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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 168 | 272 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.618 | 0.010 | 0.706 | 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 | 260 | 256 | 240 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.935 | 0.102 | 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 | 348 | 346 | 322 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.216 | 0.039 | 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 | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 202 | 166 | 242 | 230 | 214 | 316 | 0 | 0 |
N.S. |
1 | 1.15 | 0.94 | 1.38 | 1.31 | 1.22 | 1.80 | 0.00 | 0.00 |
time (sec) |
N/A | 0.392 | 0.111 | 0.312 | 0.183 | 0.282 | 0.304 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 147 | 121 | 174 | 150 | 147 | 190 | 0 | 0 |
N.S. |
1 | 1.19 | 0.98 | 1.40 | 1.21 | 1.19 | 1.53 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.079 | 0.323 | 0.180 | 0.252 | 0.229 | 0.000 | 0.000 |
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 | 97 | 106 | 91 | 84 | 82 | 87 | 99 | 122 | 78 |
N.S. |
1 | 1.09 | 0.94 | 0.87 | 0.85 | 0.90 | 1.02 | 1.26 | 0.80 |
time (sec) |
N/A | 0.256 | 0.032 | 0.016 | 0.182 | 0.255 | 0.173 | 0.345 | 2.758 |
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 | 30 | 30 | 30 | 31 | 30 | 43 | 26 | 41 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.43 | 0.87 | 1.37 | 0.93 |
time (sec) |
N/A | 0.157 | 0.007 | 0.013 | 0.189 | 0.250 | 0.070 | 0.275 | 0.032 |
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 | 187 | 187 | 175 | 279 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.641 | 0.043 | 0.538 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 79 | 174 | 103 | 253 | 0 | 232 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.12 | 1.26 | 3.09 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 0.246 | 0.071 | 0.961 | 0.196 | 0.270 | 0.000 | 0.470 | 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 | 128 | 129 | 166 | 273 | 158 | 566 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.30 | 2.13 | 1.23 | 4.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.287 | 0.247 | 0.573 | 0.192 | 0.319 | 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 | 183 | 199 | 205 | 510 | 0 | 977 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.12 | 2.79 | 0.00 | 5.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.353 | 0.300 | 0.406 | 0.000 | 0.619 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 368 | 387 | 354 | 526 | 590 | 475 | 743 | 0 | 0 |
N.S. |
1 | 1.05 | 0.96 | 1.43 | 1.60 | 1.29 | 2.02 | 0.00 | 0.00 |
time (sec) |
N/A | 1.050 | 0.357 | 0.444 | 0.213 | 0.269 | 0.450 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 262 | 248 | 364 | 378 | 319 | 454 | 0 | 0 |
N.S. |
1 | 1.10 | 1.04 | 1.52 | 1.58 | 1.33 | 1.90 | 0.00 | 0.00 |
time (sec) |
N/A | 0.782 | 0.225 | 0.455 | 0.194 | 0.264 | 0.326 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 162 | 142 | 183 | 219 | 183 | 233 | 0 | 0 |
N.S. |
1 | 1.16 | 1.01 | 1.31 | 1.56 | 1.31 | 1.66 | 0.00 | 0.00 |
time (sec) |
N/A | 0.577 | 1.148 | 0.306 | 0.193 | 0.262 | 0.234 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 74 | 72 | 72 | 96 | 82 | 111 | 0 |
N.S. |
1 | 1.09 | 1.61 | 1.57 | 1.57 | 2.09 | 1.78 | 2.41 | 0.00 |
time (sec) |
N/A | 0.285 | 0.033 | 0.000 | 0.203 | 0.256 | 0.099 | 0.363 | 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 | 291 | 285 | 273 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.044 | 0.178 | 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 | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 263 | 239 | 191 | 525 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.73 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.996 | 0.145 | 0.543 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 349 | 331 | 270 | 815 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.77 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.350 | 0.443 | 0.653 | 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 | 394 | 378 | 305 | 394 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.77 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.423 | 0.535 | 1.838 | 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 | 245 | 233 | 188 | 254 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.77 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.929 | 0.345 | 1.003 | 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 | 116 | 110 | 98 | 120 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.84 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.566 | 0.148 | 0.589 | 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 | 54 | 49 | 45 | 56 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.83 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.406 | 0.043 | 0.000 | 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 | 18 | 18 | 20 | 18 | 20 | 25 | 15 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.39 | 0.83 | 1.11 | 1.11 |
time (sec) |
N/A | 0.212 | 0.162 | 0.366 | 0.257 | 0.256 | 0.893 | 0.287 | 2.669 |
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 | 20 | 49 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 2.72 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.209 | 0.317 | 0.277 | 0.265 | 0.241 | 1.707 | 0.861 | 2.630 |
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 | 359 | 359 | 288 | 616 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.847 | 1.661 | 0.973 | 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 | 180 | 180 | 150 | 272 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.534 | 0.890 | 0.556 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 71 | 118 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.84 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.598 | 0.161 | 0.001 | 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 | 18 | 18 | 20 | 18 | 746 | 51 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 41.44 | 2.83 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.202 | 5.834 | 0.308 | 0.829 | 0.262 | 1.609 | 0.318 | 2.911 |
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 | 1050 | 92 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 58.33 | 5.11 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.211 | 4.551 | 0.353 | 1.221 | 0.265 | 5.726 | 1.299 | 2.675 |
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 | 271 | 32 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 15.06 | 1.78 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.545 | 5.324 | 1.562 | 0.852 | 0.281 | 5.170 | 0.383 | 2.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 0.000 | 0.000 | 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 | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 |
time (sec) |
N/A | 0.197 | 0.302 | 0.948 | 0.239 | 0.251 | 0.901 | 0.281 | 2.899 |
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 | 607 | 34 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 33.72 | 1.89 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.205 | 0.669 | 0.928 | 0.961 | 0.277 | 14.414 | 0.297 | 2.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 640 | 363 | 410 | 1309 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.57 | 0.64 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.038 | 0.843 | 0.856 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 431 | 257 | 301 | 913 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.70 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.835 | 0.769 | 0.715 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 136 | 208 | 582 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.92 | 2.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.528 | 0.959 | 0.781 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 664 | 461 | 1358 | 747 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 2.05 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.163 | 4.933 | 0.771 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 781 | 572 | 1384 | 1701 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 1.77 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.737 | 7.674 | 0.817 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 918 | 488 | 536 | 2079 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.53 | 0.58 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.267 | 1.604 | 0.875 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 651 | 359 | 416 | 1568 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.55 | 0.64 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.005 | 1.163 | 0.818 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 188 | 289 | 1065 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.53 | 0.82 | 3.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.597 | 0.633 | 0.828 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 984 | 641 | 2869 | 1557 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 2.92 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.241 | 12.244 | 0.858 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1228 | 617 | 810 | 2884 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.50 | 0.66 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.421 | 2.221 | 1.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 901 | 470 | 555 | 2309 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 0.62 | 2.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.194 | 1.726 | 1.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 494 | 249 | 390 | 1679 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.50 | 0.79 | 3.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.691 | 0.887 | 0.997 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1536 | 945 | 7168 | 3499 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 4.67 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.731 | 23.148 | 0.937 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 430 | 256 | 304 | 785 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.71 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.860 | 1.015 | 0.930 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 258 | 158 | 233 | 484 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.61 | 0.90 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.686 | 0.710 | 0.758 | 0.000 | 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 | 120 | 84 | 158 | 227 | 87 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 1.32 | 1.89 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.471 | 0.348 | 0.830 | 0.211 | 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 | 47 | 47 | 76 | 77 | 28 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.62 | 1.64 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.217 | 0.034 | 0.375 | 0.194 | 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 | 325 | 238 | 240 | 529 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.74 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.009 | 0.352 | 0.691 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 444 | 327 | 251 | 1770 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.74 | 0.57 | 3.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.350 | 0.407 | 0.846 | 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 | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 32 | 34 | 34 | 0 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.351 | 0.103 | 2.496 | 0.923 | 0.263 | 0.000 | 73.328 | 2.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 438 | 426 | 397 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.712 | 0.141 | 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 | 332 | 328 | 304 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.281 | 0.154 | 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 | 197 | 196 | 206 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.700 | 0.016 | 0.000 | 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 | 34 | 34 | 36 | 32 | 34 | 51 | 31 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.50 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.377 | 0.294 | 1.941 | 0.806 | 0.266 | 7.693 | 0.910 | 2.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 158 | 95 | 200 | 318 | 110 | 255 | 162 | 0 |
N.S. |
1 | 1.21 | 0.73 | 1.53 | 2.43 | 0.84 | 1.95 | 1.24 | 0.00 |
time (sec) |
N/A | 0.383 | 0.063 | 0.053 | 0.183 | 0.257 | 0.323 | 0.574 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 117 | 74 | 130 | 210 | 91 | 170 | 131 | 0 |
N.S. |
1 | 1.30 | 0.82 | 1.44 | 2.33 | 1.01 | 1.89 | 1.46 | 0.00 |
time (sec) |
N/A | 0.325 | 0.043 | 0.015 | 0.184 | 0.248 | 0.248 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 82 | 60 | 74 | 149 | 75 | 104 | 111 | 0 |
N.S. |
1 | 1.08 | 0.79 | 0.97 | 1.96 | 0.99 | 1.37 | 1.46 | 0.00 |
time (sec) |
N/A | 0.292 | 0.031 | 0.012 | 0.191 | 0.251 | 0.181 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 32 | 78 | 31 | 30 | 57 | 46 | 92 | 76 |
N.S. |
1 | 0.94 | 2.29 | 0.91 | 0.88 | 1.68 | 1.35 | 2.71 | 2.24 |
time (sec) |
N/A | 0.213 | 0.158 | 0.013 | 0.179 | 0.246 | 0.078 | 0.303 | 2.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 153 | 388 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.17 | 2.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.596 | 0.011 | 0.658 | 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 | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 57 | 68 | 111 | 167 | 0 | 110 | 0 |
N.S. |
1 | 1.07 | 1.00 | 1.19 | 1.95 | 2.93 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 0.291 | 0.030 | 0.242 | 0.179 | 0.273 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 99 | 110 | 103 | 146 | 236 | 0 | 199 | 0 |
N.S. |
1 | 1.08 | 1.20 | 1.12 | 1.59 | 2.57 | 0.00 | 2.16 | 0.00 |
time (sec) |
N/A | 0.316 | 0.163 | 0.017 | 0.185 | 0.275 | 0.000 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 148 | 149 | 203 | 284 | 285 | 0 | 381 | 0 |
N.S. |
1 | 1.15 | 1.16 | 1.57 | 2.20 | 2.21 | 0.00 | 2.95 | 0.00 |
time (sec) |
N/A | 0.356 | 0.189 | 0.015 | 0.185 | 0.289 | 0.000 | 0.376 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 200 | 179 | 345 | 357 | 343 | 0 | 709 | 0 |
N.S. |
1 | 1.20 | 1.07 | 2.07 | 2.14 | 2.05 | 0.00 | 4.25 | 0.00 |
time (sec) |
N/A | 0.408 | 0.181 | 0.016 | 0.192 | 0.300 | 0.000 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 305 | 145 | 293 | 0 | 182 | 366 | 0 | 0 |
N.S. |
1 | 0.92 | 0.44 | 0.89 | 0.00 | 0.55 | 1.11 | 0.00 | 0.00 |
time (sec) |
N/A | 0.728 | 0.501 | 0.204 | 0.000 | 0.265 | 0.441 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 204 | 107 | 190 | 0 | 146 | 243 | 0 | 0 |
N.S. |
1 | 0.97 | 0.51 | 0.90 | 0.00 | 0.69 | 1.15 | 0.00 | 0.00 |
time (sec) |
N/A | 0.604 | 0.411 | 0.167 | 0.000 | 0.252 | 0.300 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 120 | 79 | 113 | 0 | 114 | 138 | 0 | 0 |
N.S. |
1 | 0.95 | 0.63 | 0.90 | 0.00 | 0.90 | 1.10 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.226 | 0.127 | 0.000 | 0.246 | 0.226 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 49 | 47 | 46 | 0 | 88 | 63 | 0 | 0 |
N.S. |
1 | 1.09 | 1.04 | 1.02 | 0.00 | 1.96 | 1.40 | 0.00 | 0.00 |
time (sec) |
N/A | 0.300 | 0.019 | 0.081 | 0.000 | 0.270 | 0.100 | 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 | 205 | 207 | 251 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.826 | 0.026 | 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 | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 174 | 178 | 206 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.814 | 0.089 | 0.250 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 237 | 279 | 374 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.19 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.067 | 0.089 | 0.461 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 478 | 696 | 1830 | 764 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.46 | 3.83 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.633 | 10.001 | 0.408 | 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 | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 355 | 317 | 175 | 297 | 0 | 225 | 432 | 0 | 0 |
N.S. |
1 | 0.89 | 0.49 | 0.84 | 0.00 | 0.63 | 1.22 | 0.00 | 0.00 |
time (sec) |
N/A | 0.681 | 0.510 | 0.199 | 0.000 | 0.256 | 0.420 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 191 | 129 | 169 | 0 | 180 | 248 | 0 | 0 |
N.S. |
1 | 0.94 | 0.64 | 0.83 | 0.00 | 0.89 | 1.22 | 0.00 | 0.00 |
time (sec) |
N/A | 0.581 | 0.281 | 0.120 | 0.000 | 0.261 | 0.292 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 70 | 67 | 0 | 139 | 109 | 0 | 0 |
N.S. |
1 | 0.95 | 0.90 | 0.86 | 0.00 | 1.78 | 1.40 | 0.00 | 0.00 |
time (sec) |
N/A | 0.372 | 0.022 | 0.093 | 0.000 | 0.295 | 0.142 | 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 | 275 | 285 | 346 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.057 | 0.031 | 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 | 268 | 246 | 259 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.129 | 0.097 | 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 | 514 | 446 | 524 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.127 | 0.160 | 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 | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 52 | 44 | 49 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.73 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.581 | 0.233 | 0.244 | 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 | 30 | 28 | 30 | 27 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.410 | 0.127 | 0.096 | 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 | 11 | 11 | 11 | 12 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.269 | 0.011 | 0.080 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.255 | 0.233 | 0.983 | 0.246 | 0.242 | 0.316 | 0.345 | 2.726 |
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 | 154 | 137 | 83 | 146 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.54 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.421 | 0.770 | 0.279 | 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 | 84 | 77 | 62 | 73 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.74 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.349 | 0.186 | 0.171 | 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 | 38 | 35 | 35 | 34 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.92 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.367 | 0.069 | 0.083 | 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 | 12 | 12 | 14 | 12 | 527 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 43.92 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.258 | 2.129 | 0.846 | 0.948 | 0.244 | 0.390 | 0.340 | 2.707 |
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 | 257 | 225 | 110 | 215 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.43 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.680 | 0.330 | 0.146 | 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 | 147 | 131 | 117 | 107 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.80 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.464 | 0.135 | 0.131 | 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 | 63 | 57 | 53 | 51 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.84 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.033 | 0.091 | 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 | 12 | 12 | 14 | 12 | 3273 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 272.75 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.255 | 1.587 | 0.835 | 15.191 | 0.246 | 0.472 | 0.330 | 2.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 0 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 0.00 | 1.12 |
time (sec) |
N/A | 0.283 | 0.344 | 0.322 | 0.575 | 0.272 | 12.848 | 0.000 | 2.820 |
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 | 545 | 525 | 345 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.140 | 0.664 | 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 | 267 | 262 | 228 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.695 | 0.135 | 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 | 128 | 131 | 109 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 0.087 | 0.000 | 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 | 16 | 18 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.281 | 0.212 | 0.310 | 0.595 | 0.257 | 0.573 | 1.398 | 2.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 496 | 525 | 656 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.860 | 2.525 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 259 | 284 | 250 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.048 | 2.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 115 | 121 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.623 | 0.133 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |