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 | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 670 | 372 | 442 | 1396 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.56 | 0.66 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.950 | 1.505 | 1.733 | 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 | 320 | 973 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.71 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.757 | 1.495 | 1.395 | 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 | 219 | 628 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.59 | 0.92 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.483 | 1.672 | 1.256 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 725 | 506 | 1095 | 816 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 1.51 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.210 | 4.191 | 2.639 | 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 | No | No | TBD | TBD | TBD | TBD | TBD |
size | 851 | 623 | 1130 | 1939 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 1.33 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.631 | 10.570 | 2.807 | 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 | 910 | 2146 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 0.95 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.160 | 5.610 | 1.668 | 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 | 591 | 1533 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.54 | 0.87 | 2.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.961 | 3.080 | 1.418 | 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 | 337 | 1012 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 0.91 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.566 | 2.246 | 1.454 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1064 | 700 | 3034 | 1559 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 2.85 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.404 | 15.835 | 3.006 | 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 | 1582 | 3019 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.49 | 1.23 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.376 | 9.407 | 1.742 | 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 | 794 | 2204 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.51 | 0.84 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.105 | 5.603 | 1.463 | 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 | 526 | 1419 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.50 | 1.02 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.608 | 3.467 | 1.424 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1637 | 1008 | 6216 | 2665 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 3.80 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.856 | 23.588 | 3.125 | 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 | 342 | 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 | 1.604 | 1.434 | 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 | 0.618 | 1.237 | 1.435 | 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 | 127 | 88 | 172 | 247 | 108 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.69 | 1.35 | 1.94 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.671 | 1.376 | 0.309 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 370 | 276 | 930 | 487 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 2.51 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.016 | 2.714 | 1.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 496 | 374 | 1108 | 1622 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 2.23 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.359 | 5.903 | 2.682 | 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 | 0.325 | 0.181 | 22.416 | 1.993 | 0.267 | 0.000 | 0.434 | 0.304 |
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 | 496 | 508 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.704 | 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 | 374 | 392 | 1248 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 3.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.254 | 6.292 | 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 | 0.698 | 0.004 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | 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 | 0.354 | 0.367 | 56.020 | 1.012 | 0.259 | 10.067 | 0.415 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 166 | 104 | 235 | 333 | 94 | 255 | 242 | 0 |
N.S. |
1 | 1.21 | 0.76 | 1.72 | 2.43 | 0.69 | 1.86 | 1.77 | 0.00 |
time (sec) |
N/A | 0.346 | 0.109 | 0.114 | 0.275 | 0.259 | 0.362 | 0.281 | 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 | 94 | 123 | 83 | 161 | 220 | 75 | 170 | 156 | 0 |
N.S. |
1 | 1.31 | 0.88 | 1.71 | 2.34 | 0.80 | 1.81 | 1.66 | 0.00 |
time (sec) |
N/A | 0.296 | 0.093 | 0.085 | 0.275 | 0.254 | 0.293 | 0.262 | 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 | 80 | 86 | 69 | 78 | 153 | 59 | 104 | 88 | 0 |
