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 | C | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 142 | 91 | 200 | 170 | 216 | 0 | 0 | 0 |
N.S. |
1 | 1.63 | 1.05 | 2.30 | 1.95 | 2.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.667 | 0.016 | 0.296 | 0.201 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 106 | 66 | 166 | 138 | 168 | 0 | 0 | 0 |
N.S. |
1 | 1.68 | 1.05 | 2.63 | 2.19 | 2.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.509 | 0.014 | 0.251 | 0.207 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 71 | 47 | 122 | 98 | 112 | 0 | 0 | 0 |
N.S. |
1 | 1.58 | 1.04 | 2.71 | 2.18 | 2.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.349 | 0.010 | 0.268 | 0.192 | 0.264 | 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 | 10 | 10 | 12 | 10 | 35 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 3.50 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.199 | 13.895 | 0.045 | 0.410 | 0.260 | 0.472 | 0.280 | 1.879 |
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 | 10 | 10 | 12 | 10 | 46 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 4.60 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.205 | 23.107 | 0.052 | 0.324 | 0.244 | 0.446 | 0.284 | 1.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 131 | 222 | 198 | 146 | 632 | 0 | 0 | 0 |
N.S. |
1 | 1.51 | 2.55 | 2.28 | 1.68 | 7.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.641 | 1.089 | 0.110 | 0.258 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 96 | 117 | 156 | 108 | 453 | 0 | 0 | 0 |
N.S. |
1 | 1.48 | 1.80 | 2.40 | 1.66 | 6.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 1.577 | 0.115 | 0.268 | 0.263 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 46 | 54 | 115 | 189 | 190 | 98 | 48 |
N.S. |
1 | 1.13 | 1.48 | 1.74 | 3.71 | 6.10 | 6.13 | 3.16 | 1.55 |
time (sec) |
N/A | 0.261 | 0.170 | 0.112 | 0.234 | 0.258 | 0.678 | 0.293 | 1.890 |
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 | 12 | 12 | 14 | 12 | 69 | 14 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 5.75 | 1.17 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.215 | 25.940 | 0.045 | 0.291 | 0.245 | 0.520 | 0.292 | 1.907 |
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 | 12 | 12 | 14 | 12 | 91 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 7.58 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.213 | 25.753 | 0.049 | 0.291 | 0.253 | 0.487 | 0.292 | 1.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 266 | 422 | 375 | 302 | 1985 | 0 | 0 | 0 |
N.S. |
1 | 1.49 | 2.36 | 2.09 | 1.69 | 11.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.447 | 3.708 | 0.171 | 0.246 | 0.313 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 168 | 314 | 246 | 226 | 1467 | 0 | 0 | 0 |
N.S. |
1 | 1.47 | 2.75 | 2.16 | 1.98 | 12.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.949 | 3.542 | 0.163 | 0.254 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 112 | 131 | 164 | 149 | 975 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 1.60 | 2.00 | 1.82 | 11.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.524 | 1.532 | 0.135 | 0.237 | 0.324 | 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 | 12 | 12 | 14 | 12 | 144 | 14 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 12.00 | 1.17 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.210 | 21.674 | 0.059 | 0.309 | 0.260 | 0.597 | 0.309 | 1.809 |
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 | 12 | 12 | 14 | 12 | 175 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 14.58 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.215 | 15.902 | 0.059 | 0.299 | 0.242 | 0.542 | 0.302 | 1.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 179 | 244 | 165 | 183 | 304 | 864 | 188 | 223 |
N.S. |
1 | 1.06 | 1.44 | 0.98 | 1.08 | 1.80 | 5.11 | 1.11 | 1.32 |
time (sec) |
N/A | 0.690 | 0.929 | 0.385 | 0.262 | 0.261 | 0.763 | 0.290 | 2.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 169 | 103 | 124 | 192 | 522 | 119 | 186 |
N.S. |
1 | 1.04 | 1.39 | 0.84 | 1.02 | 1.57 | 4.28 | 0.98 | 1.52 |
time (sec) |
N/A | 0.491 | 0.590 | 0.314 | 0.246 | 0.269 | 0.634 | 0.278 | 1.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 78 | 81 | 46 | 72 | 101 | 250 | 62 | 76 |
N.S. |
1 | 1.05 | 1.09 | 0.62 | 0.97 | 1.36 | 3.38 | 0.84 | 1.03 |
time (sec) |
N/A | 0.322 | 0.707 | 0.191 | 0.215 | 0.255 | 0.542 | 0.286 | 1.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 122 | 61 | 48 | 75 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.39 | 0.31 | 0.48 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.747 | 0.631 | 0.342 | 0.334 | 0.243 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 168 | 206 | 91 | 56 | 216 | 0 | 321 | 0 |
N.S. |
1 | 1.06 | 1.30 | 0.57 | 0.35 | 1.36 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.741 | 0.929 | 0.364 | 0.474 | 0.280 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 219 | 265 | 210 | 68 | 342 | 0 | 175 | 0 |
N.S. |
1 | 1.04 | 1.26 | 1.00 | 0.32 | 1.62 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.955 | 1.232 | 0.400 | 0.650 | 0.259 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 230 | 230 | 420 | 273 | 297 | 571 | 2193 | 368 | 266 |
N.S. |
1 | 1.00 | 1.83 | 1.19 | 1.29 | 2.48 | 9.53 | 1.60 | 1.16 |
time (sec) |
N/A | 0.528 | 2.909 | 0.496 | 0.501 | 0.254 | 1.060 | 0.298 | 2.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 207 | 163 | 191 | 359 | 1353 | 217 | 164 |
N.S. |
1 | 1.00 | 1.22 | 0.96 | 1.12 | 2.11 | 7.96 | 1.28 | 0.96 |
time (sec) |
N/A | 0.430 | 2.308 | 0.435 | 0.406 | 0.274 | 0.885 | 0.293 | 1.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 114 | 74 | 107 | 190 | 700 | 103 | 88 |
N.S. |
1 | 1.00 | 0.86 | 0.56 | 0.80 | 1.43 | 5.26 | 0.77 | 0.66 |
time (sec) |
N/A | 0.386 | 1.459 | 0.377 | 0.321 | 0.250 | 0.798 | 0.275 | 1.907 |
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 | 297 | 297 | 199 | 106 | 81 | 137 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.36 | 0.27 | 0.46 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.047 | 1.127 | 0.335 | 0.698 | 0.263 | 0.000 | 0.282 | 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 | 420 | 420 | 442 | 164 | 100 | 615 | 0 | 585 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.39 | 0.24 | 1.46 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 1.121 | 2.391 | 0.391 | 1.322 | 0.265 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 336 | 336 | 615 | 379 | 406 | 844 | 3918 | 548 | 374 |
N.S. |
1 | 1.00 | 1.83 | 1.13 | 1.21 | 2.51 | 11.66 | 1.63 | 1.11 |
time (sec) |
N/A | 0.690 | 4.566 | 0.584 | 1.640 | 0.277 | 1.466 | 0.296 | 2.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 246 | 371 | 223 | 254 | 532 | 2443 | 315 | 234 |
N.S. |
1 | 1.00 | 1.51 | 0.91 | 1.03 | 2.16 | 9.93 | 1.28 | 0.95 |
time (sec) |
N/A | 0.518 | 3.166 | 0.523 | 1.149 | 0.259 | 1.205 | 0.284 | 2.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 182 | 185 | 102 | 138 | 286 | 1287 | 142 | 127 |
N.S. |
1 | 0.99 | 1.01 | 0.56 | 0.75 | 1.56 | 7.03 | 0.78 | 0.69 |
time (sec) |
N/A | 0.487 | 1.756 | 0.430 | 0.675 | 0.262 | 1.110 | 0.304 | 2.012 |
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 | 437 | 437 | 312 | 151 | 114 | 195 | 0 | 104 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.35 | 0.26 | 0.45 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 2.028 | 1.319 | 0.374 | 2.288 | 0.254 | 0.000 | 0.289 | 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 | 692 | 692 | 796 | 239 | 140 | 1162 | 0 | 841 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.35 | 0.20 | 1.68 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 2.223 | 3.767 | 0.471 | 5.164 | 0.262 | 0.000 | 0.324 | 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 | 20 | 20 | 22 | 20 | 122 | 37 | 44 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 6.10 | 1.85 | 2.20 | 1.10 | 1.10 |
time (sec) |
N/A | 0.217 | 41.615 | 0.066 | 0.389 | 0.244 | 4.418 | 0.329 | 2.154 |
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 | 18 | 18 | 20 | 18 | 68 | 20 | 24 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 3.78 | 1.11 | 1.33 | 1.11 | 1.11 |
time (sec) |
N/A | 0.213 | 20.068 | 0.056 | 0.292 | 0.261 | 2.784 | 0.303 | 2.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 115 | 0 | 0 | 148 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 1.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.334 | 1.200 | 0.000 | 0.000 | 0.079 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 162 | 0 | 0 | 248 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.425 | 1.734 | 0.000 | 0.000 | 0.086 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 223 | 223 | 228 | 0 | 0 | 345 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 1.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.529 | 1.974 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 249 | 766 | 419 | 488 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.87 | 5.76 | 3.15 | 3.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 0.355 | 0.416 | 0.258 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 149 | 465 | 240 | 303 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.48 | 4.60 | 2.38 | 3.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 0.213 | 0.364 | 0.257 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 87 | 201 | 0 | 156 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 2.68 | 0.00 | 2.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.337 | 0.055 | 0.186 | 0.000 | 0.260 | 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 | 18 | 18 | 20 | 18 | 78 | 20 | 15 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.33 | 1.11 | 0.83 | 1.11 | 1.11 |
time (sec) |
N/A | 0.214 | 5.728 | 0.058 | 0.257 | 0.259 | 0.960 | 0.275 | 1.970 |
