Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 8 | 8 | 8 | 9 | 0 | 9 | 7 | 0 | 10 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.00 | 1.12 | 0.88 | 0.00 | 1.25 | 0.00 |
| time (sec) |
N/A | 0.173 | 0.010 | 0.060 | 0.000 | 0.080 | 0.256 | 0.000 | 0.308 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 5 | 5 | 5 | 6 | 0 | 6 | 7 | 0 | 12 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.20 | 0.00 | 1.20 | 1.40 | 0.00 | 2.40 | 0.00 |
| time (sec) |
N/A | 0.184 | 0.018 | 0.101 | 0.000 | 0.072 | 0.120 | 0.000 | 0.261 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 18 | 0 | 0 | 0 | 0 | 50 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 3.12 | 0.00 |
| time (sec) |
N/A | 0.264 | 0.006 | 0.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 28 | 35 | 0 | 0 | 0 | 0 | 54 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 1.93 | 0.00 |
| time (sec) |
N/A | 0.374 | 0.005 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.323 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 47 | 46 | 50 | 0 | 0 | 0 | 0 | 54 | 0 |
| N.S. |
1 | 1.02 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
| time (sec) |
N/A | 0.475 | 0.008 | 0.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 55 | 46 | 0 | 0 | 43 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.20 | 1.00 | 0.00 | 0.00 | 0.93 | 0.00 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.501 | 0.015 | 0.000 | 0.000 | 0.072 | 0.000 | 0.000 | 0.253 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 35 | 31 | 0 | 0 | 29 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.13 | 1.00 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.356 | 0.009 | 0.000 | 0.000 | 0.073 | 0.000 | 0.000 | 0.243 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 15 | 14 | 0 | 14 | 15 | 0 | 13 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.93 | 1.00 | 0.00 | 0.87 | 0.00 |
| time (sec) |
N/A | 0.237 | 0.009 | 0.063 | 0.000 | 0.076 | 0.261 | 0.000 | 0.218 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 11 | 11 | 10 | 0 | 10 | 10 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 0.91 | 0.91 | 0.00 | 1.27 | 0.00 |
| time (sec) |
N/A | 0.192 | 0.031 | 0.100 | 0.000 | 0.077 | 0.107 | 0.000 | 0.326 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 22 | 22 | 22 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.73 | 0.00 |
| time (sec) |
N/A | 0.351 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 36 | 34 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 1.06 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.76 | 0.00 |
| time (sec) |
N/A | 0.464 | 0.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.363 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.387 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.278 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.355 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 53 | 52 | 57 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.02 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
| time (sec) |
N/A | 0.574 | 0.009 | 0.227 | 0.000 | 0.000 | 0.000 | 0.000 | 0.271 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 33 | 40 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.428 | 0.007 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 13 | 19 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
| time (sec) |
N/A | 0.326 | 0.006 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.330 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 9 | 9 | 9 | 10 | 0 | 12 | 7 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 1.33 | 0.78 | 0.00 | 1.56 | 0.00 |
| time (sec) |
N/A | 0.194 | 0.032 | 0.102 | 0.000 | 0.078 | 0.109 | 0.000 | 0.386 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 13 | 14 | 0 | 14 | 14 | 0 | 13 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.00 | 1.08 | 1.08 | 0.00 | 1.00 | 0.00 |
| time (sec) |
N/A | 0.238 | 0.007 | 0.067 | 0.000 | 0.070 | 0.304 | 0.000 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 31 | 39 | 0 | 25 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.26 | 0.00 | 0.81 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.332 | 0.005 | 0.234 | 0.000 | 0.074 | 0.000 | 0.000 | 0.326 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 51 | 46 | 55 | 0 | 36 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.11 | 1.00 | 1.20 | 0.00 | 0.78 | 0.00 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.468 | 0.007 | 0.237 | 0.000 | 0.070 | 0.000 | 0.000 | 0.336 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 57 | 52 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.10 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
| time (sec) |
N/A | 0.660 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 37 | 35 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.06 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 0.564 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 22 | 17 | 22 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 0.77 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
| time (sec) |
N/A | 0.723 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 11 | 11 | 10 | 0 | 12 | 10 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 1.09 | 0.91 | 0.00 | 1.27 | 0.00 |
| time (sec) |
N/A | 0.323 | 0.033 | 0.101 | 0.000 | 0.069 | 0.178 | 0.000 | 0.237 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 15 | 14 | 0 | 14 | 22 | 0 | 13 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.93 | 1.47 | 0.00 | 0.87 | 0.00 |
| time (sec) |
N/A | 0.498 | 0.009 | 0.073 | 0.000 | 0.076 | 0.355 | 0.000 | 0.329 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 35 | 31 | 0 | 0 | 25 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.13 | 1.00 | 0.00 | 0.00 | 0.81 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.595 | 0.008 | 0.000 | 0.000 | 0.070 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 55 | 46 | 0 | 0 | 36 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 1.20 | 1.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.701 | 0.010 | 0.000 | 0.000 | 0.074 | 0.000 | 0.000 | 0.237 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.327 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.311 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.377 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 50 | 50 | 0 | 0 | 0 | 0 | 0 | 88 | 0 |
| N.S. |
1 | 0.96 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.69 | 0.00 |
| time (sec) |
N/A | 0.227 | 0.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.69 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 11 | 0 | 11 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.92 | 0.00 | 0.00 | 1.75 | 0.00 |
| time (sec) |
N/A | 0.194 | 0.005 | 1.161 | 0.000 | 0.076 | 0.000 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 11 | 0 | 11 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.92 | 0.00 | 0.00 | 1.75 | 0.00 |
| time (sec) |
N/A | 0.193 | 0.005 | 1.125 | 0.000 | 0.076 | 0.000 | 0.000 | 0.354 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 11 | 0 | 11 | 10 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.92 | 0.83 | 0.00 | 1.92 | 0.00 |
| time (sec) |
N/A | 0.187 | 0.004 | 1.142 | 0.000 | 0.078 | 0.437 | 0.000 | 0.297 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 8 | 8 | 8 | 9 | 0 | 9 | 5 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.00 | 1.12 | 0.62 | 0.00 | 2.62 | 0.00 |
| time (sec) |
N/A | 0.189 | 0.004 | 0.236 | 0.000 | 0.080 | 0.104 | 0.000 | 0.321 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 11 | 0 | 11 | 10 | 0 | 17 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.92 | 0.83 | 0.00 | 1.42 | 0.00 |
| time (sec) |
N/A | 0.191 | 0.005 | 0.256 | 0.000 | 0.074 | 0.445 | 0.000 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 11 | 0 | 11 | 10 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.92 | 0.83 | 0.00 | 1.75 | 0.00 |
| time (sec) |
N/A | 0.187 | 0.005 | 0.180 | 0.000 | 0.080 | 0.715 | 0.000 | 0.261 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 11 | 0 | 11 | 10 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.92 | 0.83 | 0.00 | 1.75 | 0.00 |
| time (sec) |
N/A | 0.189 | 0.006 | 0.210 | 0.000 | 0.072 | 1.257 | 0.000 | 0.296 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 16 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.192 | 0.004 | 1.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.315 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 16 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.191 | 0.004 | 1.148 | 0.000 | 0.000 | 0.000 | 0.000 | 0.264 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 16 | 0 | 0 | 0 | 0 | 23 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 |
| time (sec) |
N/A | 0.189 | 0.004 | 1.207 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 12 | 11 | 0 | 0 | 0 | 0 | 19 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
| time (sec) |
N/A | 0.181 | 0.003 | 0.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 9 | 9 | 9 | 14 | 0 | 0 | 0 | 0 | 15 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 1.67 | 0.00 |
| time (sec) |
N/A | 0.183 | 0.004 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.343 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 16 | 0 | 0 | 0 | 0 | 19 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
| time (sec) |
N/A | 0.191 | 0.005 | 0.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.300 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 16 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.194 | 0.005 | 0.190 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 16 | 0 | 0 | 0 | 0 | 21 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.194 | 0.005 | 0.279 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 122 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.54 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.278 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 14 | 14 | 14 | 25 | 0 | 0 | 27 | 0 | 39 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.79 | 0.00 | 0.00 | 1.93 | 0.00 | 2.79 | 0.00 |
| time (sec) |
N/A | 0.206 | 0.007 | 0.243 | 0.000 | 0.000 | 0.888 | 0.000 | 0.313 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 18 | 18 | 18 | 31 | 0 | 0 | 0 | 0 | 1281 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 71.17 | 0.00 |
| time (sec) |
N/A | 0.214 | 0.008 | 0.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.623 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1043 | 0 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.54 | 0.00 |
| time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.388 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 98 | 63 | 85 | 0 | 126 | 131 | 0 | 60 | 0 |
| N.S. |
1 | 1.08 | 0.69 | 0.93 | 0.00 | 1.38 | 1.44 | 0.00 | 0.66 | 0.00 |
| time (sec) |
N/A | 0.675 | 0.041 | 0.123 | 0.000 | 0.079 | 0.684 | 0.000 | 0.304 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 78 | 45 | 70 | 0 | 112 | 105 | 0 | 50 | 0 |
| N.S. |
1 | 1.07 | 0.62 | 0.96 | 0.00 | 1.53 | 1.44 | 0.00 | 0.68 | 0.00 |
| time (sec) |
N/A | 0.538 | 0.008 | 0.091 | 0.000 | 0.087 | 0.419 | 0.000 | 0.275 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 58 | 45 | 55 | 0 | 96 | 80 | 0 | 40 | 0 |
| N.S. |
1 | 1.05 | 0.82 | 1.00 | 0.00 | 1.75 | 1.45 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.421 | 0.008 | 0.076 | 0.000 | 0.087 | 0.545 | 0.000 | 0.297 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 36 | 36 | 35 | 39 | 38 | 76 | 48 | 0 | 30 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 1.08 | 1.06 | 2.11 | 1.33 | 0.00 | 0.83 | 0.00 |
| time (sec) |
N/A | 0.302 | 0.005 | 0.076 | 0.035 | 0.077 | 0.345 | 0.000 | 0.205 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 26 | 32 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
| time (sec) |
N/A | 0.253 | 0.010 | 0.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.343 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 35 | 33 | 0 | 0 | 0 | 0 | 10 | 0 |
| N.S. |
1 | 1.00 | 1.13 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.260 | 0.008 | 0.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.321 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 50 | 48 | 0 | 0 | 0 | 0 | 10 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.348 | 0.011 | 0.089 | 0.000 | 0.000 | 0.000 | 0.000 | 0.320 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 80 | 67 | 63 | 0 | 0 | 0 | 0 | 10 | 0 |
| N.S. |
1 | 1.07 | 0.89 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
| time (sec) |
N/A | 0.655 | 0.049 | 0.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 105 | 83 | 78 | 0 | 0 | 0 | 0 | 10 | 0 |
| N.S. |
1 | 1.11 | 0.87 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.798 | 0.058 | 0.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 141 | 101 | 158 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.03 | 0.74 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 1.067 | 0.131 | 0.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 113 | 86 | 128 | 0 | 0 | 0 | 0 | 20 | 0 |
| N.S. |
1 | 1.03 | 0.78 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.838 | 0.134 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 86 | 68 | 98 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 1.04 | 0.82 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.458 | 0.021 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.346 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 54 | 68 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 0.291 | 0.017 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 52 | 102 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.291 | 0.097 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.373 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 89 | 68 | 160 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.01 | 0.77 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.415 | 0.111 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.342 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 121 | 94 | 222 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.05 | 0.82 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.550 | 0.132 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.353 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 149 | 102 | 154 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.05 | 0.72 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.689 | 0.025 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.292 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 119 | 87 | 123 | 0 | 0 | 0 | 0 | 22 | 0 |
| N.S. |
1 | 1.04 | 0.76 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.537 | 0.020 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.328 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 88 | 69 | 92 | 0 | 0 | 0 | 0 | 13 | 0 |
| N.S. |
1 | 1.02 | 0.80 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.399 | 0.019 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.348 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 55 | 61 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 0.290 | 0.017 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 54 | 88 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 0.295 | 0.018 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 92 | 69 | 146 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 1.01 | 0.76 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.420 | 0.020 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 125 | 95 | 210 | 0 | 0 | 0 | 0 | 25 | 0 |
| N.S. |
1 | 1.05 | 0.80 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.556 | 0.034 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 53 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
| time (sec) |
N/A | 0.293 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 364 | 318 | 210 | 419 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 0.87 | 0.58 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 0.672 | 0.171 | 0.134 | 0.000 | 0.000 | 0.000 | 0.000 | 0.308 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 200 | 141 | 253 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 0.88 | 0.62 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 0.476 | 0.073 | 0.131 | 0.000 | 0.000 | 0.000 | 0.000 | 0.333 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 108 | 73 | 125 | 0 | 143 | 0 | 0 | 10 | 0 |
| N.S. |
1 | 0.89 | 0.60 | 1.03 | 0.00 | 1.18 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.302 | 0.032 | 0.129 | 0.000 | 0.080 | 0.000 | 0.000 | 0.341 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 36 | 36 | 35 | 39 | 38 | 76 | 48 | 0 | 30 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 1.08 | 1.06 | 2.11 | 1.33 | 0.00 | 0.83 | 0.00 |
| time (sec) |
N/A | 0.487 | 0.001 | 0.082 | 0.028 | 0.082 | 0.354 | 0.000 | 0.332 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 10 | 10 | 12 | 10 | 13 | 13 | 8 | 13 | 24 | 12 |
| N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.30 | 1.30 | 0.80 | 1.30 | 2.40 | 1.20 |
| time (sec) |
N/A | 0.286 | 0.011 | 0.016 | 0.076 | 0.075 | 0.353 | 0.105 | 0.289 | 0.126 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 10 | 10 | 12 | 10 | 13 | 13 | 10 | 13 | 47 | 12 |
| N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.30 | 1.30 | 1.00 | 1.30 | 4.70 | 1.20 |
| time (sec) |
N/A | 0.276 | 0.012 | 0.017 | 0.083 | 0.079 | 0.400 | 0.097 | 0.333 | 0.118 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 456 | 398 | 250 | 530 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 0.87 | 0.55 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 1.122 | 0.212 | 0.160 | 0.000 | 0.000 | 0.000 | 0.000 | 0.279 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 255 | 170 | 332 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 0.87 | 0.58 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 0.863 | 0.093 | 0.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 144 | 94 | 172 | 0 | 178 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 0.88 | 0.58 | 1.06 | 0.00 | 1.09 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 0.388 | 0.043 | 0.138 | 0.000 | 0.087 | 0.000 | 0.000 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 58 | 45 | 55 | 0 | 96 | 80 | 0 | 40 | 0 |
| N.S. |
1 | 1.05 | 0.82 | 1.00 | 0.00 | 1.75 | 1.45 | 0.00 | 0.73 | 0.00 |
| time (sec) |
N/A | 0.438 | 0.003 | 0.080 | 0.000 | 0.088 | 0.431 | 0.000 | 0.312 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 14 | 12 | 15 | 15 | 10 | 15 | 24 | 14 |
| N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.25 | 1.25 | 0.83 | 1.25 | 2.00 | 1.17 |
| time (sec) |
N/A | 0.232 | 0.015 | 0.014 | 0.052 | 0.073 | 0.398 | 0.105 | 0.235 | 0.117 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 14 | 12 | 15 | 15 | 12 | 15 | 107 | 14 |
| N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.25 | 1.25 | 1.00 | 1.25 | 8.92 | 1.17 |
| time (sec) |
N/A | 0.202 | 0.019 | 0.020 | 0.051 | 0.076 | 0.397 | 0.106 | 0.323 | 0.116 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 568 | 518 | 271 | 787 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 0.91 | 0.48 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
| time (sec) |
N/A | 1.309 | 1.168 | 0.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 377 | 345 | 203 | 502 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 0.92 | 0.54 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
| time (sec) |
N/A | 0.835 | 0.416 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 197 | 137 | 274 | 0 | 0 | 0 | 0 | 14 | 0 |
| N.S. |
1 | 0.92 | 0.64 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 0.487 | 0.150 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.306 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 86 | 68 | 98 | 0 | 0 | 0 | 0 | 12 | 0 |
| N.S. |
1 | 1.04 | 0.82 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.394 | 0.013 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |