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 | C | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 156 | 93 | 47 | 331 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 2.36 | 1.41 | 0.71 | 5.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.262 | 2.601 | 0.092 | 0.312 | 0.354 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 95 | 204 | 340 | 76 | 435 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 2.04 | 3.40 | 0.76 | 4.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.278 | 4.584 | 3.979 | 0.283 | 0.446 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 141 | 145 | 287 | 508 | 131 | 587 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 2.04 | 3.60 | 0.93 | 4.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 3.816 | 5.039 | 0.288 | 0.866 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 206 | 233 | 3604 | 330 | 426 | 0 | 4702 | 0 |
N.S. |
1 | 0.91 | 1.03 | 15.88 | 1.45 | 1.88 | 0.00 | 20.71 | 0.00 |
time (sec) |
N/A | 0.371 | 6.340 | 3.007 | 0.372 | 0.527 | 0.000 | 4.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 168 | 188 | 1639 | 296 | 307 | 0 | 2688 | 0 |
N.S. |
1 | 0.90 | 1.01 | 8.81 | 1.59 | 1.65 | 0.00 | 14.45 | 0.00 |
time (sec) |
N/A | 0.327 | 2.578 | 2.681 | 0.644 | 0.491 | 0.000 | 2.961 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 111 | 170 | 920 | 176 | 268 | 0 | 1366 | 0 |
N.S. |
1 | 0.98 | 1.50 | 8.14 | 1.56 | 2.37 | 0.00 | 12.09 | 0.00 |
time (sec) |
N/A | 0.264 | 1.724 | 2.487 | 0.526 | 0.480 | 0.000 | 1.883 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 127 | 124 | 492 | 678 | 0 | 747 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 3.87 | 5.34 | 0.00 | 5.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 5.224 | 2.522 | 0.000 | 0.821 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 167 | 168 | 1012 | 1728 | 0 | 994 | 0 | 1467 | 0 |
N.S. |
1 | 1.01 | 6.06 | 10.35 | 0.00 | 5.95 | 0.00 | 8.78 | 0.00 |
time (sec) |
N/A | 0.392 | 7.578 | 2.574 | 0.000 | 0.987 | 0.000 | 2.442 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 223 | 231 | 415 | 2518 | 0 | 1365 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.86 | 11.29 | 0.00 | 6.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.493 | 5.530 | 2.564 | 0.000 | 1.217 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 226 | 278 | 1078 | 0 | 2163 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.25 | 4.86 | 0.00 | 9.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.479 | 5.938 | 9.819 | 0.000 | 66.512 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 163 | 324 | 824 | 0 | 1931 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.96 | 4.99 | 0.00 | 11.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.378 | 6.152 | 6.076 | 0.000 | 4.322 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 123 | 142 | 297 | 0 | 537 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.14 | 2.38 | 0.00 | 4.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.284 | 0.886 | 0.051 | 0.000 | 0.540 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 98 | 220 | 121 | 73 | 387 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 2.20 | 1.21 | 0.73 | 3.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.286 | 3.614 | 0.085 | 0.212 | 0.464 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 162 | 144 | 177 | 579 | 175 | 497 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 1.09 | 3.57 | 1.08 | 3.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 2.488 | 5.329 | 0.221 | 0.862 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 196 | 175 | 213 | 769 | 202 | 655 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 1.09 | 3.92 | 1.03 | 3.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.334 | 3.025 | 6.129 | 0.229 | 2.732 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 151 | 112 | 131 | 214 | 124 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.78 | 0.91 | 1.49 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 1.639 | 0.890 | 0.250 | 0.312 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 86 | 74 | 78 | 106 | 75 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.84 | 0.89 | 1.20 | 0.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 2.330 | 0.838 | 0.236 | 0.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 52 | 50 | 35 | 45 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.35 | 0.95 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 1.042 | 0.854 | 0.227 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 221 | 307 | 0 | 134 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 5.26 | 7.31 | 0.00 | 3.