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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 215 | 336 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.831 | 0.781 | 0.506 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 316 | 266 | 313 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.43 | 1.20 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 3.522 | 1.898 | 0.543 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 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 | 24 | 24 | 26 | 22 | 24 | 43 | 26 | 24 | 48 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 1.08 | 1.00 | 2.00 | 1.00 |
time (sec) |
N/A | 0.271 | 0.483 | 0.731 | 0.370 | 0.094 | 97.119 | 0.174 | 0.244 | 4.048 |
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 | 220 | 220 | 249 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.394 | 0.348 | 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 | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 234 | 541 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.95 | 2.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.302 | 0.661 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 93 | 45 | 56 | 88 | 91 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.99 | 0.48 | 0.60 | 0.94 | 0.97 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.386 | 0.049 | 0.524 | 0.034 | 0.092 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 90 | 45 | 56 | 86 | 87 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 0.51 | 0.64 | 0.98 | 0.99 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.339 | 0.037 | 0.510 | 0.034 | 0.099 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 220 | 230 | 305 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.19 | 1.24 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.441 | 0.268 | 0.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 201 | 270 | 488 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.07 | 1.44 | 2.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.420 | 1.399 | 0.697 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 488 | 377 | 482 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.36 | 1.05 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 4.165 | 6.246 | 0.651 | 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 | 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 | 24 | 24 | 26 | 22 | 24 | 43 | 24 | 24 | 50 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 1.00 | 1.00 | 2.08 | 1.00 |
time (sec) |
N/A | 0.277 | 0.428 | 0.735 | 0.128 | 0.087 | 65.500 | 0.169 | 0.165 | 4.228 |
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 | 24 | 24 | 26 | 22 | 24 | 43 | 24 | 24 | 50 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 1.00 | 1.00 | 2.08 | 1.00 |
time (sec) |
N/A | 0.279 | 2.385 | 0.174 | 0.122 | 0.083 | 3.112 | 0.149 | 0.165 | 4.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 5.33 | 0.00 |
time (sec) |
N/A | 0.297 | 0.091 | 0.319 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 5.11 | 0.00 |
time (sec) |
N/A | 0.261 | 0.045 | 0.329 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 40 | 24 | 0 | 47 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.67 | 1.00 | 0.00 | 1.96 | 1.00 |
time (sec) |
N/A | 0.284 | 1.437 | 0.942 | 0.126 | 0.077 | 5.437 | 0.000 | 0.174 | 3.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 43 | 0 | 24 | 54 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 0.00 | 1.00 | 2.25 | 1.00 |
time (sec) |
N/A | 0.276 | 0.540 | 0.736 | 0.129 | 0.083 | 0.000 | 0.182 | 0.184 | 4.256 |
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 | 24 | 24 | 26 | 22 | 24 | 43 | 26 | 24 | 54 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 1.08 | 1.00 | 2.25 | 1.00 |
time (sec) |
N/A | 0.823 | 2.851 | 0.184 | 0.156 | 0.084 | 4.173 | 0.166 | 0.189 | 4.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 34 | 65 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.438 | 0.068 | 0.543 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 62 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.422 | 0.098 | 0.550 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 40 | 26 | 0 | 51 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.67 | 1.08 | 0.00 | 2.12 | 1.00 |
time (sec) |
N/A | 1.133 | 5.809 | 0.197 | 0.126 | 0.082 | 7.019 | 0.000 | 0.177 | 3.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 43 | 0 | 24 | 54 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 0.00 | 1.00 | 2.25 | 1.00 |
time (sec) |
N/A | 0.291 | 0.738 | 0.763 | 0.131 | 0.092 | 0.000 | 0.190 | 0.177 | 3.935 |
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 | 24 | 24 | 26 | 22 | 24 | 43 | 26 | 24 | 54 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 1.08 | 1.00 | 2.25 | 1.00 |
time (sec) |
N/A | 1.035 | 5.164 | 0.194 | 0.150 | 0.078 | 5.745 | 0.173 | 0.180 | 3.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 71 | 43 | 87 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.04 | 0.63 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.573 | 0.125 | 0.533 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 69 | 44 | 86 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.06 | 0.68 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.549 | 0.073 | 0.537 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 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 | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 40 | 26 | 0 | 51 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.67 | 1.08 | 0.00 | 2.12 | 1.00 |
time (sec) |
N/A | 1.354 | 11.499 | 0.205 | 0.149 | 0.085 | 9.965 | 0.000 | 0.168 | 3.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 331 | 178 | 195 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.36 | 0.73 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.960 | 0.511 | 1.354 | 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 | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 210 | 79 | 120 | 128 | 91 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.54 | 0.58 | 0.88 | 0.94 | 0.67 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.698 | 0.048 | 1.060 | 0.114 | 0.109 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 226 | 160 | 175 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.16 | 0.82 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.630 | 0.360 | 1.053 | 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 | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 64 | 49 | 99 | 50 | 72 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.08 | 0.83 | 1.68 | 0.85 | 1.22 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.243 | 0.033 | 0.954 | 0.103 | 0.094 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 144 | 117 | 152 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.01 | 0.82 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.335 | 0.222 | 0.686 | 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 | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 91 | 111 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.395 | 0.122 | 0.974 | 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 | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 142 | 133 | 186 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.09 | 1.02 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.577 | 0.354 | 0.924 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 130 | 126 | 139 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.96 | 0.93 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.543 | 0.521 | 0.831 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 79 | 96 | 90 | 75 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.13 | 1.37 | 1.29 | 1.07 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.278 | 0.052 | 1.396 | 0.114 | 0.096 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 295 | 222 | 164 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.54 | 1.16 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.905 | 1.136 | 1.385 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 331 | 104 | 116 | 204 | 93 | 0 | 0 | 21 | 0 |
N.S. |
1 | 2.21 | 0.69 | 0.77 | 1.36 | 0.62 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.116 | 0.086 | 1.414 | 0.114 | 0.112 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 437 | 307 | 183 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.80 | 1.26 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.376 | 2.271 | 1.396 | 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 | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 892 | 268 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 2.65 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 7.142 | 1.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 926 | 175 | 211 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 3.30 | 0.62 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 4.342 | 0.477 | 0.582 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | 254 | 475 | 228 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.87 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 4.302 | 0.897 | 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 | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 179 | 135 | 175 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.02 | 0.77 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.494 | 0.326 | 0.525 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 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 | 158 | 150 | 187 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.95 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.701 | 0.530 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 212 | 203 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.22 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.292 | 0.239 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 193 | 223 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.98 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.474 | 0.568 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 157 | 188 | 229 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.04 | 1.25 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 2.193 | 1.001 | 0.500 | 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 | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 163 | 177 | 171 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.96 | 1.05 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.731 | 1.376 | 0.575 | 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 | B | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 791 | 272 | 215 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 2.71 | 0.93 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 2.801 | 0.980 | 1.064 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 566 | 79 | 140 | 163 | 106 | 0 | 0 | 48 | 0 |
N.S. |
1 | 3.04 | 0.42 | 0.75 | 0.88 | 0.57 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 2.137 | 0.063 | 0.964 | 0.118 | 0.106 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 562 | 224 | 195 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 2.31 | 0.92 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.894 | 0.687 | 0.952 | 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 | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 88 | 61 | 120 | 67 | 90 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.09 | 0.75 | 1.48 | 0.83 | 1.11 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.265 | 0.048 | 0.897 | 0.128 | 0.105 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 193 | 176 | 173 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 0.93 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.481 | 0.460 | 0.634 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 169 | 143 | 130 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.17 | 0.99 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.747 | 0.203 | 0.821 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 291 | 181 | 203 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.63 | 1.01 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.221 | 0.527 | 1.425 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 235 | 158 | 143 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.40 | 0.94 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.074 | 0.707 | 0.845 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 217 | 240 | 218 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.15 | 1.27 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.055 | 1.016 | 0.856 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 430 | 282 | 162 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 2.25 | 1.48 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.656 | 2.362 | 0.904 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 104 | 116 | 126 | 93 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.05 | 1.11 | 1.23 | 1.34 | 0.99 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.306 | 0.064 | 1.195 | 0.110 | 0.099 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 737 | 474 | 184 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 3.03 | 1.95 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 2.714 | 4.148 | 1.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 242 | 224 | 193 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.04 | 0.96 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.620 | 0.839 | 1.015 | 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 | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 193 | 176 | 173 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 0.93 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.506 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 144 | 117 | 152 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.01 | 0.82 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.352 | 0.043 | 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 | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 49 | 59 | 74 | 73 | 0 | 90 | 58 | 0 |
N.S. |
1 | 1.00 | 0.55 | 0.66 | 0.83 | 0.82 | 0.00 | 1.01 | 0.65 | 0.00 |
time (sec) |
N/A | 0.323 | 0.037 | 1.676 | 0.024 | 0.098 | 0.000 | 0.149 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 138 | 65 | 79 | 108 | 99 | 0 | 114 | 81 | 0 |
N.S. |
1 | 1.04 | 0.49 | 0.59 | 0.81 | 0.74 | 0.00 | 0.86 | 0.61 | 0.00 |
time (sec) |
N/A | 0.489 | 0.044 | 1.549 | 0.032 | 0.082 | 0.000 | 0.155 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 187 | 81 | 99 | 140 | 121 | 0 | 138 | 96 | 0 |
N.S. |
1 | 1.06 | 0.46 | 0.56 | 0.79 | 0.68 | 0.00 | 0.78 | 0.54 | 0.00 |
time (sec) |
N/A | 0.619 | 0.051 | 1.559 | 0.034 | 0.110 | 0.000 | 0.155 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 228 | 206 | 345 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.78 | 0.71 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.625 | 0.617 | 1.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 176 | 119 | 319 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.75 | 0.51 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.470 | 0.271 | 0.585 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 125 | 109 | 302 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.69 | 0.60 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.336 | 0.147 | 0.549 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 43 | 74 | 90 | 54 | 0 | 70 | 50 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.54 | 1.88 | 1.12 | 0.00 | 1.46 | 1.04 | 0.00 |
time (sec) |
N/A | 0.228 | 0.057 | 0.531 | 0.112 | 0.115 | 0.000 | 0.164 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 108 | 64 | 121 | 90 | 84 | 0 | 111 | 66 | 0 |
N.S. |
1 | 1.03 | 0.61 | 1.15 | 0.86 | 0.80 | 0.00 | 1.06 | 0.63 | 0.00 |
time (sec) |
N/A | 0.355 | 0.068 | 0.899 | 0.039 | 0.093 | 0.000 | 0.161 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 168 | 80 | 137 | 132 | 112 | 0 | 149 | 88 | 0 |
N.S. |
1 | 1.07 | 0.51 | 0.87 | 0.84 | 0.71 | 0.00 | 0.95 | 0.56 | 0.00 |
time (sec) |
N/A | 0.523 | 0.079 | 0.788 | 0.040 | 0.090 | 0.000 | 0.176 | 0.169 | 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 | 158 | 150 | 187 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.95 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.687 | 0.061 | 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 | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 161 | 70 | 84 | 304 | 105 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.16 | 0.50 | 0.60 | 2.19 | 0.76 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.417 | 0.055 | 0.447 | 0.162 | 0.091 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 283 | 94 | 118 | 514 | 139 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.36 | 0.45 | 0.57 | 2.47 | 0.67 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.665 | 0.063 | 0.464 | 0.186 | 0.102 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 429 | 120 | 152 | 751 | 169 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.55 | 0.43 | 0.55 | 2.71 | 0.61 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.999 | 0.078 | 0.482 | 0.186 | 0.109 | 0.000 | 0.000 | 0.173 | 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 | 302 | 291 | 569 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.96 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.197 | 2.235 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 240 | 87 | 105 | 0 | 134 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.26 | 0.46 | 0.55 | 0.00 | 0.70 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.890 | 0.065 | 0.490 | 0.000 | 0.093 | 0.000 | 0.000 | 0.174 | 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 | 289 | 439 | 119 | 153 | 0 | 176 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.52 | 0.41 | 0.53 | 0.00 | 0.61 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.890 | 0.076 | 0.542 | 0.000 | 0.101 | 0.000 | 0.000 | 0.179 | 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 | 385 | 687 | 151 | 201 | 0 | 214 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.78 | 0.39 | 0.52 | 0.00 | 0.56 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 3.803 | 0.091 | 0.550 | 0.000 | 0.096 | 0.000 | 0.000 | 0.178 | 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 | 21 | 21 | 23 | 19 | 21 | 21 | 20 | 21 | 20 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 0.95 | 1.00 | 0.95 | 1.00 |
time (sec) |
N/A | 0.207 | 1.133 | 0.137 | 0.087 | 0.072 | 0.519 | 0.148 | 0.181 | 3.375 |
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 | 21 | 21 | 23 | 19 | 21 | 33 | 22 | 21 | 22 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.57 | 1.05 | 1.00 | 1.05 | 1.00 |
time (sec) |
N/A | 0.215 | 0.310 | 0.295 | 0.085 | 0.075 | 0.690 | 0.134 | 0.176 | 3.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 5.11 | 0.00 |
time (sec) |
N/A | 0.265 | 0.034 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 24 | 21 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 0.93 | 0.89 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 2.44 | 0.00 |
time (sec) |
N/A | 0.324 | 0.053 | 0.491 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 36 | 31 | 30 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.88 | 0.76 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.347 | 0.061 | 0.489 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 42 | 39 | 0 | 0 | 0 | 0 | 112 | 0 |
N.S. |
1 | 0.85 | 0.76 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.360 | 0.065 | 0.497 | 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 | 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 | 21 | 21 | 23 | 19 | 21 | 21 | 22 | 21 | 20 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.05 | 1.00 | 0.95 | 1.00 |
time (sec) |
N/A | 0.207 | 1.266 | 0.148 | 0.096 | 0.075 | 0.768 | 0.145 | 0.174 | 3.509 |
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 | 21 | 21 | 23 | 19 | 21 | 33 | 24 | 21 | 22 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.57 | 1.14 | 1.00 | 1.05 | 1.00 |
time (sec) |
N/A | 0.218 | 0.927 | 0.115 | 0.092 | 0.085 | 1.001 | 0.151 | 0.192 | 3.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 62 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.414 | 0.092 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 46 | 120 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 0.88 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.461 | 0.099 | 1.006 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 63 | 56 | 176 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.95 | 0.85 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.494 | 0.117 | 1.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 74 | 64 | 232 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 0.92 | 0.80 | 2.90 | 0.00 | 0.00 | 0.00 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.509 | 0.141 | 1.146 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 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 | 21 | 21 | 23 | 19 | 21 | 21 | 22 | 21 | 20 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.05 | 1.00 | 0.95 | 1.00 |
time (sec) |
N/A | 0.213 | 1.383 | 0.143 | 0.091 | 0.075 | 1.082 | 0.149 | 0.161 | 3.747 |
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 | 21 | 21 | 23 | 19 | 21 | 33 | 24 | 21 | 22 | 21 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.57 | 1.14 | 1.00 | 1.05 | 1.00 |
time (sec) |
N/A | 0.219 | 0.879 | 0.609 | 0.106 | 0.072 | 1.416 | 0.159 | 0.164 | 3.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 69 | 44 | 86 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.06 | 0.68 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.562 | 0.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 111 | 56 | 180 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.41 | 0.71 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 1.296 | 0.155 | 1.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 133 | 79 | 272 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.43 | 0.85 | 2.92 | 0.00 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 1.350 | 0.186 | 1.047 | 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 | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 155 | 99 | 364 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.45 | 0.93 | 3.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 1.398 | 0.174 | 1.462 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 193 | 1435 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 1.58 | 11.76 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.599 | 0.602 | 18.464 | 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 | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 247 | 213 | 245 | 276 | 248 | 372 | 1471 | 358 | 288 |
N.S. |
1 | 1.01 | 0.87 | 1.00 | 1.13 | 1.01 | 1.52 | 6.00 | 1.46 | 1.18 |
time (sec) |
N/A | 0.744 | 0.055 | 0.545 | 0.029 | 0.086 | 0.730 | 0.184 | 0.172 | 3.960 |
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 | 169 | 171 | 150 | 167 | 198 | 178 | 245 | 930 | 253 | 190 |
N.S. |
1 | 1.01 | 0.89 | 0.99 | 1.17 | 1.05 | 1.45 | 5.50 | 1.50 | 1.12 |
time (sec) |
N/A | 0.578 | 0.041 | 0.341 | 0.036 | 0.092 | 0.498 | 0.157 | 0.179 | 3.964 |
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 | 110 | 112 | 98 | 105 | 131 | 119 | 155 | 527 | 162 | 118 |
N.S. |
1 | 1.02 | 0.89 | 0.95 | 1.19 | 1.08 | 1.41 | 4.79 | 1.47 | 1.07 |
time (sec) |
N/A | 0.404 | 0.029 | 0.527 | 0.034 | 0.092 | 0.386 | 0.137 | 0.168 | 3.754 |