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 | 18 | 18 | 20 | 18 | 131 | 31 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 7.28 | 1.72 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.209 | 31.405 | 0.058 | 0.271 | 0.252 | 3.172 | 0.356 | 2.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 843 | 1425 | 781 | 3239 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.11 | 5.26 | 2.88 | 11.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.809 | 4.907 | 0.524 | 0.279 | 0.316 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 473 | 825 | 494 | 1854 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.26 | 3.95 | 2.36 | 8.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.661 | 6.924 | 0.461 | 0.267 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 218 | 318 | 244 | 851 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.72 | 2.50 | 1.92 | 6.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.426 | 7.225 | 0.392 | 0.260 | 0.263 | 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 | 20 | 20 | 22 | 20 | 226 | 36 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 11.30 | 1.80 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.232 | 42.155 | 0.173 | 0.400 | 0.253 | 1.491 | 0.325 | 2.195 |
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 | 20 | 20 | 22 | 20 | 375 | 47 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 18.75 | 2.35 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.227 | 34.097 | 0.177 | 0.450 | 0.257 | 2.495 | 0.464 | 2.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 556 | 556 | 2043 | 2823 | 1531 | 11137 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.67 | 5.08 | 2.75 | 20.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.426 | 8.913 | 0.776 | 0.303 | 0.388 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 401 | 392 | 585 | 1586 | 997 | 6356 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.46 | 3.96 | 2.49 | 15.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.044 | 7.466 | 0.629 | 0.282 | 0.337 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 259 | 318 | 651 | 528 | 2907 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.22 | 2.49 | 2.02 | 11.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.640 | 8.176 | 0.490 | 0.268 | 0.296 | 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 | 20 | 20 | 22 | 20 | 644 | 52 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 32.20 | 2.60 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.236 | 48.149 | 0.342 | 0.746 | 0.265 | 1.982 | 0.415 | 2.069 |
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 | 20 | 20 | 22 | 20 | 1144 | 63 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 57.20 | 3.15 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.234 | 56.003 | 0.318 | 0.952 | 0.265 | 3.207 | 0.796 | 2.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 200 | 247 | 1158 | 521 | 730 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.18 | 5.51 | 2.48 | 3.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.965 | 1.530 | 0.448 | 0.323 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 155 | 200 | 735 | 332 | 492 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.28 | 4.71 | 2.13 | 3.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.761 | 1.081 | 0.414 | 0.290 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 112 | 152 | 357 | 0 | 300 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.41 | 3.31 | 0.00 | 2.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.496 | 1.041 | 0.359 | 0.000 | 0.277 | 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 | 20 | 20 | 22 | 20 | 117 | 27 | 17 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 5.85 | 1.35 | 0.85 | 1.10 | 1.10 |
time (sec) |
N/A | 0.239 | 7.377 | 0.068 | 0.345 | 0.243 | 1.179 | 0.280 | 1.907 |
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 | 20 | 20 | 22 | 20 | 202 | 51 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 10.10 | 2.55 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.238 | 13.540 | 0.073 | 0.509 | 0.249 | 1.970 | 0.368 | 2.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 638 | 638 | 659 | 2444 | 1056 | 6171 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 3.83 | 1.66 | 9.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.444 | 7.975 | 0.581 | 0.533 | 0.360 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 475 | 475 | 519 | 1238 | 751 | 3702 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.09 | 2.61 | 1.58 | 7.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.931 | 5.060 | 0.501 | 0.511 | 0.316 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 214 | 244 | 524 | 0 | 1797 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.24 | 2.67 | 0.00 | 9.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.817 | 3.873 | 0.445 | 0.000 | 0.310 | 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 | 20 | 20 | 22 | 20 | 472 | 55 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 23.60 | 2.75 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.241 | 41.450 | 0.073 | 1.101 | 0.261 | 1.827 | 0.311 | 2.272 |
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 | 20 | 20 | 22 | 20 | 789 | 96 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 39.45 | 4.80 | 1.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.245 | 39.171 | 0.071 | 2.157 | 0.274 | 3.323 | 0.511 | 2.714 |