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 | F | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 0 | 109 | 130 | 0 | 323 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 0.00 | 2.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 8.033 | 35.419 | 0.000 | 219.358 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 0 | 113 | 0 | 0 | 96 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.04 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.393 | 0.000 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 0 | 106 | 0 | 0 | 96 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.97 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.130 | 0.000 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | C | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 0 | 77 | 29 | 0 | 239 | 42 | 0 | 0 |
N.S. |
1 | 0.00 | 0.71 | 0.27 | 0.00 | 2.19 | 0.39 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.139 | 0.033 | 0.000 | 26.269 | 0.488 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 0 | 109 | 189 | 0 | 93 | 1100 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.73 | 0.00 | 0.85 | 10.09 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.153 | 0.158 | 0.000 | 0.290 | 4.281 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 107 | 667 | 0 | 117 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.97 | 6.06 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 15.265 | 1.088 | 0.000 | 0.463 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 107 | 656 | 0 | 117 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.97 | 5.96 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 15.254 | 1.302 | 0.000 | 0.478 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 110 | 107 | 138 | 27 | 0 | 113 | 0 | 74 | 0 |
N.S. |
1 | 0.97 | 1.25 | 0.25 | 0.00 | 1.03 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.205 | 0.196 | 0.393 | 0.000 | 0.254 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 106 | 110 | 119 | 0 | 136 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.00 | 1.08 | 0.00 | 1.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.204 | 2.640 | 0.000 | 0.532 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 528 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 4.80 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.142 | 0.272 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 122 | 94 | 0 | 233 | 0 | 101 | 0 |
N.S. |
1 | 1.04 | 1.11 | 0.85 | 0.00 | 2.12 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.314 | 0.567 | 1.263 | 0.000 | 1.039 | 0.000 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 97 | 106 | 17 | 121 | 100 | 31 | 0 | 0 |
N.S. |
1 | 0.88 | 0.96 | 0.15 | 1.10 | 0.91 | 0.28 | 0.00 | 0.00 |
time (sec) |
N/A | 0.202 | 0.631 | 1.809 | 0.273 | 0.268 | 1.197 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 281 | 110 | 83 | 25 | 0 | 27 | 25 | 25 |
N.S. |
1 | 2.55 | 1.00 | 0.75 | 0.23 | 0.00 | 0.25 | 0.23 | 0.23 |
time (sec) |
N/A | 0.759 | 0.207 | 196.124 | 0.315 | 0.000 | 6.015 | 0.294 | 5.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 281 | 110 | 83 | 25 | 0 | 27 | 25 | 25 |
N.S. |
1 | 2.55 | 1.00 | 0.75 | 0.23 | 0.00 | 0.25 | 0.23 | 0.23 |
time (sec) |
N/A | 0.648 | 0.001 | 183.590 | 0.304 | 0.000 | 5.880 | 0.292 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 167 | 83 | 119 | 0 | 0 | 0 | 212 | 77 |
N.S. |
1 | 1.52 | 0.75 | 1.08 | 0.00 | 0.00 | 0.00 | 1.93 | 0.70 |
time (sec) |
N/A | 0.398 | 10.049 | 0.383 | 0.000 | 0.000 | 0.000 | 0.299 | 5.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 167 | 138 | 117 | 0 | 0 | 0 | 209 | 71 |
N.S. |
1 | 1.52 | 1.25 | 1.06 | 0.00 | 0.00 | 0.00 | 1.90 | 0.65 |
time (sec) |
N/A | 0.394 | 10.104 | 0.364 | 0.000 | 0.000 | 0.000 | 0.309 | 6.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 167 | 138 | 117 | 0 | 0 | 0 | 209 | 71 |
N.S. |
1 | 1.52 | 1.25 | 1.06 | 0.00 | 0.00 | 0.00 | 1.90 | 0.65 |
time (sec) |
N/A | 0.371 | 10.077 | 0.336 | 0.000 | 0.000 | 0.000 | 0.293 | 5.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 0 | 137 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 147 | 97 | 33 | 0 | 27 | 33 | 33 |
N.S. |
1 | 0.00 | 1.34 | 0.88 | 0.30 | 0.00 | 0.25 | 0.30 | 0.30 |
time (sec) |
N/A | 0.000 | 0.749 | 0.898 | 0.225 | 0.000 | 6.532 | 0.734 | 5.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 147 | 97 | 33 | 0 | 27 | 33 | 33 |
N.S. |
1 | 0.00 | 1.34 | 0.88 | 0.30 | 0.00 | 0.25 | 0.30 | 0.30 |
time (sec) |
N/A | 0.000 | 0.001 | 0.444 | 0.225 | 0.000 | 6.471 | 0.730 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 73 | 152 | 0 | 146 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.66 | 1.38 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.830 | 2.398 | 0.000 | 0.396 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | N/A | N/A | C | N/A | N/A | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 285 | 100 | 112 | 30 | 1308 | 24 | 30 | 30 |
N.S. |
1 | 2.59 | 0.91 | 1.02 | 0.27 | 11.89 | 0.22 | 0.27 | 0.27 |
time (sec) |
N/A | 0.829 | 0.981 | 0.292 | 0.260 | 0.312 | 15.039 | 0.321 | 5.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | N/A | N/A | C | N/A | N/A | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 285 | 100 | 112 | 30 | 1308 | 24 | 30 | 30 |
N.S. |
1 | 2.59 | 0.91 | 1.02 | 0.27 | 11.89 | 0.22 | 0.27 | 0.27 |
time (sec) |
N/A | 0.666 | 0.001 | 0.224 | 0.257 | 0.278 | 15.514 | 0.304 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F | B | F | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 0 | 92 | 0 | 743 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.84 | 0.00 | 6.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 6.708 | 0.000 | 0.487 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 107 | 84 | 298 | 0 | 87 | 0 | 188 | 0 |
N.S. |
1 | 0.97 | 0.76 | 2.71 | 0.00 | 0.79 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.563 | 0.175 | 0.117 | 0.000 | 1.578 | 0.000 | 0.518 | 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 | 110 | 96 | 84 | 170 | 0 | 74 | 0 | 86 | 0 |
N.S. |
1 | 0.87 | 0.76 | 1.55 | 0.00 | 0.67 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.496 | 0.101 | 0.109 | 0.000 | 1.666 | 0.000 | 0.508 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 92 | 89 | 71 | 0 | 0 | 122 | 74 | 0 |
N.S. |
1 | 0.84 | 0.81 | 0.65 | 0.00 | 0.00 | 1.11 | 0.67 | 0.00 |
time (sec) |
N/A | 0.365 | 0.136 | 0.150 | 0.000 | 0.000 | 0.449 | 0.605 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 118 | 107 | 106 | 125 | 392 | 126 | 100 | 279 |
N.S. |
1 | 1.07 | 0.97 | 0.96 | 1.14 | 3.56 | 1.15 | 0.91 | 2.54 |
time (sec) |
N/A | 0.737 | 0.118 | 0.137 | 0.178 | 0.269 | 5.223 | 0.273 | 5.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | C | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 78 | 31 | 0 | 213 | 48 | 0 | 0 |
N.S. |
1 | 0.00 | 0.71 | 0.28 | 0.00 | 1.94 | 0.44 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.123 | 0.034 | 0.000 | 22.886 | 0.580 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 0 | 124 | 0 | 0 | 71 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.13 | 0.00 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.232 | 0.000 | 0.000 | 0.291 | 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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 73 | 105 | 0 | 0 | 66 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.95 | 0.00 | 0.00 | 0.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.284 | 0.147 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 111 | 307 | 0 | 107 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 2.77 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.100 | 1.175 | 0.000 | 0.679 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 90 | 105 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.81 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 13.284 | 1.128 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | C | F | B | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 111 | 412 | 106 | 584 | 0 | 373 | 0 | 0 | 509 |
N.S. |
1 | 3.71 | 0.95 | 5.26 | 0.00 | 3.36 | 0.00 | 0.00 | 4.59 |
time (sec) |
N/A | 1.085 | 1.149 | 3.814 | 0.000 | 0.306 | 0.000 | 0.000 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 111 | 155 | 129 | 42 | 0 | 119 | 0 | 74 | 44 |
N.S. |
1 | 1.40 | 1.16 | 0.38 | 0.00 | 1.07 | 0.00 | 0.67 | 0.40 |
time (sec) |
N/A | 0.292 | 0.189 | 0.363 | 0.000 | 0.288 | 0.000 | 0.299 | 5.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 111 | 107 | 138 | 42 | 0 | 119 | 0 | 74 | 44 |
N.S. |
1 | 0.96 | 1.24 | 0.38 | 0.00 | 1.07 | 0.00 | 0.67 | 0.40 |
time (sec) |
N/A | 0.222 | 0.176 | 0.330 | 0.000 | 0.262 | 0.000 | 0.282 | 5.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 123 | 146 | 15 | 0 | 108 | 0 | 79 | 0 |
N.S. |
1 | 1.11 | 1.32 | 0.14 | 0.00 | 0.97 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.240 | 0.233 | 0.384 | 0.000 | 0.253 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 212 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 43.697 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | F | F | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 312 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.81 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 104 | 111 | 119 | 0 | 133 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.00 | 1.07 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.243 | 2.480 | 0.000 | 0.621 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 66 | 97 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.59 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 11.946 | 0.946 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 155 | 139 | 122 | 0 | 622 | 0 | 257 | 0 |
N.S. |
1 | 1.40 | 1.25 | 1.10 | 0.00 | 5.60 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.340 | 0.461 | 0.454 | 0.000 | 0.317 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 111 | 104 | 0 | 136 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.266 | 6.138 | 0.000 | 3.646 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 107 | 110 | 0 | 141 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.99 | 0.00 | 1.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.374 | 5.631 | 0.000 | 4.886 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 111 | 86 | 107 | 58 | 93 | 116 | 167 | 0 | 0 |
N.S. |
1 | 0.77 | 0.96 | 0.52 | 0.84 | 1.05 | 1.50 | 0.00 | 0.00 |
time (sec) |
N/A | 0.216 | 0.426 | 3.513 | 0.269 | 0.430 | 1.784 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 148 | 98 | 33 | 0 | 27 | 33 | 36 |
N.S. |
1 | 0.00 | 1.33 | 0.88 | 0.30 | 0.00 | 0.24 | 0.30 | 0.32 |
time (sec) |
N/A | 0.000 | 0.784 | 0.736 | 0.223 | 0.000 | 4.474 | 0.729 | 5.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 148 | 98 | 33 | 0 | 27 | 33 | 36 |
N.S. |
1 | 0.00 | 1.33 | 0.88 | 0.30 | 0.00 | 0.24 | 0.30 | 0.32 |
time (sec) |
N/A | 0.000 | 0.001 | 0.463 | 0.218 | 0.000 | 4.533 | 0.732 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 111 | 88 | 75 | 639 | 0 | 666 | 0 | 0 | 0 |
N.S. |
1 | 0.79 | 0.68 | 5.76 | 0.00 | 6.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.312 | 0.219 | 8.050 | 0.000 | 2.887 | 0.000 | 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 | 111 | 128 | 102 | 160 | 162 | 84 | 187 | 160 | 0 |
N.S. |
1 | 1.15 | 0.92 | 1.44 | 1.46 | 0.76 | 1.68 | 1.44 | 0.00 |
time (sec) |
N/A | 0.681 | 0.108 | 0.263 | 0.190 | 0.277 | 0.664 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 91 | 90 | 0 | 0 | 68 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 0.81 | 0.00 | 0.00 | 0.61 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.483 | 0.137 | 0.000 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 118 | 153 | 33 | 0 | 107 | 0 | 89 | 0 |
N.S. |
1 | 1.05 | 1.37 | 0.29 | 0.00 | 0.96 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.284 | 0.704 | 1.707 | 0.000 | 0.363 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 154 | 183 | 17 | 0 | 108 | 0 | 97 | 0 |
N.S. |
1 | 1.38 | 1.63 | 0.15 | 0.00 | 0.96 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.345 | 3.226 | 1.951 | 0.000 | 0.398 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | C | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 153 | 107 | 110 | 148 | 279 | 61 | 0 | 72 |
N.S. |
1 | 1.37 | 0.96 | 0.98 | 1.32 | 2.49 | 0.54 | 0.00 | 0.64 |
time (sec) |
N/A | 0.387 | 5.624 | 9.693 | 0.264 | 11.771 | 1.325 | 0.000 | 5.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 112 | 114 | 0 | 137 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.02 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.448 | 3.891 | 0.000 | 1.282 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 128 | 129 | 104 | 0 | 247 | 0 | 100 | 0 |
N.S. |
1 | 1.14 | 1.15 | 0.93 | 0.00 | 2.21 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.354 | 0.619 | 1.566 | 0.000 | 1.019 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 142 | 156 | 206 | 0 | 434 | 0 | 97 | 0 |
N.S. |
1 | 1.27 | 1.39 | 1.84 | 0.00 | 3.88 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.663 | 0.354 | 2.358 | 0.000 | 10.414 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 55 | 140 | 127 | 0 | 611 | 0 | 208 | 0 |
N.S. |
1 | 0.49 | 1.25 | 1.13 | 0.00 | 5.46 | 0.00 | 1.86 | 0.00 |
time (sec) |
N/A | 0.487 | 0.395 | 0.533 | 0.000 | 42.421 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 176 | 129 | 131 | 0 | 253 | 0 | 261 | 0 |
N.S. |
1 | 1.57 | 1.15 | 1.17 | 0.00 | 2.26 | 0.00 | 2.33 | 0.00 |
time (sec) |
N/A | 0.373 | 0.467 | 0.419 | 0.000 | 0.258 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 115 | 136 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.03 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.341 | 0.881 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | F | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 469 | 0 | 136 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 4.19 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.556 | 0.000 | 1.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 96 | 107 | 33 | 122 | 102 | 31 | 0 | 0 |
N.S. |
1 | 0.86 | 0.96 | 0.29 | 1.09 | 0.91 | 0.28 | 0.00 | 0.00 |
time (sec) |
N/A | 0.212 | 1.811 | 2.138 | 0.267 | 0.282 | 1.615 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 97 | 107 | 33 | 121 | 102 | 32 | 0 | 0 |
N.S. |
1 | 0.87 | 0.96 | 0.29 | 1.08 | 0.91 | 0.29 | 0.00 | 0.00 |
time (sec) |
N/A | 0.208 | 0.628 | 1.824 | 0.275 | 0.272 | 1.275 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 97 | 107 | 33 | 121 | 102 | 34 | 0 | 0 |
N.S. |
1 | 0.87 | 0.96 | 0.29 | 1.08 | 0.91 | 0.30 | 0.00 | 0.00 |
time (sec) |
N/A | 0.211 | 0.758 | 2.085 | 0.271 | 0.263 | 1.155 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 97 | 107 | 17 | 122 | 102 | 29 | 0 | 0 |
N.S. |
1 | 0.87 | 0.96 | 0.15 | 1.09 | 0.91 | 0.26 | 0.00 | 0.00 |
time (sec) |
N/A | 0.202 | 1.765 | 2.105 | 0.264 | 0.268 | 1.716 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 97 | 111 | 17 | 121 | 102 | 31 | 0 | 0 |
N.S. |
1 | 0.87 | 0.99 | 0.15 | 1.08 | 0.91 | 0.28 | 0.00 | 0.00 |
time (sec) |
N/A | 0.204 | 0.758 | 1.957 | 0.254 | 0.272 | 1.186 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 112 | 85 | 30 | 0 | 49 | 30 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.76 | 0.27 | 0.00 | 0.44 | 0.27 | 0.27 |
time (sec) |
N/A | 0.000 | 0.226 | 158.563 | 0.323 | 0.000 | 54.695 | 0.278 | 5.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 112 | 85 | 30 | 0 | 49 | 30 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.76 | 0.27 | 0.00 | 0.44 | 0.27 | 0.27 |
time (sec) |
N/A | 0.000 | 0.001 | 152.099 | 0.324 | 0.000 | 53.335 | 0.285 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F(-1) | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 587 | 112 | 0 | 37 | 0 | 0 | 37 | 37 |
N.S. |
1 | 5.24 | 1.00 | 0.00 | 0.33 | 0.00 | 0.00 | 0.33 | 0.33 |
time (sec) |
N/A | 1.340 | 0.236 | 0.000 | 0.323 | 0.000 | 0.000 | 0.325 | 6.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F(-1) | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 587 | 112 | 0 | 37 | 0 | 0 | 37 | 37 |
N.S. |
1 | 5.24 | 1.00 | 0.00 | 0.33 | 0.00 | 0.00 | 0.33 | 0.33 |
time (sec) |
N/A | 1.141 | 0.001 | 0.000 | 0.314 | 0.000 | 0.000 | 0.326 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F(-1) | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 679 | 112 | 0 | 30 | 0 | 0 | 30 | 30 |
N.S. |
1 | 6.06 | 1.00 | 0.00 | 0.27 | 0.00 | 0.00 | 0.27 | 0.27 |
time (sec) |
N/A | 1.157 | 0.220 | 0.000 | 0.317 | 0.000 | 0.000 | 0.300 | 6.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | C | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 679 | 112 | 1803 | 30 | 0 | 0 | 30 | 30 |
N.S. |
1 | 6.06 | 1.00 | 16.10 | 0.27 | 0.00 | 0.00 | 0.27 | 0.27 |
time (sec) |
N/A | 1.009 | 0.001 | 5.320 | 0.315 | 0.000 | 0.000 | 0.298 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | C | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 505 | 112 | 9294 | 37 | 0 | 0 | 37 | 36 |
N.S. |
1 | 4.51 | 1.00 | 82.98 | 0.33 | 0.00 | 0.00 | 0.33 | 0.32 |
time (sec) |
N/A | 1.125 | 0.240 | 33.408 | 0.328 | 0.000 | 0.000 | 0.279 | 5.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | C | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 505 | 112 | 7521 | 37 | 0 | 0 | 37 | 36 |
N.S. |
1 | 4.51 | 1.00 | 67.15 | 0.33 | 0.00 | 0.00 | 0.33 | 0.32 |
time (sec) |
N/A | 0.912 | 0.001 | 37.957 | 0.318 | 0.000 | 0.000 | 0.298 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 615 | 112 | 85 | 39 | 0 | 0 | 0 | 39 |
N.S. |
1 | 5.49 | 1.00 | 0.76 | 0.35 | 0.00 | 0.00 | 0.00 | 0.35 |
time (sec) |
N/A | 1.313 | 0.229 | 152.860 | 0.332 | 0.000 | 0.000 | 0.000 | 5.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 615 | 112 | 85 | 39 | 0 | 0 | 0 | 39 |
N.S. |
1 | 5.49 | 1.00 | 0.76 | 0.35 | 0.00 | 0.00 | 0.00 | 0.35 |
time (sec) |
N/A | 1.082 | 0.001 | 138.905 | 0.320 | 0.000 | 0.000 | 0.000 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 112 | 114 | 0 | 152 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.02 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.404 | 34.090 | 0.000 | 11.165 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 94 | 24 | 26 | 6296 | 31 | 26 | 26 |
N.S. |
1 | 0.00 | 0.84 | 0.21 | 0.23 | 56.21 | 0.28 | 0.23 | 0.23 |
time (sec) |
N/A | 0.000 | 0.228 | 0.015 | 0.324 | 9.682 | 10.701 | 0.301 | 5.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | C | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 0 | 94 | 24 | 26 | 6296 | 31 | 26 | 26 |
N.S. |
1 | 0.00 | 0.84 | 0.21 | 0.23 | 56.21 | 0.28 | 0.23 | 0.23 |
time (sec) |
N/A | 0.000 | 0.001 | 0.002 | 0.329 | 9.656 | 10.641 | 0.323 | 0.002 |
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 | 112 | 93 | 91 | 0 | 0 | 72 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.81 | 0.00 | 0.00 | 0.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.283 | 0.127 | 0.000 | 0.000 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 95 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.291 | 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 | C | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 145 | 153 | 15 | 0 | 105 | 0 | 88 | 0 |
N.S. |
1 | 1.28 | 1.35 | 0.13 | 0.00 | 0.93 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.281 | 0.271 | 0.648 | 0.000 | 0.266 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 151 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.598 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 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 | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 136 | 113 | 94 | 0 | 555 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 1.00 | 0.83 | 0.00 | 4.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.377 | 0.323 | 0.671 | 0.000 | 0.374 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 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 | N/A | N/A | C | N/A | C | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 422 | 144 | 175 | 24 | 451 | 31 | 57 | 24 |
N.S. |
1 | 3.73 | 1.27 | 1.55 | 0.21 | 3.99 | 0.27 | 0.50 | 0.21 |
time (sec) |
N/A | 1.217 | 0.364 | 23.171 | 0.326 | 0.281 | 0.962 | 0.313 | 5.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 59 | 149 | 130 | 0 | 622 | 0 | 213 | 0 |
N.S. |
1 | 0.52 | 1.32 | 1.15 | 0.00 | 5.50 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.508 | 0.420 | 0.556 | 0.000 | 42.721 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 10.325 | 0.000 | 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(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 155 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 4.446 | 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 | N/A | N/A | C | N/A | C | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 152 | 142 | 121 | 53 | 1149 | 32 | 218 | 22 |
N.S. |
1 | 1.35 | 1.26 | 1.07 | 0.47 | 10.17 | 0.28 | 1.93 | 0.19 |
time (sec) |
N/A | 1.050 | 0.347 | 48.372 | 0.335 | 3.560 | 0.670 | 0.315 | 5.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | C | N/A | C | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 152 | 142 | 121 | 53 | 1149 | 32 | 218 | 22 |
N.S. |
1 | 1.35 | 1.26 | 1.07 | 0.47 | 10.17 | 0.28 | 1.93 | 0.19 |
time (sec) |
N/A | 1.015 | 0.002 | 45.010 | 0.321 | 3.595 | 0.683 | 0.317 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | C | N/A | F(-2) | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 884 | 148 | 100 | 100 | 3429 | 37 | 0 | 25 |
N.S. |
1 | 7.82 | 1.31 | 0.88 | 0.88 | 30.35 | 0.33 | 0.00 | 0.22 |
time (sec) |
N/A | 2.129 | 0.358 | 102.074 | 0.331 | 10.149 | 1.410 | 0.000 | 5.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | N/A | N/A | C | N/A | F(-2) | N/A |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 884 | 148 | 100 | 100 | 3429 | 37 | 0 | 25 |
N.S. |
1 | 7.82 | 1.31 | 0.88 | 0.88 | 30.35 | 0.33 | 0.00 | 0.22 |
time (sec) |
N/A | 1.746 | 0.001 | 127.428 | 0.310 | 10.119 | 1.398 | 0.000 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 107 | 375 | 0 | 154 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.95 | 3.32 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.019 | 1.383 | 0.000 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 114 | 131 | 109 | 33 | 170 | 106 | 32 | 0 | 0 |
N.S. |
1 | 1.15 | 0.96 | 0.29 | 1.49 | 0.93 | 0.28 | 0.00 | 0.00 |
time (sec) |
N/A | 0.240 | 0.278 | 1.060 | 0.273 | 0.255 | 18.657 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 114 | 100 | 131 | 27 | 0 | 137 | 0 | 74 | 0 |
N.S. |
1 | 0.88 | 1.15 | 0.24 | 0.00 | 1.20 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.253 | 0.171 | 0.376 | 0.000 | 0.246 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 114 | 100 | 131 | 40 | 0 | 137 | 0 | 74 | 0 |
N.S. |
1 | 0.88 | 1.15 | 0.35 | 0.00 | 1.20 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.238 | 0.181 | 0.398 | 0.000 | 0.251 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 2392 | 116 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 20.98 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 10.625 | 0.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 0 | 135 | 74 | 29 | 0 | 26 | 1 | 29 |
N.S. |
1 | 0.00 | 1.18 | 0.65 | 0.25 | 0.00 | 0.23 | 0.01 | 0.25 |
time (sec) |
N/A | 0.000 | 1.785 | 168.425 | 0.326 | 0.000 | 1.709 | 0.380 | 5.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | C | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 797 | 87 | 390 | 0 | 413 | 0 | 0 | 0 |
N.S. |
1 | 6.99 | 0.76 | 3.42 | 0.00 | 3.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.710 | 1.651 | 3.275 | 0.000 | 4.548 | 0.000 | 0.000 | 0.000 |