N.S. |
1 | 1.08 | 0.86 | 0.98 | 1.91 | 0.74 | 1.30 | 1.10 | 0.00 |
time (sec) |
N/A | 0.258 | 0.054 | 0.086 | 0.284 | 0.242 | 0.196 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 34 | 154 | 33 | 32 | 41 | 46 | 32 | 88 |
N.S. |
1 | 0.94 | 4.28 | 0.92 | 0.89 | 1.14 | 1.28 | 0.89 | 2.44 |
time (sec) |
N/A | 0.200 | 0.095 | 0.083 | 0.275 | 0.248 | 0.113 | 0.261 | 0.599 |
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 | 177 | 177 | 228 | 199 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.29 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.582 | 0.321 | 3.970 | 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) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 67 | 79 | 74 | 0 | 360 | 0 | 79 | 0 |
N.S. |
1 | 1.06 | 1.25 | 1.17 | 0.00 | 5.71 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.257 | 0.069 | 0.700 | 0.000 | 0.285 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 109 | 126 | 116 | 0 | 482 | 0 | 242 | 0 |
N.S. |
1 | 1.06 | 1.22 | 1.13 | 0.00 | 4.68 | 0.00 | 2.35 | 0.00 |
time (sec) |
N/A | 0.291 | 0.196 | 0.862 | 0.000 | 0.307 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 163 | 168 | 230 | 0 | 580 | 0 | 557 | 0 |
N.S. |
1 | 1.13 | 1.17 | 1.60 | 0.00 | 4.03 | 0.00 | 3.87 | 0.00 |
time (sec) |
N/A | 0.330 | 0.203 | 0.832 | 0.000 | 0.319 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 79 | 74 | 71 | 0 | 66 | 109 | 78 | 60 |
N.S. |
1 | 0.96 | 0.90 | 0.87 | 0.00 | 0.80 | 1.33 | 0.95 | 0.73 |
time (sec) |
N/A | 0.330 | 0.042 | 0.717 | 0.000 | 0.249 | 0.158 | 0.297 | 0.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 49 | 48 | 0 | 53 | 63 | 52 | 44 |
N.S. |
1 | 1.11 | 1.04 | 1.02 | 0.00 | 1.13 | 1.34 | 1.11 | 0.94 |
time (sec) |
N/A | 0.259 | 0.029 | 0.696 | 0.000 | 0.254 | 0.108 | 0.311 | 0.307 |
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 | 12 | 12 | 12 | 13 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.242 | 0.034 | 0.578 | 0.000 | 0.000 | 0.000 | 0.284 | 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 | 40 | 38 | 40 | 37 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.95 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.339 | 0.064 | 0.714 | 0.000 | 0.000 | 0.000 | 0.287 | 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 | 65 | 58 | 65 | 53 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.89 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.382 | 0.048 | 0.715 | 0.000 | 0.000 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 106 | 79 | 140 | 0 | 0 | 0 | 183 | 0 |
N.S. |
1 | 0.95 | 0.71 | 1.26 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.529 | 0.036 | 0.947 | 0.000 | 0.000 | 0.000 | 0.409 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 84 | 76 | 105 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.94 | 0.85 | 1.18 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.441 | 0.036 | 1.019 | 0.000 | 0.000 | 0.000 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 79 | 66 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.96 | 1.44 | 1.20 | 0.00 | 0.00 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.361 | 0.036 | 1.013 | 0.000 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 78 | 28 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 2.36 | 0.85 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.279 | 0.033 | 0.796 | 0.000 | 0.000 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 62 | 97 | 82 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.52 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.379 | 0.055 | 0.976 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 86 | 139 | 120 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.54 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.430 | 0.337 | 1.002 | 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(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 128 | 93 | 0 | 0 | 0 | 167 | 0 |
N.S. |
1 | 1.02 | 1.21 | 0.88 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.526 | 0.144 | 1.872 | 0.000 | 0.000 | 0.000 | 0.392 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 109 | 133 | 95 | 0 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.01 | 1.23 | 0.88 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.513 | 0.166 | 1.822 | 0.000 | 0.000 | 0.000 | 0.419 | 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 | 68 | 66 | 59 | 92 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.87 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.382 | 0.074 | 1.100 | 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 | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 30 | 33 | 30 | 26 | 31 | 27 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.97 | 0.88 | 0.76 | 0.91 | 0.79 | 0.00 |
time (sec) |
N/A | 0.227 | 0.021 | 0.959 | 0.278 | 0.244 | 0.665 | 0.262 | 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 | 51 | 57 | 48 | 69 | 79 | 41 | 48 | 46 | 42 |
N.S. |
1 | 1.12 | 0.94 | 1.35 | 1.55 | 0.80 | 0.94 | 0.90 | 0.82 |
time (sec) |
N/A | 0.212 | 0.033 | 0.134 | 0.279 | 0.247 | 0.263 | 0.264 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 61 | 63 | 79 | 0 | 33 | 48 | 0 | 0 |
N.S. |
1 | 1.11 | 1.15 | 1.44 | 0.00 | 0.60 | 0.87 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 0.180 | 0.658 | 0.000 | 0.081 | 0.743 | 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 | 35 | 34 | 35 | 30 | 31 | 31 | 32 | 31 | 29 |
N.S. |
1 | 0.97 | 1.00 | 0.86 | 0.89 | 0.89 | 0.91 | 0.89 | 0.83 |
time (sec) |
N/A | 0.213 | 0.017 | 0.094 | 0.286 | 0.262 | 0.109 | 0.271 | 0.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 46 | 34 | 65 | 0 | 33 | 44 | 0 | 0 |
N.S. |
1 | 1.07 | 0.79 | 1.51 | 0.00 | 0.77 | 1.02 | 0.00 | 0.00 |
time (sec) |
N/A | 0.213 | 10.015 | 0.585 | 0.000 | 0.091 | 0.554 | 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 | 62 | 71 | 56 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.316 | 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 | A | C | B | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 40 | 57 | 0 | 11 | 44 | 0 | 0 |
N.S. |
1 | 1.00 | 1.38 | 1.97 | 0.00 | 0.38 | 1.52 | 0.00 | 0.00 |
time (sec) |
N/A | 0.180 | 0.048 | 0.509 | 0.000 | 0.110 | 0.713 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 61 | 56 | 72 | 93 | 95 | 77 | 0 |
N.S. |
1 | 1.02 | 1.05 | 0.97 | 1.24 | 1.60 | 1.64 | 1.33 | 0.00 |
time (sec) |
N/A | 0.241 | 0.059 | 0.325 | 0.277 | 0.264 | 1.859 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 33 | 39 | 28 | 32 | 48 | 64 | 28 |
N.S. |
1 | 1.00 | 0.97 | 1.15 | 0.82 | 0.94 | 1.41 | 1.88 | 0.82 |
time (sec) |
N/A | 0.205 | 0.029 | 0.276 | 0.269 | 0.247 | 0.788 | 0.296 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 84 | 30 | 45 | 65 | 27 | 55 | 28 |
N.S. |
1 | 1.00 | 3.11 | 1.11 | 1.67 | 2.41 | 1.00 | 2.04 | 1.04 |
time (sec) |
N/A | 0.218 | 0.121 | 0.292 | 0.274 | 0.273 | 0.961 | 0.266 | 0.611 |
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 | 60 | 67 | 60 | 77 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.316 | 0.022 | 1.144 | 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 | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 32 | 31 | 36 | 26 | 31 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.03 | 1.20 | 0.87 | 1.03 | 0.93 |
time (sec) |
N/A | 0.212 | 0.025 | 0.091 | 0.279 | 0.235 | 0.388 | 0.285 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 57 | 50 | 47 | 77 | 47 | 100 | 44 | 42 |
N.S. |
1 | 1.12 | 0.98 | 0.92 | 1.51 | 0.92 | 1.96 | 0.86 | 0.82 |
time (sec) |
N/A | 0.233 | 0.031 | 0.303 | 0.299 | 0.249 | 1.919 | 0.292 | 0.311 |
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 | 56 | 60 | 47 | 55 | 49 | 49 | 100 | 52 | 0 |
N.S. |
1 | 1.07 | 0.84 | 0.98 | 0.88 | 0.88 | 1.79 | 0.93 | 0.00 |
time (sec) |
N/A | 0.247 | 0.036 | 0.306 | 0.285 | 0.254 | 1.713 | 0.283 | 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 | 78 | 91 | 46 | 53 | 52 | 36 | 54 | 52 | 0 |
N.S. |
1 | 1.17 | 0.59 | 0.68 | 0.67 | 0.46 | 0.69 | 0.67 | 0.00 |
time (sec) |
N/A | 0.218 | 0.044 | 0.081 | 0.283 | 0.252 | 1.211 | 0.267 | 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 | 60 | 68 | 41 | 41 | 40 | 31 | 46 | 40 | 0 |
N.S. |
1 | 1.13 | 0.68 | 0.68 | 0.67 | 0.52 | 0.77 | 0.67 | 0.00 |
time (sec) |
N/A | 0.196 | 0.035 | 0.095 | 0.277 | 0.241 | 0.493 | 0.277 | 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 | 37 | 40 | 43 | 26 | 25 | 24 | 29 | 25 | 35 |
N.S. |
1 | 1.08 | 1.16 | 0.70 | 0.68 | 0.65 | 0.78 | 0.68 | 0.95 |
time (sec) |
N/A | 0.177 | 0.020 | 0.093 | 0.271 | 0.241 | 0.117 | 0.269 | 0.721 |
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 | 56 | 69 | 54 | 59 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.96 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 0.035 | 0.946 | 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 | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 24 | 22 | 21 | 22 | 44 | 40 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.81 | 0.78 | 0.81 | 1.63 | 1.48 | 0.00 |
time (sec) |
N/A | 0.169 | 0.022 | 0.092 | 0.272 | 0.248 | 1.571 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 55 | 43 | 35 | 34 | 28 | 53 | 74 | 0 |
N.S. |
1 | 1.10 | 0.86 | 0.70 | 0.68 | 0.56 | 1.06 | 1.48 | 0.00 |
time (sec) |
N/A | 0.182 | 0.028 | 0.082 | 0.263 | 0.250 | 2.795 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 78 | 37 | 47 | 46 | 33 | 68 | 106 | 0 |
N.S. |
1 | 1.15 | 0.54 | 0.69 | 0.68 | 0.49 | 1.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.192 | 0.048 | 0.086 | 0.261 | 0.254 | 8.479 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 101 | 42 | 59 | 58 | 38 | 80 | 138 | 0 |
N.S. |
1 | 1.17 | 0.49 | 0.69 | 0.67 | 0.44 | 0.93 | 1.60 | 0.00 |
time (sec) |
N/A | 0.199 | 0.056 | 0.095 | 0.264 | 0.254 | 26.546 | 0.281 | 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 | 25 | 26 | 25 | 20 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 1.04 | 1.00 | 0.80 | 0.76 | 0.76 | 0.80 | 0.76 | 0.76 |