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.248 | 3.136 | 0.856 | 0.000 | 0.353 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 91 | 97 | 367 | 955 | 0 | 284 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 4.03 | 10.49 | 0.00 | 3.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 3.791 | 0.938 | 0.000 | 0.391 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 143 | 160 | 273 | 1627 | 0 | 437 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.91 | 11.38 | 0.00 | 3.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.355 | 4.690 | 0.886 | 0.000 | 0.373 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 163 | 314 | 411 | 0 | 788 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 2.15 | 2.82 | 0.00 | 5.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.343 | 5.165 | 7.355 | 0.000 | 2.254 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 97 | 270 | 280 | 0 | 696 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 2.90 | 3.01 | 0.00 | 7.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.282 | 4.128 | 4.398 | 0.000 | 0.469 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 67 | 0 | 125 | 0 | 0 | 40 |
N.S. |
1 | 1.00 | 1.00 | 1.46 | 0.00 | 2.72 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.205 | 0.116 | 0.092 | 0.000 | 0.283 | 0.000 | 0.000 | 11.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 49 | 31 | 30 | 49 | 0 | 0 | 36 |
N.S. |
1 | 1.00 | 1.63 | 1.03 | 1.00 | 1.63 | 0.00 | 0.00 | 1.20 |
time (sec) |
N/A | 0.239 | 0.693 | 0.106 | 0.219 | 0.309 | 0.000 | 0.000 | 11.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 68 | 84 | 87 | 90 | 0 | 0 | 145 |
N.S. |
1 | 0.97 | 0.92 | 1.14 | 1.18 | 1.22 | 0.00 | 0.00 | 1.96 |
time (sec) |
N/A | 0.265 | 0.747 | 1.783 | 0.216 | 0.374 | 0.000 | 0.000 | 17.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 126 | 90 | 135 | 173 | 141 | 0 | 0 | 761 |
N.S. |
1 | 1.02 | 0.73 | 1.10 | 1.41 | 1.15 | 0.00 | 0.00 | 6.19 |
time (sec) |
N/A | 0.316 | 2.396 | 2.511 | 0.230 | 0.634 | 0.000 | 0.000 | 20.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 196 | 186 | 273 | 389 | 233 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.93 | 1.37 | 1.95 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 3.629 | 2.997 | 0.263 | 0.403 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 129 | 106 | 208 | 216 | 158 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.81 | 1.59 | 1.65 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.308 | 5.503 | 1.122 | 0.232 | 0.348 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 74 | 72 | 124 | 83 | 104 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.95 | 1.63 | 1.09 | 1.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.242 | 3.527 | 0.866 | 0.229 | 0.289 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 84 | 82 | 1007 | 1046 | 0 | 355 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 11.99 | 12.45 | 0.00 | 4.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 8.775 | 0.853 | 0.000 | 0.361 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-1) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 127 | 133 | 304 | 1238 | 0 | 455 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 2.39 | 9.75 | 0.00 | 3.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 4.740 | 0.968 | 0.000 | 0.426 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 187 | 211 | 345 | 1846 | 0 | 705 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.84 | 9.87 | 0.00 | 3.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 5.498 | 0.879 | 0.000 | 0.417 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 187 | 211 | 325 | 4726 | 0 | 1046 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.74 | 25.27 | 0.00 | 5.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.385 | 4.593 | 4.432 | 0.000 | 80.815 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 142 | 282 | 1597 | 0 | 908 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 2.10 | 11.92 | 0.00 | 6.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.328 | 4.362 | 2.919 | 0.000 | 3.776 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 83 | 232 | 102 | 0 | 310 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 2.73 | 1.20 | 0.00 | 3.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 6.406 | 0.057 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 60 | 74 | 59 | 58 | 90 | 0 | 0 | 2978 |
N.S. |
1 | 0.97 | 1.19 | 0.95 | 0.94 | 1.45 | 0.00 | 0.00 | 48.03 |
time (sec) |
N/A | 0.259 | 2.707 | 0.118 | 0.226 | 0.483 | 0.000 | 0.000 | 18.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 106 | 119 | 132 | 141 | 155 | 0 | 0 | 269040 |
N.S. |
1 | 0.93 | 1.04 | 1.16 | 1.24 | 1.36 | 0.00 | 0.00 | 2360.00 |
time (sec) |
N/A | 0.292 | 1.539 | 2.884 | 0.241 | 2.130 | 0.000 | 0.000 | 34.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 161 | 135 | 207 | 255 | 232 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.79 | 1.21 | 1.49 | 1.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 2.081 | 5.470 | 0.296 | 18.753 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 240 | 294 | 382 | 534 | 370 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.19 | 1.54 | 2.15 | 1.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.393 | 2.906 | 3.573 | 0.330 | 0.558 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 172 | 205 | 247 | 308 | 270 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.22 | 1.47 | 1.83 | 1.61 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 6.908 | 1.332 | 0.308 | 0.447 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 122 | 124 | 155 | 135 | 202 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.05 | 1.31 | 1.14 | 1.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.258 | 6.315 | 1.023 | 0.300 | 0.328 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 136 | 148 | 300 | 17400 | 0 | 696 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 2.21 | 127.94 | 0.00 | 5.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 10.677 | 3.227 | 0.000 | 0.395 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 177 | 188 | 380 | 26227 | 0 | 889 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 2.15 | 148.18 | 0.00 | 5.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 5.785 | 6.767 | 0.000 | 0.474 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-1) | B | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 237 | 260 | 1132 | 18432 | 0 | 1037 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 4.78 | 77.77 | 0.00 | 4.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.503 | 8.494 | 4.462 | 0.000 | 0.508 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 277 | 378 | 10810 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.54 | 43.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.465 | 6.578 | 17.353 | 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 | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 199 | 309 | 1895 | 0 | 1294 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.71 | 10.47 | 0.00 | 7.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.380 | 7.598 | 4.390 | 0.000 | 118.869 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 144 | 1331 | 163 | 0 | 561 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 9.93 | 1.22 | 0.00 | 4.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.290 | 7.722 | 0.062 | 0.000 | 0.345 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 133 | 90 | 85 | 156 | 0 | 0 | 324 |
N.S. |
1 | 1.00 | 1.37 | 0.93 | 0.88 | 1.61 | 0.00 | 0.00 | 3.34 |
time (sec) |
N/A | 0.275 | 3.876 | 0.109 | 0.292 | 4.582 | 0.000 | 0.000 | 26.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 138 | 140 | 180 | 195 | 240 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.96 | 1.23 | 1.34 | 1.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.310 | 2.177 | 6.290 | 0.306 | 47.748 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 195 | 174 | 279 | 337 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.79 | 1.27 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 2.923 | 6.460 | 0.302 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 292 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.484 | 3.214 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 121 | 147 | 275 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.351 | 4.004 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 208 | 215 | 283 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 8.996 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 140 | 138 | 184 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.297 | 4.838 | 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 | 79 | 79 | 80 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.240 | 1.306 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 1215 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 13.