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 | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 247 | 103 | 262 | 0 | 148 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.11 | 0.46 | 1.18 | 0.00 | 0.67 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.296 | 8.195 | 0.968 | 0.000 | 0.071 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 283 | 109 | 329 | 0 | 168 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.14 | 0.44 | 1.32 | 0.00 | 0.67 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.339 | 8.292 | 1.132 | 0.000 | 0.092 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 283 | 109 | 273 | 0 | 138 | 0 | 0 | 792 | 0 |
N.S. |
1 | 1.12 | 0.43 | 1.08 | 0.00 | 0.55 | 0.00 | 0.00 | 3.13 | 0.00 |
time (sec) |
N/A | 0.327 | 8.857 | 0.859 | 0.000 | 0.080 | 0.000 | 0.000 | 2.750 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 247 | 104 | 253 | 0 | 133 | 0 | 0 | 769 | 0 |
N.S. |
1 | 1.11 | 0.47 | 1.14 | 0.00 | 0.60 | 0.00 | 0.00 | 3.46 | 0.00 |
time (sec) |
N/A | 0.296 | 8.529 | 0.841 | 0.000 | 0.076 | 0.000 | 0.000 | 2.375 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 211 | 99 | 234 | 0 | 128 | 0 | 0 | 746 | 0 |
N.S. |
1 | 1.10 | 0.52 | 1.23 | 0.00 | 0.67 | 0.00 | 0.00 | 3.91 | 0.00 |
time (sec) |
N/A | 0.264 | 8.392 | 0.798 | 0.000 | 0.080 | 0.000 | 0.000 | 2.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 211 | 99 | 234 | 0 | 128 | 0 | 0 | 728 | 0 |
N.S. |
1 | 1.10 | 0.52 | 1.23 | 0.00 | 0.67 | 0.00 | 0.00 | 3.81 | 0.00 |
time (sec) |
N/A | 0.266 | 8.077 | 0.846 | 0.000 | 0.076 | 0.000 | 0.000 | 1.706 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 211 | 99 | 234 | 0 | 128 | 0 | 0 | 700 | 0 |
N.S. |
1 | 1.10 | 0.52 | 1.23 | 0.00 | 0.67 | 0.00 | 0.00 | 3.66 | 0.00 |
time (sec) |
N/A | 0.269 | 7.956 | 0.818 | 0.000 | 0.100 | 0.000 | 0.000 | 1.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 207 | 98 | 234 | 0 | 128 | 0 | 0 | 679 | 0 |
N.S. |
1 | 1.11 | 0.52 | 1.25 | 0.00 | 0.68 | 0.00 | 0.00 | 3.63 | 0.00 |
time (sec) |
N/A | 0.271 | 7.093 | 0.813 | 0.000 | 0.097 | 0.000 | 0.000 | 1.425 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 211 | 98 | 234 | 0 | 128 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.10 | 0.51 | 1.23 | 0.00 | 0.67 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.268 | 7.425 | 0.807 | 0.000 | 0.069 | 0.000 | 0.000 | 1.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 211 | 98 | 234 | 0 | 128 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.10 | 0.51 | 1.23 | 0.00 | 0.67 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.266 | 7.608 | 0.887 | 0.000 | 0.089 | 0.000 | 0.000 | 1.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 247 | 103 | 262 | 0 | 148 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.11 | 0.46 | 1.18 | 0.00 | 0.67 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.297 | 7.311 | 1.012 | 0.000 | 0.101 | 0.000 | 0.000 | 1.416 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 283 | 108 | 245 | 0 | 168 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.12 | 0.43 | 0.97 | 0.00 | 0.66 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.309 | 8.239 | 1.088 | 0.000 | 0.072 | 0.000 | 0.000 | 1.691 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 319 | 113 | 310 | 0 | 188 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.14 | 0.40 | 1.11 | 0.00 | 0.67 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.342 | 8.546 | 1.253 | 0.000 | 0.081 | 0.000 | 0.000 | 1.748 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1081 | 1228 | 92 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.14 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.294 | 10.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 15.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 387 | 99 | 0 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.21 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.361 | 10.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.370 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1135 | 1247 | 204 | 0 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.10 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.151 | 21.703 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 121 | 210 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 21.672 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 51.762 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 121 | 187 | 0 | 0 | 0 | 0 | 0 | 1146 | 0 |
N.S. |
1 | 1.15 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.91 | 0.00 |
time (sec) |
N/A | 0.299 | 21.580 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 31.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 121 | 92 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.15 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.292 | 10.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 17.625 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 121 | 99 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.15 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.256 | 10.088 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 17.676 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 121 | 202 | 0 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.15 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.303 | 21.614 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 23.687 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 116 | 212 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.16 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.307 | 21.465 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 116 | 202 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.16 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.306 | 21.360 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 116 | 201 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.16 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.297 | 21.378 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 296 | 97 | 0 | 0 | 891 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.33 | 0.00 | 0.00 | 3.02 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.420 | 10.095 | 0.000 | 0.000 | 0.282 | 0.000 | 0.000 | 0.216 | 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 | 569 | 351 | 528 | 0 | 0 | 1857 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.93 | 0.00 | 0.00 | 3.26 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 1.578 | 0.000 | 0.000 | 0.353 | 0.000 | 0.000 | 96.884 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 261 | 319 | 0 | 0 | 1196 | 0 | 0 | 954 | 0 |
N.S. |
1 | 0.79 | 0.96 | 0.00 | 0.00 | 3.60 | 0.00 | 0.00 | 2.87 | 0.00 |
time (sec) |
N/A | 0.279 | 0.926 | 0.000 | 0.000 | 0.164 | 0.000 | 0.000 | 57.839 | 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 | 220 | 205 | 248 | 0 | 0 | 716 | 0 | 0 | 326 | 0 |
N.S. |
1 | 0.93 | 1.13 | 0.00 | 0.00 | 3.25 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.219 | 0.422 | 0.000 | 0.000 | 0.128 | 0.000 | 0.000 | 24.598 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 395 | 517 | 0 | 0 | 2014 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.96 | 1.26 | 0.00 | 0.00 | 4.91 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.437 | 1.479 | 0.000 | 0.000 | 2.233 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 418 | 390 | 524 | 0 | 0 | 3608 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.93 | 1.25 | 0.00 | 0.00 | 8.63 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.353 | 1.557 | 0.000 | 0.000 | 2.790 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 318 | 375 | 0 | 0 | 3990 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.98 | 1.15 | 0.00 | 0.00 | 12.28 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.313 | 2.600 | 0.000 | 0.000 | 0.314 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 482 | 409 | 577 | 0 | 0 | 7932 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.85 | 1.20 | 0.00 | 0.00 | 16.46 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.370 | 6.929 | 0.000 | 0.000 | 1.096 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 310 | 175 | 0 | 0 | 1400 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.66 | 0.37 | 0.00 | 0.00 | 2.96 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.357 | 10.130 | 0.000 | 0.000 | 0.224 | 0.000 | 0.000 | 1.164 | 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 | 274 | 220 | 295 | 0 | 0 | 892 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.80 | 1.08 | 0.00 | 0.00 | 3.26 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.245 | 9.046 | 0.000 | 0.000 | 0.124 | 0.000 | 0.000 | 0.863 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 164 | 229 | 0 | 0 | 618 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.95 | 1.33 | 0.00 | 0.00 | 3.59 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.200 | 0.069 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.290 | 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 | 340 | 339 | 491 | 0 | 0 | 509 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.00 | 1.50 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.312 | 5.298 | 0.000 | 0.000 | 0.132 | 0.000 | 0.000 | 200.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 256 | 361 | 0 | 0 | 2504 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.41 | 0.00 | 0.00 | 9.78 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.260 | 8.404 | 0.000 | 0.000 | 0.198 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 374 | 347 | 175 | 0 | 0 | 4778 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.93 | 0.47 | 0.00 | 0.00 | 12.78 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.325 | 10.143 | 0.000 | 0.000 | 0.727 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 591 | 528 | 265 | 0 | 0 | 9090 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.89 | 0.45 | 0.00 | 0.00 | 15.38 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.580 | 10.332 | 0.000 | 0.000 | 5.571 | 0.000 | 0.000 | 200.025 | 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 | 608 | 395 | 585 | 0 | 0 | 1481 | 0 | 0 | 96 | 0 |
N.S. |
1 | 0.65 | 0.96 | 0.00 | 0.00 | 2.44 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.489 | 1.099 | 0.000 | 0.000 | 0.464 | 0.000 | 0.000 | 1.045 | 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 | 367 | 269 | 368 | 0 | 0 | 1001 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.73 | 1.00 | 0.00 | 0.00 | 2.73 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.341 | 0.685 | 0.000 | 0.000 | 0.141 | 0.000 | 0.000 | 0.694 | 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 | 201 | 179 | 234 | 0 | 0 | 660 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.89 | 1.16 | 0.00 | 0.00 | 3.28 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.217 | 0.397 | 0.000 | 0.000 | 0.104 | 0.000 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 173 | 0 | 0 | 521 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.99 | 1.36 | 0.00 | 0.00 | 4.10 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.179 | 0.026 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 197 | 225 | 0 | 0 | 1825 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 9.26 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.256 | 0.353 | 0.000 | 0.000 | 0.165 | 0.000 | 0.000 | 1.761 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 286 | 368 | 0 | 0 | 2857 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.98 | 1.26 | 0.00 | 0.00 | 9.75 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.282 | 1.111 | 0.000 | 0.000 | 0.430 | 0.000 | 0.000 | 4.466 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 477 | 415 | 525 | 0 | 0 | 5445 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.87 | 1.10 | 0.00 | 0.00 | 11.42 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.431 | 3.797 | 0.000 | 0.000 | 3.814 | 0.000 | 0.000 | 10.027 | 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 | 187 | 200 | 173 | 0 | 0 | 0 | 0 | 0 | 124 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.340 | 10.422 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.037 | 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 | 140 | 182 | 144 | 0 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.30 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.289 | 10.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.438 | 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 | 91 | 129 | 109 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.42 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.219 | 10.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.843 | 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 | 68 | 88 | 87 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.29 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.179 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 300 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.241 | 5.653 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.947 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 332 | 288 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.15 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.346 | 22.729 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.446 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 393 | 305 | 0 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.16 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.420 | 22.684 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.036 | 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 | 182 | 197 | 144 | 0 | 0 | 0 | 0 | 0 | 347 | 0 |
N.S. |
1 | 1.08 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.347 | 10.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.281 | 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 | 131 | 177 | 111 | 0 | 0 | 0 | 0 | 0 | 256 | 0 |
N.S. |
1 | 1.35 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 0.261 | 10.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.554 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 26 | 44 | 0 | 0 | 165 | 75 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 1.38 | 0.00 | 0.00 | 5.16 | 2.34 |
time (sec) |
N/A | 0.138 | 10.020 | 0.477 | 0.096 | 0.147 | 0.000 | 0.000 | 0.945 | 2.301 |
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 | 68 | 98 | 87 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.44 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.187 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 676 | 113 | 145 | 0 | 0 | 0 | 0 | 0 | 140 | 0 |
N.S. |
1 | 0.17 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.217 | 22.550 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.078 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 729 | 114 | 289 | 0 | 0 | 0 | 0 | 0 | 206 | 0 |
N.S. |
1 | 0.16 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.228 | 22.780 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.490 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 790 | 116 | 324 | 0 | 0 | 0 | 0 | 0 | 272 | 0 |
N.S. |
1 | 0.15 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.221 | 22.830 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.105 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 439 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 3.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.190 | 1.144 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.656 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 563 | 362 | 175 | 0 | 0 | 2267 | 0 | 0 | 234 | 0 |
N.S. |
1 | 0.64 | 0.31 | 0.00 | 0.00 | 4.03 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.405 | 10.152 | 0.000 | 0.000 | 0.206 | 0.000 | 0.000 | 2.388 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 277 | 114 | 0 | 0 | 1386 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.94 | 0.39 | 0.00 | 0.00 | 4.70 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.312 | 10.088 | 0.000 | 0.000 | 0.147 | 0.000 | 0.000 | 1.431 | 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 | 196 | 194 | 247 | 0 | 0 | 306 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.99 | 1.26 | 0.00 | 0.00 | 1.56 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.234 | 0.180 | 0.000 | 0.000 | 0.111 | 0.000 | 0.000 | 0.713 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 412 | 148 | 0 | 0 | 738 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.08 | 0.39 | 0.00 | 0.00 | 1.94 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.428 | 10.138 | 0.000 | 0.000 | 0.283 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 314 | 123 | 0 | 0 | 651 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.07 | 0.42 | 0.00 | 0.00 | 2.22 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.310 | 10.044 | 0.000 | 0.000 | 0.119 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 404 | 214 | 0 | 0 | 6825 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.94 | 0.50 | 0.00 | 0.00 | 15.95 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.370 | 10.262 | 0.000 | 0.000 | 0.814 | 0.000 | 0.000 | 200.095 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 645 | 588 | 320 | 0 | 0 | 12723 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.91 | 0.50 | 0.00 | 0.00 | 19.73 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.755 | 10.466 | 0.000 | 0.000 | 5.509 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 241 | 118 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.439 | 10.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 57.761 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 227 | 118 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.90 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.379 | 10.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 237 | 136 | 0 | 0 | 2271 | 0 | 0 | 168 | 0 |
N.S. |
1 | 1.11 | 0.64 | 0.00 | 0.00 | 10.66 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.362 | 10.073 | 0.000 | 0.000 | 0.171 | 0.000 | 0.000 | 6.961 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | C | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 256 | 122 | 0 | 0 | 2736 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.08 | 0.52 | 0.00 | 0.00 | 11.59 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.370 | 10.049 | 0.000 | 0.000 | 0.302 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 473 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 3.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.259 | 22.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 318 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 2.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.239 | 21.505 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 536 | 0 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.00 | 4.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.239 | 22.574 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 13.758 | 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 | 118 | 156 | 118 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.32 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.234 | 10.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 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 | 206 | 248 | 172 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.20 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.291 | 10.200 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.143 | 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 | 90 | 90 | 71 | 0 | 0 | 0 | 0 | 0 | 289 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.21 | 0.00 |
time (sec) |
N/A | 0.204 | 0.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 72 | 72 | 60 | 0 | 0 | 0 | 0 | 0 | 175 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 0.190 | 0.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 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 | 54 | 54 | 39 | 0 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 0.158 | 0.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 55 | 0 | 0 | 0 | 105 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 1.52 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.169 | 0.147 | 0.000 | 0.000 | 0.000 | 0.802 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 82 | 0 | 0 | 0 | 366 | 0 | 29 | 0 |
N.S. |
1 | 1.05 | 0.87 | 0.00 | 0.00 | 0.00 | 3.89 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.205 | 0.082 | 0.000 | 0.000 | 0.000 | 1.415 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 134 | 104 | 0 | 0 | 0 | 1062 | 0 | 34 | 0 |
N.S. |
1 | 1.08 | 0.84 | 0.00 | 0.00 | 0.00 | 8.56 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.250 | 0.107 | 0.000 | 0.000 | 0.000 | 1.950 | 0.000 | 0.155 | 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 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 1219 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 23.44 | 0.00 |
time (sec) |
N/A | 0.164 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 220 | 174 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.18 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.331 | 0.189 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 332 | 247 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.18 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.504 | 0.356 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 50 | 50 | 47 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.159 | 1.257 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | 43 | 43 | 48 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.152 | 1.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 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 | 45 | 45 | 47 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.158 | 1.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 38 | 38 | 48 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.146 | 1.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 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 | 83 | 83 | 144 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.205 | 0.318 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 183 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.198 | 0.778 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 186 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.206 | 3.329 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.293 | 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 | 82 | 82 | 124 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.186 | 1.512 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 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 | 82 | 82 | 151 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.191 | 0.323 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 263 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 3.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.201 | 3.626 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 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 | 123 | 123 | 121 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.262 | 1.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.299 | 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 | 121 | 121 | 119 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.238 | 1.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.310 | 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 | 128 | 128 | 241 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.240 | 2.649 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.592 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 262 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.235 | 2.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.435 | 0.000 |