Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 59 | 69 | 57 | 65 | 65 | 73 | 266 | 60 |
N.S. |
1 | 1.04 | 1.21 | 1.00 | 1.14 | 1.14 | 1.28 | 4.67 | 1.05 |
time (sec) |
N/A | 0.260 | 0.021 | 0.044 | 0.186 | 0.259 | 0.280 | 0.282 | 4.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 429 | 439 | 662 | 364 | 406 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.54 | 0.85 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.735 | 1.366 | 0.414 | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 590 | 618 | 746 | 1951 | 550 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.26 | 3.31 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.200 | 5.314 | 0.952 | 0.329 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 657 | 682 | 1541 | 4047 | 1087 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 2.35 | 6.16 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.270 | 9.751 | 0.756 | 0.408 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 23 | 22 | 14 | 48 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.35 | 1.29 | 0.82 | 2.82 | 0.88 |
time (sec) |
N/A | 0.216 | 0.078 | 0.210 | 0.198 | 0.254 | 0.253 | 0.288 | 3.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 181 | 576 | 160 | 180 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 3.37 | 0.94 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.504 | 0.722 | 0.419 | 0.192 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 213 | 203 | 184 | 198 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.91 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.536 | 0.035 | 0.804 | 0.192 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 260 | 106 | 119 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.02 | 1.23 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.389 | 0.062 | 0.219 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 397 | 407 | 485 | 294 | 304 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.22 | 0.74 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.727 | 1.112 | 0.299 | 0.340 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 0 | 434 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.583 | 0.000 | 0.573 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 16 | 16 | 18 | 14 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.198 | 5.577 | 0.152 | 0.581 | 0.263 | 0.586 | 0.310 | 3.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 16 | 16 | 18 | 14 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.202 | 2.981 | 0.114 | 0.586 | 0.247 | 0.469 | 0.314 | 3.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 119 | 0 | 153 | 356 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.92 | 0.00 | 2.47 | 5.74 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.284 | 0.078 | 0.000 | 0.216 | 0.267 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 130 | 226 | 0 | 223 | 730 | 0 | 135 | 0 |
N.S. |
1 | 1.02 | 1.77 | 0.00 | 1.74 | 5.70 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.341 | 0.208 | 0.000 | 0.266 | 0.280 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | A | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 200 | 194 | 329 | 0 | 401 | 1280 | 0 | 218 | 0 |
N.S. |
1 | 0.97 | 1.64 | 0.00 | 2.00 | 6.40 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 1.071 | 0.393 | 0.000 | 0.272 | 0.316 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 283 | 281 | 431 | 0 | 639 | 2006 | 0 | 349 | 0 |
N.S. |
1 | 0.99 | 1.52 | 0.00 | 2.26 | 7.09 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 1.287 | 0.629 | 0.000 | 0.283 | 0.403 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 139 | 97 | 229 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.52 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.406 | 0.307 | 0.258 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 99 | 90 | 210 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 0.62 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.290 | 0.135 | 0.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 30 | 47 | 63 | 42 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.81 | 1.27 | 1.70 | 1.14 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.202 | 0.054 | 0.263 | 0.277 | 0.262 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 86 | 45 | 85 | 67 | 62 | 0 | 86 | 0 |
N.S. |
1 | 1.04 | 0.54 | 1.02 | 0.81 | 0.75 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.312 | 0.060 | 0.198 | 0.203 | 0.266 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 135 | 55 | 106 | 99 | 82 | 0 | 118 | 0 |
N.S. |
1 | 1.09 | 0.44 | 0.85 | 0.80 | 0.66 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.434 | 0.070 | 0.286 | 0.202 | 0.260 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 315 | 286 | 236 | 296 | 317 | 251 | 338 | 313 | 599 |
N.S. |
1 | 0.91 | 0.75 | 0.94 | 1.01 | 0.80 | 1.07 | 0.99 | 1.90 |
time (sec) |
N/A | 0.945 | 0.101 | 2.351 | 0.193 | 0.246 | 2.192 | 0.444 | 7.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 222 | 192 | 249 | 271 | 196 | 279 | 0 | 851 |
N.S. |
1 | 0.99 | 0.85 | 1.11 | 1.20 | 0.87 | 1.24 | 0.00 | 3.78 |
time (sec) |
N/A | 0.497 | 0.095 | 1.376 | 0.189 | 0.254 | 1.407 | 0.000 | 4.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 247 | 223 | 183 | 229 | 252 | 200 | 258 | 244 | 515 |
N.S. |
1 | 0.90 | 0.74 | 0.93 | 1.02 | 0.81 | 1.04 | 0.99 | 2.09 |
time (sec) |
N/A | 0.795 | 0.081 | 1.263 | 0.195 | 0.257 | 0.997 | 0.405 | 6.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 129 | 174 | 171 | 139 | 202 | 209 | 557 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 1.22 | 0.99 | 1.44 | 1.49 | 3.98 |
time (sec) |
N/A | 0.361 | 0.066 | 0.862 | 0.191 | 0.242 | 0.700 | 0.379 | 4.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 116 | 144 | 141 | 178 | 132 | 148 | 165 | 385 |
N.S. |
1 | 1.12 | 1.38 | 1.36 | 1.71 | 1.27 | 1.42 | 1.59 | 3.70 |
time (sec) |
N/A | 0.853 | 0.027 | 0.606 | 0.186 | 0.271 | 0.420 | 0.341 | 4.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 216 | 190 | 0 | 1227 | 152 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.00 | 5.68 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.144 | 0.000 | 2.092 | 0.297 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 105 | 85 | 332 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.81 | 3.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.713 | 0.138 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 157 | 146 | 152 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.378 | 0.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 197 | 178 | 460 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.511 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 244 | 234 | 299 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.542 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 256 | 293 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.525 | 0.000 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 512 | 504 | 1145 | 971 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 2.24 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.978 | 5.427 | 4.599 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 599 | 609 | 1251 | 3550 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 2.09 | 5.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.777 | 2.587 | 4.704 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 24 | 24 | 26 | 24 | 77 | 37 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 3.21 | 1.54 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.763 | 0.151 | 0.510 | 0.353 | 0.247 | 126.285 | 0.298 | 5.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 613 | 602 | 1226 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.384 | 2.668 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 470 | 487 | 1211 | 961 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 2.58 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.974 | 5.896 | 4.987 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 102 | 70 | 73 | 226 | 74 | 0 | 93 | 67 |
N.S. |
1 | 1.31 | 0.90 | 0.94 | 2.90 | 0.95 | 0.00 | 1.19 | 0.86 |
time (sec) |
N/A | 0.510 | 0.127 | 0.470 | 0.244 | 0.251 | 0.000 | 0.280 | 4.292 |