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.267 | 15.629 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 252 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.280 | 21.803 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 3698 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 44.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.263 | 17.391 | 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 | 78 | 78 | 192 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.567 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.240 | 0.879 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 118 | 111 | 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 | 0.276 | 1.416 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 180 | 183 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.349 | 0.989 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 295 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.521 | 3.115 | 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 | 63 | 63 | 63 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.805 | 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 | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 0.165 | 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 | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 31 | 9186 | 37 | 51 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 278.36 | 1.12 | 1.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.331 | 0.576 | 3.974 | 0.244 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 69 | 84 | 59 | 29777 | 73 | 104 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 0.86 | 431.55 | 1.06 | 1.51 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.382 | 0.623 | 75.510 | 0.251 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 89 | 60670 | 108 | 180 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.86 | 583.37 | 1.04 | 1.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.402 | 0.816 | 0.323 | 0.267 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 506 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 5.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.444 | 3.579 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 284 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.409 | 1.808 | 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 | 81 | 81 | 77 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.444 | 0.576 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 1399 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 15.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.436 | 14.732 | 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 | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 25 | 27 | 27 | 0 | 27 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.223 | 5.937 | 0.362 | 10.904 | 0.286 | 0.000 | 6.249 | 11.406 |
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 | 99 | 99 | 81 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.461 | 0.940 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 2033 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 18.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.387 | 17.453 | 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 | 101 | 101 | 91 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 1.047 | 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 | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 29 | 29 | 0 | 29 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.374 | 4.161 | 0.398 | 7.946 | 0.276 | 0.000 | 43.581 | 11.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 51 | 46 | 43 | 157 | 56 | 68 | 519 | 53 |
N.S. |
1 | 0.78 | 0.71 | 0.66 | 2.42 | 0.86 | 1.05 | 7.98 | 0.82 |
time (sec) |
N/A | 0.251 | 0.236 | 0.067 | 0.306 | 0.250 | 0.196 | 1.027 | 11.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 41 | 38 | 35 | 102 | 43 | 54 | 297 | 36 |
N.S. |
1 | 0.82 | 0.76 | 0.70 | 2.04 | 0.86 | 1.08 | 5.94 | 0.72 |
time (sec) |
N/A | 0.249 | 0.119 | 0.046 | 0.313 | 0.238 | 0.139 | 0.591 | 11.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 29 | 26 | 25 | 59 | 29 | 37 | 133 | 24 |
N.S. |
1 | 0.91 | 0.81 | 0.78 | 1.84 | 0.91 | 1.16 | 4.16 | 0.75 |
time (sec) |
N/A | 0.250 | 0.043 | 0.032 | 0.303 | 0.256 | 0.099 | 0.444 | 11.394 |
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 | 31 | 29 | 26 | 25 | 36 | 40 | 87 | 37 | 26 |
N.S. |
1 | 0.94 | 0.84 | 0.81 | 1.16 | 1.29 | 2.81 | 1.19 | 0.84 |
time (sec) |
N/A | 0.224 | 0.027 | 0.043 | 0.308 | 0.258 | 0.279 | 0.406 | 11.038 |
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 | 55 | 55 | 36 | 42 | 67 | 84 | 248 | 51 | 35 |
N.S. |
1 | 1.00 | 0.65 | 0.76 | 1.22 | 1.53 | 4.51 | 0.93 | 0.64 |
time (sec) |
N/A | 0.284 | 0.055 | 0.052 | 0.308 | 0.264 | 0.368 | 0.432 | 11.280 |
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 | 79 | 81 | 46 | 59 | 90 | 120 | 454 | 61 | 51 |
N.S. |
1 | 1.03 | 0.58 | 0.75 | 1.14 | 1.52 | 5.75 | 0.77 | 0.65 |
time (sec) |
N/A | 0.368 | 0.050 | 0.080 | 0.309 | 0.272 | 0.505 | 0.477 | 11.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 66 | 63 | 73 | 99 | 67 | 116 | 1450 | 68 |
N.S. |
1 | 0.89 | 0.85 | 0.99 | 1.34 | 0.91 | 1.57 | 19.59 | 0.92 |
time (sec) |
N/A | 0.395 | 0.279 | 0.073 | 0.247 | 0.258 | 0.166 | 3.792 | 11.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 50 | 65 | 55 | 70 | 51 | 88 | 890 | 57 |
N.S. |
1 | 0.94 | 1.23 | 1.04 | 1.32 | 0.96 | 1.66 | 16.79 | 1.08 |
time (sec) |
N/A | 0.328 | 0.189 | 0.067 | 0.222 | 0.259 | 0.120 | 1.382 | 11.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 40 | 35 | 37 | 36 | 60 | 402 | 37 |
N.S. |
1 | 1.00 | 1.18 | 1.03 | 1.09 | 1.06 | 1.76 | 11.82 | 1.09 |
time (sec) |
N/A | 0.251 | 0.083 | 0.042 | 0.235 | 0.297 | 0.090 | 0.574 | 11.669 |
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 | 26 | 28 | 38 | 25 | 31 | 46 | 58 | 32 | 36 |
N.S. |
1 | 1.08 | 1.46 | 0.96 | 1.19 | 1.77 | 2.23 | 1.23 | 1.38 |
time (sec) |
N/A | 0.251 | 0.045 | 0.165 | 0.233 | 0.281 | 0.207 | 0.465 | 11.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 36 | 40 | 37 | 31 | 61 | 97 | 153 | 54 |
N.S. |
1 | 1.06 | 1.18 | 1.09 | 0.91 | 1.79 | 2.85 | 4.50 | 1.59 |
time (sec) |
N/A | 0.271 | 0.176 | 0.161 | 0.223 | 0.257 | 0.591 | 0.597 | 11.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 52 | 56 | 58 | 52 | 85 | 124 | 245 | 74 |
N.S. |
1 | 0.98 | 1.06 | 1.09 | 0.98 | 1.60 | 2.34 | 4.62 | 1.40 |
time (sec) |
N/A | 0.340 | 0.257 | 0.185 | 0.238 | 0.262 | 1.323 | 0.734 | 11.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 67 | 129 | 74 | 72 | 69 | 109 | 1011 | 70 |
N.S. |
1 | 0.84 | 1.61 | 0.92 | 0.90 | 0.86 | 1.36 | 12.64 | 0.88 |
time (sec) |
N/A | 0.400 | 0.071 | 0.067 | 0.305 | 0.252 | 0.203 | 3.434 | 11.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 51 | 97 | 57 | 57 | 54 | 82 | 589 | 53 |
N.S. |
1 | 0.85 | 1.62 | 0.95 | 0.95 | 0.90 | 1.37 | 9.82 | 0.88 |
time (sec) |
N/A | 0.328 | 0.040 | 0.052 | 0.305 | 0.255 | 0.141 | 1.114 | 11.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 37 | 65 | 38 | 41 | 38 | 54 | 269 | 37 |
N.S. |
1 | 0.92 | 1.62 | 0.95 | 1.02 | 0.95 | 1.35 | 6.72 | 0.92 |
time (sec) |
N/A | 0.256 | 0.032 | 0.038 | 0.329 | 0.251 | 0.100 | 0.556 | 11.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 28 | 20 | 23 | 21 | 20 | 231 | 21 |
N.S. |
1 | 1.00 | 1.47 | 1.05 | 1.21 | 1.11 | 1.05 | 12.16 | 1.11 |
time (sec) |
N/A | 0.151 | 0.002 | 0.020 | 0.326 | 0.259 | 0.072 | 0.364 | 11.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 34 | 29 | 27 | 29 | 42 | 43 | 21 |
N.S. |
1 | 1.00 | 1.62 | 1.38 | 1.29 | 1.38 | 2.00 | 2.05 | 1.00 |
time (sec) |
N/A | 0.196 | 0.020 | 0.090 | 0.315 | 0.265 | 0.285 | 0.518 | 11.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 65 | 41 | 46 | 49 | 66 | 99 | 40 |
N.S. |
1 | 1.00 | 1.67 | 1.05 | 1.18 | 1.26 | 1.69 | 2.54 | 1.03 |
time (sec) |
N/A | 0.268 | 0.044 | 0.156 | 0.313 | 0.252 | 0.791 | 0.638 | 11.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 51 | 69 | 55 | 61 | 64 | 94 | 157 | 57 |
N.S. |
1 | 0.84 | 1.13 | 0.90 | 1.00 | 1.05 | 1.54 | 2.57 | 0.93 |
time (sec) |
N/A | 0.339 | 0.058 | 0.168 | 0.307 | 0.260 | 1.786 | 0.801 | 11.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 98 | 89 | 114 | 162 | 107 | 206 | 3275 | 113 |
N.S. |
1 | 0.93 | 0.85 | 1.09 | 1.54 | 1.02 | 1.96 | 31.19 | 1.08 |
time (sec) |
N/A | 0.296 | 0.393 | 0.089 | 0.223 | 0.257 | 0.237 | 11.464 | 11.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 79 | 72 | 90 | 127 | 86 | 160 | 2205 | 97 |
N.S. |
1 | 0.96 | 0.88 | 1.10 | 1.55 | 1.05 | 1.95 | 26.89 | 1.18 |
time (sec) |
N/A | 0.287 | 0.321 | 0.075 | 0.235 | 0.267 | 0.184 | 4.151 | 11.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 60 | 54 | 66 | 82 | 64 | 112 | 1250 | 68 |
N.S. |
1 | 0.97 | 0.87 | 1.06 | 1.32 | 1.03 | 1.81 | 20.16 | 1.10 |
time (sec) |
N/A | 0.250 | 0.248 | 0.052 | 0.228 | 0.267 | 0.129 | 1.619 | 11.256 |