Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 162 | 248 | 213 | 0 | 1007 | 0 | 182 | 5491 |
| N.S. |
1 | 1.00 | 1.53 | 1.31 | 0.00 | 6.22 | 0.00 | 1.12 | 33.90 |
| time (sec) |
N/A | 0.181 | 0.177 | 0.124 | 0.000 | 0.371 | 0.000 | 0.599 | 11.262 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 361 | 361 | 344 | 334 | 0 | 3435 | 0 | 3651 | 8739 |
| N.S. |
1 | 1.00 | 0.95 | 0.93 | 0.00 | 9.52 | 0.00 | 10.11 | 24.21 |
| time (sec) |
N/A | 1.899 | 0.485 | 0.155 | 0.000 | 0.703 | 0.000 | 0.981 | 10.321 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 219 | 219 | 328 | 263 | 0 | 1242 | 0 | 274 | 5999 |
| N.S. |
1 | 1.00 | 1.50 | 1.20 | 0.00 | 5.67 | 0.00 | 1.25 | 27.39 |
| time (sec) |
N/A | 0.222 | 0.228 | 0.149 | 0.000 | 0.447 | 0.000 | 0.650 | 11.776 |
| 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 | 142 | 142 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.107 | 11.074 | 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 | C | A | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 380 | 380 | 486 | 455 | 0 | 368 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.28 | 1.20 | 0.00 | 0.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.183 | 1.958 | 2.260 | 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 | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 108 | 123 | 0 | 232 | 0 | 121 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.95 | 0.00 | 1.80 | 0.00 | 0.94 | 0.00 |
| time (sec) |
N/A | 0.061 | 0.091 | 0.067 | 0.000 | 0.291 | 0.000 | 0.319 | 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 | 347 | 347 | 452 | 430 | 0 | 314 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.30 | 1.24 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.140 | 1.639 | 1.511 | 0.000 | 0.093 | 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(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 194 | 154 | 136 | 0 | 666 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.70 | 0.00 | 3.43 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.128 | 0.055 | 0.053 | 0.000 | 0.301 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 244 | 181 | 202 | 0 | 396 | 0 | 640 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.83 | 0.00 | 1.62 | 0.00 | 2.62 | 0.00 |
| time (sec) |
N/A | 0.224 | 0.086 | 0.090 | 0.000 | 0.275 | 0.000 | 0.453 | 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 | 487 | 487 | 609 | 654 | 0 | 485 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 1.34 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.293 | 2.382 | 3.134 | 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 | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 151 | 170 | 0 | 332 | 0 | 498 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 0.96 | 0.00 | 1.88 | 0.00 | 2.81 | 0.00 |
| time (sec) |
N/A | 0.086 | 0.159 | 0.082 | 0.000 | 0.274 | 0.000 | 0.452 | 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 | 425 | 425 | 540 | 620 | 0 | 409 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.27 | 1.46 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.273 | 2.127 | 2.135 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 80 | 72 | 0 | 135 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.88 | 0.00 | 1.65 | 0.00 | 0.68 | 0.00 |
| time (sec) |
N/A | 0.037 | 0.013 | 0.048 | 0.000 | 0.270 | 0.000 | 0.311 | 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 | 121 | 121 | 193 | 177 | 0 | 123 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.60 | 1.46 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.028 | 11.081 | 0.521 | 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 | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 80 | 72 | 0 | 137 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 1.57 | 1.41 | 0.00 | 2.69 | 0.00 | 1.10 | 0.00 |
| time (sec) |
N/A | 0.018 | 0.018 | 0.053 | 0.000 | 0.249 | 0.000 | 0.434 | 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 | 303 | 258 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.124 | 11.314 | 1.039 | 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 | 391 | 391 | 463 | 533 | 0 | 479 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.18 | 1.36 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.156 | 11.656 | 0.515 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 123 | 179 | 0 | 424 | 0 | 193 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 1.74 | 0.00 | 4.12 | 0.00 | 1.87 | 0.00 |
| time (sec) |
N/A | 0.042 | 0.047 | 0.063 | 0.000 | 0.311 | 0.000 | 0.289 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 468 | 468 | 519 | 1136 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.11 | 2.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.257 | 12.413 | 4.442 | 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 | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 154 | 159 | 220 | 0 | 508 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 1.43 | 0.00 | 3.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.103 | 0.057 | 0.123 | 0.000 | 0.327 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 46 | 0 | 0 | 83 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.032 | 0.048 | 0.000 | 0.000 | 0.268 | 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 | 287 | 287 | 239 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.248 | 11.177 | 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 | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 66 | 34 | 0 | 55 | 0 | 60 | 0 |
| N.S. |
1 | 1.00 | 1.47 | 0.76 | 0.00 | 1.22 | 0.00 | 1.33 | 0.00 |
| time (sec) |
N/A | 0.006 | 0.087 | 0.812 | 0.000 | 0.244 | 0.000 | 0.316 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 66 | 34 | 0 | 55 | 0 | 60 | 0 |
| N.S. |
1 | 1.00 | 1.47 | 0.76 | 0.00 | 1.22 | 0.00 | 1.33 | 0.00 |
| time (sec) |
N/A | 0.008 | 0.001 | 0.456 | 0.000 | 0.245 | 0.000 | 0.315 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 66 | 34 | 0 | 55 | 0 | 60 | 0 |
| N.S. |
1 | 1.00 | 1.47 | 0.76 | 0.00 | 1.22 | 0.00 | 1.33 | 0.00 |
| time (sec) |
N/A | 0.009 | 0.001 | 0.410 | 0.000 | 0.265 | 0.000 | 0.308 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 80 | 62 | 0 | 70 | 0 | 69 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.72 | 0.00 | 0.81 | 0.00 | 0.80 | 0.00 |
| time (sec) |
N/A | 0.028 | 0.071 | 0.295 | 0.000 | 0.259 | 0.000 | 0.314 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 80 | 62 | 0 | 70 | 0 | 69 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.72 | 0.00 | 0.81 | 0.00 | 0.80 | 0.00 |
| time (sec) |
N/A | 0.029 | 0.001 | 0.271 | 0.000 | 0.260 | 0.000 | 0.311 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 80 | 62 | 0 | 70 | 0 | 69 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.72 | 0.00 | 0.81 | 0.00 | 0.80 | 0.00 |
| time (sec) |
N/A | 0.028 | 0.001 | 0.266 | 0.000 | 0.278 | 0.000 | 0.347 | 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 | 38 | 38 | 37 | 35 | 0 | 111 | 0 | 35 | 34 |
| N.S. |
1 | 1.00 | 0.97 | 0.92 | 0.00 | 2.92 | 0.00 | 0.92 | 0.89 |
| time (sec) |
N/A | 0.010 | 0.011 | 1.014 | 0.000 | 0.277 | 0.000 | 0.298 | 0.045 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 68 | 42 | 0 | 130 | 0 | 59 | 0 |
| N.S. |
1 | 1.00 | 1.51 | 0.93 | 0.00 | 2.89 | 0.00 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.014 | 0.013 | 0.089 | 0.000 | 0.257 | 0.000 | 0.308 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 70 | 64 | 0 | 131 | 0 | 53 | 0 |
| N.S. |
1 | 1.00 | 1.49 | 1.36 | 0.00 | 2.79 | 0.00 | 1.13 | 0.00 |
| time (sec) |
N/A | 0.048 | 0.021 | 0.067 | 0.000 | 0.337 | 0.000 | 0.318 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 49 | 72 | 66 | 0 | 139 | 0 | 58 | 0 |
| N.S. |
1 | 1.00 | 1.47 | 1.35 | 0.00 | 2.84 | 0.00 | 1.18 | 0.00 |
| time (sec) |
N/A | 0.057 | 0.018 | 0.064 | 0.000 | 0.288 | 0.000 | 0.290 | 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 | 44 | 44 | 41 | 39 | 0 | 124 | 0 | 38 | 44 |
| N.S. |
1 | 1.00 | 0.93 | 0.89 | 0.00 | 2.82 | 0.00 | 0.86 | 1.00 |
| time (sec) |
N/A | 0.024 | 0.005 | 0.071 | 0.000 | 0.273 | 0.000 | 0.296 | 9.476 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 49 | 78 | 72 | 0 | 135 | 0 | 62 | 0 |
| N.S. |
1 | 1.00 | 1.59 | 1.47 | 0.00 | 2.76 | 0.00 | 1.27 | 0.00 |
| time (sec) |
N/A | 0.010 | 0.011 | 1.708 | 0.000 | 0.271 | 0.000 | 0.308 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 80 | 72 | 0 | 137 | 0 | 56 | 0 |
| N.S. |
1 | 1.00 | 1.57 | 1.41 | 0.00 | 2.69 | 0.00 | 1.10 | 0.00 |
| time (sec) |
N/A | 0.041 | 0.011 | 0.052 | 0.000 | 0.271 | 0.000 | 0.284 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 82 | 74 | 0 | 145 | 0 | 61 | 0 |
| N.S. |
1 | 1.00 | 1.55 | 1.40 | 0.00 | 2.74 | 0.00 | 1.15 | 0.00 |
| time (sec) |
N/A | 0.045 | 0.013 | 0.074 | 0.000 | 0.266 | 0.000 | 0.299 | 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 | 40 | 40 | 33 | 29 | 20 | 47 | 0 | 55 | 33 |
| N.S. |
1 | 1.00 | 0.82 | 0.72 | 0.50 | 1.18 | 0.00 | 1.38 | 0.82 |
| time (sec) |
N/A | 0.018 | 0.003 | 0.392 | 0.291 | 0.245 | 0.000 | 0.300 | 0.251 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 66 | 34 | 0 | 55 | 0 | 60 | 0 |
| N.S. |
1 | 1.00 | 1.47 | 0.76 | 0.00 | 1.22 | 0.00 | 1.33 | 0.00 |
| time (sec) |
N/A | 0.012 | 0.002 | 0.412 | 0.000 | 0.237 | 0.000 | 0.315 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 43 | 61 | 50 | 0 | 49 | 0 | 47 | 0 |
| N.S. |
1 | 1.00 | 1.42 | 1.16 | 0.00 | 1.14 | 0.00 | 1.09 | 0.00 |
| time (sec) |
N/A | 0.029 | 0.074 | 0.071 | 0.000 | 0.249 | 0.000 | 0.302 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |