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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 490 | 479 | 564 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.98 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.143 | 1.200 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 458 | 447 | 516 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.98 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.092 | 0.949 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 508 | 497 | 619 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.98 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.990 | 4.876 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 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 | 23 | 23 | 25 | 23 | 25 | 25 | 20 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.87 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.206 | 0.116 | 0.033 | 0.056 | 0.064 | 5.493 | 0.136 | 0.165 | 24.744 |
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 | 104 | 106 | 99 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.02 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.478 | 0.036 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 73 | 69 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.387 | 0.015 | 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 | 40 | 40 | 51 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.275 | 0.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 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 | 23 | 23 | 25 | 23 | 25 | 25 | 19 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.83 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.204 | 0.065 | 0.030 | 0.060 | 0.063 | 1.497 | 0.127 | 0.155 | 25.219 |
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 | 23 | 23 | 25 | 23 | 25 | 42 | 20 | 25 | 42 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.83 | 0.87 | 1.09 | 1.83 | 1.09 |
time (sec) |
N/A | 0.292 | 0.043 | 0.032 | 0.056 | 0.065 | 2.993 | 0.120 | 0.160 | 26.900 |
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 | 23 | 23 | 25 | 23 | 25 | 59 | 20 | 25 | 59 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.57 | 0.87 | 1.09 | 2.57 | 1.09 |
time (sec) |
N/A | 0.389 | 0.047 | 0.033 | 0.070 | 0.088 | 7.525 | 0.127 | 0.168 | 26.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 0 | 0 | 0 | 15 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.234 | 0.005 | 0.000 | 0.000 | 0.000 | 1.030 | 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 | 33 | 35 | 33 | 0 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.295 | 0.005 | 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 | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 0 | 0 | 0 | 0 | 0 | 0 | 154 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.92 | 0.00 |
time (sec) |
N/A | 0.266 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 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 | 217 | 280 | 196 | 269 | 0 | 247 | 250 | 0 | 33 | 0 |
N.S. |
1 | 1.29 | 0.90 | 1.24 | 0.00 | 1.14 | 1.15 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.618 | 0.629 | 21.110 | 0.000 | 0.076 | 59.211 | 0.000 | 0.158 | 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 | 185 | 240 | 168 | 228 | 0 | 207 | 206 | 0 | 29 | 0 |
N.S. |
1 | 1.30 | 0.91 | 1.23 | 0.00 | 1.12 | 1.11 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.551 | 0.310 | 8.194 | 0.000 | 0.091 | 19.553 | 0.000 | 0.162 | 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 | 106 | 129 | 113 | 169 | 0 | 137 | 136 | 0 | 26 | 0 |
N.S. |
1 | 1.22 | 1.07 | 1.59 | 0.00 | 1.29 | 1.28 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.475 | 0.086 | 3.210 | 0.000 | 0.096 | 5.033 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 0 | 0 | 0 | 26 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.242 | 0.006 | 0.000 | 0.000 | 0.000 | 7.419 | 0.000 | 0.158 | 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 | 142 | 166 | 115 | 204 | 0 | 134 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.17 | 0.81 | 1.44 | 0.00 | 0.94 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.481 | 0.164 | 3.190 | 0.000 | 0.075 | 0.000 | 0.000 | 0.156 | 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 | 202 | 245 | 163 | 268 | 0 | 190 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.21 | 0.81 | 1.33 | 0.00 | 0.94 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.604 | 0.190 | 3.148 | 0.000 | 0.074 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 402 | 0 | 0 | 0 | 296 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.59 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.183 | 0.000 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 352 | 0 | 0 | 0 | 257 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.59 | 0.00 | 0.00 | 0.00 | 1.16 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.067 | 0.000 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 189 | 0 | 0 | 0 | 172 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.44 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.804 | 0.000 | 0.000 | 0.000 | 0.076 | 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 | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 0 | 0 | 0 | 26 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.241 | 0.006 | 0.000 | 0.000 | 0.000 | 3.666 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 237 | 0 | 0 | 0 | 156 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.36 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.890 | 0.000 | 0.000 | 0.000 | 0.079 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 349 | 0 | 0 | 0 | 221 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.47 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.092 | 0.000 | 0.000 | 0.000 | 0.077 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 266 | 844 | 172 | 43 | 0 | 28 | 871 | 28 |
N.S. |
1 | 1.00 | 10.23 | 32.46 | 6.62 | 1.65 | 0.00 | 1.08 | 33.50 | 1.08 |
time (sec) |
N/A | 0.213 | 0.315 | 104.701 | 0.181 | 0.076 | 0.000 | 0.573 | 0.162 | 25.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | B | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 867 | 302 | 35 | 0 | 24 | 41 | 25 |
N.S. |
1 | 1.00 | 1.09 | 37.70 | 13.13 | 1.52 | 0.00 | 1.04 | 1.78 | 1.09 |
time (sec) |
N/A | 0.502 | 0.111 | 0.067 | 0.148 | 0.095 | 0.000 | 0.148 | 0.160 | 25.324 |
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 | 23 | 23 | 25 | 1065 | 427 | 31 | 22 | 25 | 41 | 25 |
N.S. |
1 | 1.00 | 1.09 | 46.30 | 18.57 | 1.35 | 0.96 | 1.09 | 1.78 | 1.09 |
time (sec) |
N/A | 1.091 | 0.064 | 1.328 | 0.179 | 0.106 | 11.995 | 0.129 | 0.148 | 25.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 23 | 32 | 22 | 32 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.85 | 1.19 | 0.81 | 1.19 | 0.85 | 0.85 |
time (sec) |
N/A | 0.235 | 0.005 | 0.396 | 0.034 | 0.069 | 0.344 | 0.125 | 0.150 | 25.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 23 | 32 | 22 | 32 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.85 | 1.19 | 0.81 | 1.19 | 0.85 | 0.85 |
time (sec) |
N/A | 0.225 | 0.003 | 0.083 | 0.034 | 0.067 | 0.202 | 0.112 | 0.150 | 25.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 21 | 15 | 21 | 18 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.17 | 0.83 | 1.17 | 1.00 | 0.94 |
time (sec) |
N/A | 0.210 | 0.003 | 0.050 | 0.029 | 0.064 | 0.246 | 0.136 | 0.157 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 20 | 19 | 37 | 20 | 21 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.86 | 1.68 | 0.91 | 0.95 | 0.91 |
time (sec) |
N/A | 0.228 | 0.003 | 0.172 | 0.034 | 0.065 | 0.597 | 0.133 | 0.147 | 25.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 23 | 20 | 17 | 25 | 22 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 1.00 | 0.87 | 0.74 | 1.09 | 0.96 | 0.83 |
time (sec) |
N/A | 0.227 | 0.004 | 0.105 | 0.033 | 0.068 | 0.202 | 0.107 | 0.156 | 25.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 22 | 23 | 24 | 24 | 28 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.85 | 0.89 | 0.89 | 1.04 | 0.85 | 0.85 |
time (sec) |
N/A | 0.227 | 0.003 | 0.151 | 0.028 | 0.079 | 0.401 | 0.114 | 0.152 | 25.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 22 | 23 | 24 | 24 | 28 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.85 | 0.89 | 0.89 | 1.04 | 0.85 | 0.85 |
time (sec) |
N/A | 0.233 | 0.003 | 0.232 | 0.027 | 0.067 | 0.680 | 0.111 | 0.150 | 25.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 53 | 52 | 47 | 46 | 113 | 49 | 115 | 44 | 46 |
N.S. |
1 | 1.02 | 1.00 | 0.90 | 0.88 | 2.17 | 0.94 | 2.21 | 0.85 | 0.88 |
time (sec) |
N/A | 0.302 | 0.005 | 0.231 | 0.034 | 0.072 | 0.595 | 0.123 | 0.155 | 25.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 43 | 47 | 46 | 113 | 46 | 112 | 43 | 46 |
N.S. |
1 | 0.98 | 0.83 | 0.90 | 0.88 | 2.17 | 0.88 | 2.15 | 0.83 | 0.88 |
time (sec) |
N/A | 0.272 | 0.007 | 0.142 | 0.030 | 0.093 | 0.343 | 0.116 | 0.160 | 25.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 37 | 37 | 40 | 39 | 90 | 39 | 92 | 39 | 39 |
N.S. |
1 | 0.95 | 0.95 | 1.03 | 1.00 | 2.31 | 1.00 | 2.36 | 1.00 | 1.00 |
time (sec) |
N/A | 0.248 | 0.004 | 0.067 | 0.033 | 0.067 | 0.201 | 0.111 | 0.148 | 25.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 20 | 54 | 41 | 59 | 21 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 2.45 | 1.86 | 2.68 | 0.95 | 0.91 |
time (sec) |
N/A | 0.230 | 0.004 | 0.147 | 0.027 | 0.071 | 0.558 | 0.110 | 0.161 | 25.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 45 | 40 | 41 | 46 | 81 | 41 | 90 | 43 | 40 |
N.S. |
1 | 0.98 | 0.87 | 0.89 | 1.00 | 1.76 | 0.89 | 1.96 | 0.93 | 0.87 |
time (sec) |
N/A | 0.290 | 0.006 | 0.112 | 0.032 | 0.067 | 0.204 | 0.115 | 0.151 | 25.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 50 | 43 | 42 | 46 | 87 | 48 | 94 | 44 | 46 |
N.S. |
1 | 0.96 | 0.83 | 0.81 | 0.88 | 1.67 | 0.92 | 1.81 | 0.85 | 0.88 |
time (sec) |
N/A | 0.288 | 0.006 | 0.143 | 0.034 | 0.091 | 0.409 | 0.138 | 0.148 | 25.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 53 | 52 | 43 | 46 | 88 | 51 | 95 | 44 | 46 |
N.S. |
1 | 1.02 | 1.00 | 0.83 | 0.88 | 1.69 | 0.98 | 1.83 | 0.85 | 0.88 |
time (sec) |
N/A | 0.281 | 0.003 | 0.233 | 0.027 | 0.069 | 0.696 | 0.113 | 0.158 | 25.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 137 | 91 | 677 | 282 | 1358 | 0 | 1857 | 522 | 0 |
N.S. |
1 | 1.01 | 0.67 | 5.01 | 2.09 | 10.06 | 0.00 | 13.76 | 3.87 | 0.00 |
time (sec) |
N/A | 0.550 | 0.045 | 13.194 | 0.047 | 0.135 | 0.000 | 0.202 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 94 | 90 | 282 | 149 | 391 | 0 | 576 | 206 | 0 |
N.S. |
1 | 1.01 | 0.97 | 3.03 | 1.60 | 4.20 | 0.00 | 6.19 | 2.22 | 0.00 |
time (sec) |
N/A | 0.402 | 0.030 | 1.969 | 0.041 | 0.085 | 0.000 | 0.148 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 37 | 82 | 62 | 72 | 109 | 114 | 55 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.61 | 1.22 | 1.41 | 2.14 | 2.24 | 1.08 | 0.00 |
time (sec) |
N/A | 0.267 | 0.011 | 0.362 | 0.036 | 0.087 | 1.501 | 0.121 | 0.167 | 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 | 86 | 86 | 85 | 0 | 0 | 105 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 1.22 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.500 | 0.142 | 0.000 | 0.000 | 0.078 | 0.000 | 0.000 | 0.151 | 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 | 127 | 127 | 112 | 0 | 0 | 202 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 1.59 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.630 | 0.254 | 0.000 | 0.000 | 0.074 | 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(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 133 | 0 | 0 | 0 | 0 | 0 | 364 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.72 | 0.00 |
time (sec) |
N/A | 0.510 | 0.186 | 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 | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 0 | 0 | 0 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.480 | 0.139 | 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(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 0 | 0 | 0 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.442 | 0.127 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 108 | 0 | 0 | 73 | 0 | 0 | 202 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.68 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.382 | 0.109 | 0.000 | 0.000 | 0.073 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 34 | 33 | 49 | 80 | 36 | 47 | 33 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.48 | 2.42 | 1.09 | 1.42 | 1.00 |
time (sec) |
N/A | 0.298 | 0.009 | 0.509 | 0.027 | 0.087 | 1.215 | 0.118 | 0.150 | 25.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 107 | 0 | 0 | 0 | 0 | 0 | 239 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 0.441 | 0.126 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 0 | 0 | 0 | 0 | 0 | 249 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.13 | 0.00 |
time (sec) |
N/A | 0.459 | 0.130 | 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 | C | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 101 | 113 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.92 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.512 | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |