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 | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 206 | 165 | 248 | 231 | 201 | 316 | 317 | 0 |
N.S. |
1 | 1.15 | 0.92 | 1.39 | 1.29 | 1.12 | 1.77 | 1.77 | 0.00 |
time (sec) |
N/A | 0.369 | 0.108 | 0.220 | 0.266 | 0.258 | 0.310 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 151 | 121 | 178 | 150 | 135 | 190 | 194 | 0 |
N.S. |
1 | 1.22 | 0.98 | 1.44 | 1.21 | 1.09 | 1.53 | 1.56 | 0.00 |
time (sec) |
N/A | 0.289 | 0.077 | 0.230 | 0.267 | 0.259 | 0.237 | 0.283 | 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 | 98 | 106 | 92 | 86 | 81 | 76 | 99 | 98 | 77 |
N.S. |
1 | 1.08 | 0.94 | 0.88 | 0.83 | 0.78 | 1.01 | 1.00 | 0.79 |
time (sec) |
N/A | 0.234 | 0.028 | 0.016 | 0.268 | 0.251 | 0.172 | 0.279 | 0.419 |
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 | 30 | 29 | 31 | 26 | 29 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.97 | 1.03 | 0.87 | 0.97 | 0.93 |
time (sec) |
N/A | 0.148 | 0.008 | 0.043 | 0.266 | 0.243 | 0.069 | 0.269 | 0.295 |
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 | 229 | 229 | 214 | 758 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.654 | 0.133 | 1.005 | 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) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 83 | 187 | 0 | 371 | 0 | 200 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.20 | 0.00 | 4.36 | 0.00 | 2.35 | 0.00 |
time (sec) |
N/A | 0.227 | 0.101 | 1.010 | 0.000 | 0.280 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 134 | 207 | 295 | 0 | 673 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.53 | 2.19 | 0.00 | 4.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.269 | 0.288 | 0.326 | 0.000 | 0.354 | 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 | 191 | 208 | 241 | 554 | 0 | 1125 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.26 | 2.90 | 0.00 | 5.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.339 | 0.361 | 0.211 | 0.000 | 0.860 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 374 | 393 | 355 | 541 | 0 | 446 | 743 | 816 | 0 |
N.S. |
1 | 1.05 | 0.95 | 1.45 | 0.00 | 1.19 | 1.99 | 2.18 | 0.00 |
time (sec) |
N/A | 0.966 | 0.351 | 0.568 | 0.000 | 0.275 | 0.478 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 242 | 266 | 249 | 374 | 0 | 290 | 454 | 487 | 0 |
N.S. |
1 | 1.10 | 1.03 | 1.55 | 0.00 | 1.20 | 1.88 | 2.01 | 0.00 |
time (sec) |
N/A | 0.719 | 0.239 | 0.316 | 0.000 | 0.273 | 0.320 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 164 | 154 | 189 | 0 | 156 | 233 | 244 | 0 |
N.S. |
1 | 1.15 | 1.08 | 1.33 | 0.00 | 1.10 | 1.64 | 1.72 | 0.00 |
time (sec) |
N/A | 0.531 | 0.695 | 0.197 | 0.000 | 0.243 | 0.246 | 0.284 | 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 | 47 | 51 | 47 | 72 | 72 | 65 | 82 | 75 | 142 |
N.S. |
1 | 1.09 | 1.00 | 1.53 | 1.53 | 1.38 | 1.74 | 1.60 | 3.02 |
time (sec) |
N/A | 0.249 | 0.030 | 0.000 | 0.275 | 0.254 | 0.102 | 0.273 | 0.387 |
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 | 347 | 343 | 332 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.053 | 0.263 | 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 | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 309 | 287 | 231 | 642 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.75 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.972 | 0.273 | 0.780 | 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 | 401 | 386 | 315 | 966 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.79 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.283 | 0.826 | 1.338 | 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 | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 393 | 377 | 304 | 327 | 0 | 0 | 0 | 609 | 0 |
N.S. |
1 | 0.96 | 0.77 | 0.83 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 1.249 | 0.606 | 0.214 | 0.000 | 0.000 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 232 | 187 | 206 | 0 | 0 | 0 | 337 | 0 |
N.S. |
1 | 0.95 | 0.77 | 0.84 | 0.00 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.866 | 0.402 | 0.204 | 0.000 | 0.000 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 109 | 98 | 103 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.95 | 0.85 | 0.90 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.510 | 0.169 | 0.080 | 0.000 | 0.000 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 48 | 44 | 48 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.91 | 0.83 | 0.91 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.356 | 0.013 | 0.011 | 0.000 | 0.000 | 0.000 | 0.297 | 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 | 0.184 | 0.196 | 3.372 | 0.348 | 0.251 | 0.904 | 0.337 | 0.232 |
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 | 0.184 | 0.338 | 1.359 | 0.358 | 0.253 | 1.782 | 0.823 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 362 | 362 | 290 | 526 | 0 | 0 | 0 | 1276 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.45 | 0.00 | 0.00 | 0.00 | 3.52 | 0.00 |
time (sec) |
N/A | 0.784 | 1.634 | 0.355 | 0.000 | 0.000 | 0.000 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 149 | 257 | 0 | 0 | 0 | 554 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.42 | 0.00 | 0.00 | 0.00 | 3.06 | 0.00 |
time (sec) |
N/A | 0.487 | 0.893 | 0.154 | 0.000 | 0.000 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 83 | 72 | 76 | 0 | 0 | 0 | 192 | 0 |
N.S. |
1 | 0.97 | 0.84 | 0.88 | 0.00 | 0.00 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 0.546 | 0.179 | 0.014 | 0.000 | 0.000 | 0.000 | 0.311 | 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 | 297 | 51 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 16.50 | 2.83 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.182 | 10.233 | 5.662 | 1.603 | 0.245 | 1.668 | 0.398 | 0.237 |
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 | 426 | 92 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 23.67 | 5.11 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.184 | 12.804 | 1.961 | 2.601 | 0.249 | 6.159 | 0.965 | 0.224 |
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 | 227 | 32 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 12.61 | 1.78 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.416 | 11.395 | 0.236 | 1.682 | 0.264 | 14.916 | 0.420 | 0.386 |
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 | 154 | 125 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.279 | 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 | 0.190 | 0.353 | 2.317 | 0.368 | 0.242 | 0.952 | 0.363 | 0.229 |
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 | 237 | 34 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 13.17 | 1.89 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.187 | 0.732 | 1.448 | 1.793 | 0.260 | 15.553 | 0.455 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 669 | 371 | 356 | 1396 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.55 | 0.53 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.960 | 0.331 | 0.625 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 450 | 263 | 237 | 973 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.53 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.743 | 0.409 | 0.499 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 140 | 132 | 628 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.59 | 0.55 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.481 | 0.178 | 0.499 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 736 | 517 | 368 | 823 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.50 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.214 | 0.746 | 0.647 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 860 | 632 | 600 | 1352 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.70 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.693 | 2.373 | 0.661 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 959 | 498 | 463 | 2074 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 0.48 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.180 | 0.831 | 0.721 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 680 | 367 | 332 | 1535 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.54 | 0.49 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.948 | 0.356 | 0.565 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 370 | 193 | 216 | 1014 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 0.58 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.547 | 0.219 | 0.557 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1073 | 709 | 507 | 1546 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.47 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.337 | 1.192 | 0.643 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1281 | 630 | 587 | 2903 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.49 | 0.46 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.342 | 0.745 | 0.766 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 940 | 481 | 390 | 2090 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.51 | 0.41 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.092 | 0.523 | 0.657 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 517 | 256 | 251 | 1423 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.50 | 0.49 | 2.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.633 | 0.292 | 0.627 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1648 | 1019 | 787 | 2580 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.48 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.854 | 2.131 | 0.734 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 450 | 262 | 343 | 856 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.76 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.791 | 1.139 | 0.546 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 162 | 266 | 505 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.99 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.624 | 0.661 | 0.497 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 87 | 172 | 247 | 90 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 1.37 | 1.96 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.426 | 0.264 | 0.472 | 0.310 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 380 | 288 | 232 | 508 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.61 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.015 | 0.159 | 0.494 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 507 | 384 | 295 | 932 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.58 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.352 | 0.372 | 0.654 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 315 | 213 | 194 | 724 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.62 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.730 | 0.814 | 0.860 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 143 | 156 | 488 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.67 | 0.73 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.610 | 0.555 | 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 | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 100 | 135 | 305 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 0.94 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.388 | 0.419 | 0.867 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 654 | 431 | 359 | 1094 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.55 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.402 | 1.564 | 1.388 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 528 | 452 | 868 | 6743 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.86 | 1.64 | 12.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.896 | 2.548 | 1.023 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 410 | 277 | 366 | 5114 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.89 | 12.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.661 | 0.946 | 1.009 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 192 | 285 | 3783 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 1.05 | 13.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.537 | 0.754 | 0.877 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 159 | 208 | 2237 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.91 | 9.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 0.571 | 0.959 | 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(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1300 | 821 | 2078 | 7971 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 1.60 | 6.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.080 | 12.894 | 1.497 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1154 | 750 | 708 | 2728 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.61 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.740 | 0.744 | 0.865 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 737 | 477 | 441 | 1852 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.60 | 2.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.141 | 0.595 | 0.728 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 396 | 256 | 225 | 1236 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.57 | 3.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.695 | 0.176 | 0.646 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1442 | 1018 | 516 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.193 | 0.967 | 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 | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1685 | 1066 | 872 | 4176 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.52 | 2.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.413 | 1.495 | 1.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1108 | 699 | 616 | 3032 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.56 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.585 | 0.667 | 0.928 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 621 | 384 | 395 | 2021 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.64 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.875 | 0.418 | 0.799 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1992 | 1369 | 740 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.772 | 1.730 | 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 | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 2290 | 1379 | 1114 | 5977 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.49 | 2.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.236 | 1.282 | 1.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1533 | 922 | 742 | 4170 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.48 | 2.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.150 | 0.940 | 1.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 878 | 513 | 470 | 2852 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.54 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.121 | 0.594 | 0.941 | 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(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 2989 | 1986 | 1275 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.963 | 3.674 | 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 | C | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 692 | 417 | 582 | 1636 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.84 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.865 | 1.565 | 0.810 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 410 | 240 | 400 | 928 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.59 | 0.98 | 2.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.740 | 1.348 | 0.700 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 128 | 118 | 460 | 184 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.69 | 2.69 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.557 | 0.677 | 0.639 | 0.313 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 589 | 402 | 357 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.596 | 0.294 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1113 | 721 | 651 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.998 | 0.573 | 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 | B | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 738 | 447 | 325 | 1528 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.61 | 0.44 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.274 | 2.523 | 1.193 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 513 | 314 | 259 | 975 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.61 | 0.50 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.107 | 1.583 | 1.075 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 410 | 243 | 237 | 612 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.59 | 0.58 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.783 | 0.999 | 1.204 | 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(-2) | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1137 | 722 | 597 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.64 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.259 | 3.807 | 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 | B | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1589 | 918 | 715 | 13140 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.45 | 8.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.341 | 6.256 | 1.402 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1025 | 614 | 711 | 9720 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.69 | 9.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.435 | 6.275 | 1.239 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 641 | 398 | 683 | 5894 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 1.07 | 9.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.941 | 6.232 | 1.248 | 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 | 35 | 35 | 37 | 33 | 35 | 47 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.34 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.317 | 0.167 | 7.071 | 1.933 | 0.260 | 0.000 | 0.425 | 0.254 |
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 | 634 | 628 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.081 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 514 | 506 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.655 | 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 | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 390 | 386 | 2724 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 6.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.260 | 10.459 | 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 | 237 | 238 | 246 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.704 | 0.034 | 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 | 35 | 35 | 37 | 33 | 35 | 57 | 34 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.63 | 0.97 | 1.00 | 1.00 |
time (sec) |
N/A | 0.335 | 0.420 | 12.391 | 1.011 | 0.241 | 9.436 | 0.419 | 0.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 379 | 305 | 445 | 528 | 441 | 770 | 784 | 0 |
N.S. |
1 | 1.08 | 0.87 | 1.27 | 1.50 | 1.26 | 2.19 | 2.23 | 0.00 |
time (sec) |
N/A | 1.280 | 0.421 | 0.197 | 0.282 | 0.269 | 0.505 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 275 | 211 | 304 | 353 | 295 | 502 | 491 | 0 |
N.S. |
1 | 1.11 | 0.85 | 1.23 | 1.42 | 1.19 | 2.02 | 1.98 | 0.00 |
time (sec) |
N/A | 0.807 | 0.323 | 0.198 | 0.281 | 0.269 | 0.357 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 168 | 138 | 178 | 199 | 161 | 267 | 259 | 0 |
N.S. |
1 | 1.14 | 0.93 | 1.20 | 1.34 | 1.09 | 1.80 | 1.75 | 0.00 |
time (sec) |
N/A | 0.438 | 0.203 | 0.080 | 0.279 | 0.255 | 0.246 | 0.308 | 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 | 344 | 345 | 322 | 1566 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 4.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.916 | 0.593 | 1.905 | 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 | 358 | 354 | 334 | 954 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.93 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.523 | 0.587 | 2.267 | 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) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 238 | 263 | 535 | 0 | 1184 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 1.30 | 2.65 | 0.00 | 5.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 0.739 | 2.562 | 0.000 | 3.243 | 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 | 257 | 271 | 321 | 908 | 0 | 1920 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.25 | 3.53 | 0.00 | 7.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.531 | 0.757 | 3.434 | 0.000 | 16.148 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 360 | 382 | 418 | 1550 | 0 | 2839 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.16 | 4.31 | 0.00 | 7.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.686 | 1.069 | 3.389 | 0.000 | 64.657 | 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 | 457 | 497 | 494 | 2406 | 0 | 3904 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.08 | 5.26 | 0.00 | 8.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.906 | 1.314 | 3.401 | 0.000 | 175.625 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 512 | 556 | 463 | 633 | 859 | 676 | 1263 | 1337 | 0 |
N.S. |
1 | 1.09 | 0.90 | 1.24 | 1.68 | 1.32 | 2.47 | 2.61 | 0.00 |
time (sec) |
N/A | 2.235 | 0.527 | 0.366 | 0.287 | 0.288 | 0.670 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 361 | 389 | 307 | 449 | 581 | 449 | 821 | 847 | 0 |
N.S. |
1 | 1.08 | 0.85 | 1.24 | 1.61 | 1.24 | 2.27 | 2.35 | 0.00 |
time (sec) |
N/A | 1.362 | 0.519 | 0.375 | 0.291 | 0.275 | 0.506 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 249 | 186 | 273 | 334 | 245 | 449 | 448 | 0 |
N.S. |
1 | 1.12 | 0.83 | 1.22 | 1.50 | 1.10 | 2.01 | 2.01 | 0.00 |
time (sec) |
N/A | 0.735 | 0.298 | 0.315 | 0.292 | 0.262 | 0.341 | 0.295 | 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 | 459 | 476 | 457 | 2438 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.00 | 5.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.169 | 0.929 | 2.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |