 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 | 28 | 28 | 30 | 26 | 28 | 40 | 27 | 28 | 28 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.43 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.314 | 3.420 | 0.303 | 0.305 | 0.261 | 7.796 | 0.356 | 3.109 |
| 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 | 28 | 28 | 30 | 26 | 28 | 67 | 27 | 28 | 28 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.39 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.326 | 4.435 | 0.397 | 0.358 | 0.259 | 9.435 | 0.356 | 2.989 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 30 | 26 | 28 | 78 | 27 | 28 | 28 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.79 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.326 | 4.604 | 0.455 | 0.359 | 0.275 | 165.867 | 0.377 | 2.998 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 23 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.259 | 0.460 | 0.175 | 0.297 | 0.260 | 1.150 | 0.335 | 3.097 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 359 | 563 | 169 | 270 | 276 | 248 | 355 | 0 | 0 |
| N.S. |
1 | 1.57 | 0.47 | 0.75 | 0.77 | 0.69 | 0.99 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.568 | 0.191 | 0.215 | 0.207 | 0.280 | 1.189 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 367 | 137 | 200 | 210 | 204 | 262 | 0 | 0 |
| N.S. |
1 | 1.38 | 0.52 | 0.75 | 0.79 | 0.77 | 0.99 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.431 | 0.102 | 0.292 | 0.211 | 0.272 | 0.573 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 196 | 99 | 128 | 124 | 140 | 150 | 0 | 0 |
| N.S. |
1 | 1.28 | 0.65 | 0.84 | 0.81 | 0.92 | 0.98 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.816 | 0.093 | 0.046 | 0.199 | 0.265 | 0.300 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 174 | 141 | 223 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.81 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.596 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 254 | 568 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.688 | 1.790 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 409 | 414 | 654 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.859 | 3.736 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | F | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 509 | 591 | 177 | 802 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.16 | 0.35 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.202 | 0.603 | 0.242 | 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) | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 348 | 354 | 136 | 484 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.39 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.224 | 0.278 | 0.212 | 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) | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 164 | 86 | 231 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.80 | 0.42 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.810 | 0.162 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 41 | 39 | 14 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 0.98 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.219 | 0.047 | 0.237 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 218 | 138 | 133 | 262 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.63 | 0.61 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.718 | 0.255 | 0.278 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 363 | 273 | 195 | 550 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 0.54 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.655 | 0.474 | 0.297 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 515 | 458 | 297 | 888 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.89 | 0.58 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.977 | 0.590 | 0.294 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 25 | 21 | 23 | 23 | 22 | 23 | 23 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.250 | 0.470 | 0.178 | 0.299 | 0.264 | 2.539 | 0.363 | 2.549 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 271 | 121 | 156 | 0 | 166 | 185 | 0 | 0 |
| N.S. |
1 | 1.45 | 0.65 | 0.83 | 0.00 | 0.89 | 0.99 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.560 | 0.060 | 0.199 | 0.000 | 0.258 | 0.730 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 203 | 98 | 164 | 127 | 128 | 148 | 0 | 0 |
| N.S. |
1 | 1.33 | 0.64 | 1.07 | 0.83 | 0.84 | 0.97 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.283 | 0.049 | 0.260 | 0.204 | 0.264 | 0.518 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 114 | 83 | 84 | 0 | 128 | 100 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.79 | 0.80 | 0.00 | 1.22 | 0.95 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.770 | 0.058 | 0.214 | 0.000 | 0.251 | 0.406 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 64 | 69 | 58 | 90 | 61 | 92 | 61 | 101 | 0 |
| N.S. |
1 | 1.08 | 0.91 | 1.41 | 0.95 | 1.44 | 0.95 | 1.58 | 0.00 |
| time (sec) |
N/A | 0.403 | 0.030 | 0.287 | 0.198 | 0.251 | 0.343 | 0.329 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 13 | 12 | 11 | 23 | 10 | 0 | 11 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.77 | 0.77 | 0.00 | 0.85 |
| time (sec) |
N/A | 0.199 | 0.006 | 0.254 | 0.203 | 0.250 | 0.246 | 0.000 | 2.552 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 122 | 146 | 197 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.20 | 1.43 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.614 | 0.136 | 0.320 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | C | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 103 | 97 | 187 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.17 | 1.10 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.664 | 0.225 | 0.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 218 | 304 | 377 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.45 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.355 | 3.265 | 0.244 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 50 | 43 | 42 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.75 | 0.64 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.350 | 0.137 | 0.208 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 39 | 34 | 33 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.78 | 0.68 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.332 | 0.073 | 0.225 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 26 | 23 | 22 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.79 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.299 | 0.026 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 19 | 21 | 19 | 21 | 21 | 20 | 21 | 21 |
| N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 1.05 | 1.11 | 1.11 |
| time (sec) |
N/A | 0.210 | 0.491 | 0.200 | 0.247 | 0.245 | 0.526 | 0.294 | 2.587 |
| 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 | 19 | 19 | 21 | 19 | 21 | 36 | 36 | 21 | 21 |
| N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.89 | 1.89 | 1.11 | 1.11 |
| time (sec) |
N/A | 0.205 | 1.529 | 0.068 | 0.249 | 0.248 | 0.984 | 0.319 | 2.543 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 171 | 152 | 163 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.638 | 0.297 | 1.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 154 | 135 | 148 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.84 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.635 | 0.255 | 0.286 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 71 | 65 | 67 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.79 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.475 | 0.186 | 0.281 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 104 | 91 | 100 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 0.75 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.499 | 0.204 | 0.226 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 71 | 63 | 67 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.77 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.389 | 0.231 | 0.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 29 | 25 | 27 | 27 | 22 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.81 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.587 | 2.529 | 0.140 | 0.265 | 0.256 | 0.714 | 0.000 | 2.547 |
| 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 | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.470 | 2.092 | 0.107 | 0.274 | 0.263 | 0.620 | 0.291 | 2.557 |
| 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 | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.291 | 4.321 | 0.161 | 0.263 | 0.255 | 0.655 | 0.000 | 2.501 |
| 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 | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.290 | 1.529 | 0.174 | 0.272 | 0.240 | 0.809 | 0.276 | 2.635 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 204 | 179 | 196 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.73 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.693 | 0.530 | 0.241 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 171 | 152 | 163 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.615 | 0.428 | 0.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 154 | 136 | 149 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.84 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.561 | 0.401 | 0.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 121 | 109 | 115 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.84 | 0.76 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.450 | 0.306 | 0.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 29 | 25 | 27 | 27 | 22 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.81 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.908 | 2.433 | 0.076 | 0.265 | 0.253 | 2.143 | 0.000 | 2.548 |
| 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 | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.745 | 2.628 | 0.078 | 0.263 | 0.249 | 1.630 | 0.297 | 2.529 |
| 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 | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.320 | 4.359 | 0.088 | 0.268 | 0.258 | 1.944 | 0.000 | 2.536 |
| 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 | 27 | 27 | 29 | 25 | 27 | 31 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.15 | 0.89 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.309 | 1.576 | 0.171 | 0.259 | 0.252 | 2.592 | 0.308 | 2.548 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 204 | 180 | 197 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.73 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.693 | 0.808 | 0.252 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 268 | 221 | 197 | 211 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.82 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.699 | 0.734 | 0.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 204 | 180 | 197 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.73 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.658 | 0.683 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 171 | 153 | 163 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.83 | 0.74 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.525 | 0.562 | 0.465 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 29 | 25 | 27 | 44 | 22 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.63 | 0.81 | 0.00 | 1.00 |
| time (sec) |
N/A | 1.294 | 2.399 | 0.076 | 0.264 | 0.246 | 5.234 | 0.000 | 2.666 |
| 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 | 27 | 27 | 29 | 25 | 27 | 48 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.78 | 0.89 | 1.00 | 1.00 |
| time (sec) |
N/A | 1.063 | 2.408 | 0.079 | 0.273 | 0.252 | 3.881 | 0.319 | 2.682 |
| 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 | 27 | 27 | 29 | 25 | 27 | 48 | 24 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.78 | 0.89 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.312 | 4.280 | 0.093 | 0.270 | 0.258 | 4.047 | 0.000 | 2.720 |
| 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 | 27 | 27 | 29 | 25 | 27 | 48 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.78 | 0.89 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.311 | 1.728 | 0.181 | 0.278 | 0.246 | 4.635 | 0.321 | 2.650 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 36 | 31 | 30 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.76 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.386 | 0.071 | 0.221 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 32 | 22 | 23 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.19 | 0.81 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.373 | 0.143 | 0.264 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 25 | 22 | 21 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.81 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.361 | 0.088 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 25 | 22 | 21 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.81 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.357 | 0.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.287 | 0.098 | 0.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 9 | 9 | 9 | 10 | 9 | 21 | 7 | 0 | 9 |
| N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 2.33 | 0.78 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.207 | 0.033 | 0.248 | 0.189 | 0.248 | 0.211 | 0.000 | 2.715 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 25 | 21 | 23 | 31 | 20 | 23 | 23 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.35 | 0.87 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.261 | 1.267 | 0.236 | 0.260 | 0.254 | 0.453 | 0.276 | 2.685 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 25 | 21 | 23 | 33 | 22 | 23 | 23 |
| N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.43 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.258 | 0.116 | 0.067 | 0.268 | 0.248 | 0.451 | 0.289 | 2.794 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 169 | 136 | 149 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.597 | 0.442 | 0.229 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 121 | 109 | 115 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.84 | 0.76 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.526 | 0.351 | 0.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 115 | 92 | 101 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.76 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.534 | 0.334 | 0.270 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 71 | 65 | 67 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.87 | 0.79 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.454 | 0.289 | 0.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | C | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 57 | 46 | 53 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.85 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.484 | 0.172 | 0.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 17 | 16 | 28 | 26 | 0 | 16 |
| N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.75 | 1.62 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.214 | 0.048 | 0.303 | 0.193 | 0.265 | 0.920 | 0.000 | 2.752 |
| 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 | 27 | 27 | 29 | 25 | 27 | 45 | 24 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.67 | 0.89 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.297 | 2.150 | 0.107 | 0.263 | 0.254 | 1.143 | 0.000 | 2.921 |
| 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 | 27 | 27 | 29 | 25 | 27 | 49 | 26 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.81 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.293 | 1.221 | 0.065 | 0.272 | 0.256 | 0.934 | 0.286 | 2.803 |
| 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 | 27 | 27 | 29 | 25 | 27 | 62 | 24 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.30 | 0.89 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.303 | 2.285 | 0.111 | 0.265 | 0.258 | 1.119 | 0.277 | 2.695 |
| 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 | 25 | 25 | 27 | 23 | 25 | 60 | 22 | 0 | 25 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.40 | 0.88 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.266 | 2.226 | 0.115 | 0.258 | 0.258 | 1.126 | 0.000 | 2.672 |
| 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 | 24 | 24 | 26 | 22 | 24 | 59 | 22 | 24 | 24 |
| N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.46 | 0.92 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.223 | 0.104 | 0.064 | 0.258 | 0.254 | 1.255 | 0.287 | 2.569 |
| 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 | 27 | 27 | 29 | 25 | 27 | 63 | 24 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.33 | 0.89 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.303 | 2.323 | 0.159 | 0.276 | 0.255 | 2.753 | 0.000 | 2.618 |
| 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 | 27 | 27 | 29 | 25 | 27 | 67 | 26 | 27 | 27 |
| N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.48 | 0.96 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.299 | 1.964 | 0.144 | 0.267 | 0.265 | 1.606 | 0.292 | 2.668 |