time (sec) |
N/A | 0.208 | 0.010 | 0.099 | 0.259 | 0.236 | 0.113 | 0.284 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 72 | 141 | 84 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 2.07 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.333 | 0.159 | 1.080 | 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 | 62 | 71 | 56 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.317 | 0.038 | 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 | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 37 | 43 | 40 | 39 | 48 | 61 | 39 | 99 |
N.S. |
1 | 0.79 | 0.91 | 0.85 | 0.83 | 1.02 | 1.30 | 0.83 | 2.11 |
time (sec) |
N/A | 0.258 | 0.034 | 0.099 | 0.278 | 0.249 | 0.213 | 0.278 | 0.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | B | A | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 39 | 43 | 0 | 41 | 59 | 80 | 41 | 111 |
N.S. |
1 | 0.81 | 0.90 | 0.00 | 0.85 | 1.23 | 1.67 | 0.85 | 2.31 |
time (sec) |
N/A | 0.273 | 0.050 | 0.000 | 0.275 | 0.273 | 12.296 | 0.276 | 0.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 249 | 0 | 0 | 207 | 0 | 577 | 0 |
N.S. |
1 | 1.00 | 1.96 | 0.00 | 0.00 | 1.63 | 0.00 | 4.54 | 0.00 |
time (sec) |
N/A | 0.295 | 0.232 | 0.000 | 0.000 | 0.253 | 0.000 | 1.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 107 | 162 | 0 | 0 | 144 | 0 | 335 | 0 |
N.S. |
1 | 0.97 | 1.47 | 0.00 | 0.00 | 1.31 | 0.00 | 3.05 | 0.00 |
time (sec) |
N/A | 0.264 | 0.135 | 0.000 | 0.000 | 0.249 | 0.000 | 0.663 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 98 | 0 | 0 | 91 | 0 | 153 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.00 | 0.00 | 1.44 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 0.192 | 0.070 | 0.000 | 0.000 | 0.250 | 0.000 | 0.467 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 41 | 45 | 45 | 48 | 0 | 55 | 39 |
N.S. |
1 | 1.00 | 0.95 | 1.05 | 1.05 | 1.12 | 0.00 | 1.28 | 0.91 |
time (sec) |
N/A | 0.173 | 0.031 | 0.050 | 0.275 | 0.252 | 0.000 | 0.282 | 0.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 85 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.180 | 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(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 133 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.236 | 0.737 | 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(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 173 | 175 | 147 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.208 | 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 | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 249 | 0 | 0 | 207 | 0 | 586 | 0 |
N.S. |
1 | 1.00 | 1.96 | 0.00 | 0.00 | 1.63 | 0.00 | 4.61 | 0.00 |
time (sec) |
N/A | 0.282 | 0.216 | 0.000 | 0.000 | 0.263 | 0.000 | 1.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 107 | 162 | 0 | 0 | 144 | 0 | 319 | 0 |
N.S. |
1 | 0.97 | 1.47 | 0.00 | 0.00 | 1.31 | 0.00 | 2.90 | 0.00 |
time (sec) |
N/A | 0.259 | 0.121 | 0.000 | 0.000 | 0.252 | 0.000 | 0.668 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 98 | 0 | 0 | 91 | 0 | 160 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.00 | 0.00 | 1.44 | 0.00 | 2.54 | 0.00 |
time (sec) |
N/A | 0.188 | 0.064 | 0.000 | 0.000 | 0.247 | 0.000 | 0.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 41 | 45 | 45 | 48 | 0 | 50 | 39 |
N.S. |
1 | 1.00 | 0.95 | 1.05 | 1.05 | 1.12 | 0.00 | 1.16 | 0.91 |
time (sec) |
N/A | 0.170 | 0.027 | 0.060 | 0.271 | 0.254 | 0.000 | 0.294 | 0.487 |
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 | 98 | 98 | 85 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.199 | 0.147 | 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 | 149 | 149 | 131 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 0.640 | 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 | 171 | 174 | 149 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.188 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 249 | 252 | 248 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.372 | 3.400 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 207 | 213 | 192 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.216 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 149 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.233 | 0.077 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 108 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.211 | 0.414 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 190 | 190 | 166 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.258 | 0.986 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 221 | 225 | 212 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.322 | 1.206 | 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(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 269 | 270 | 234 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.336 | 1.050 | 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 | 249 | 252 | 248 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.337 | 1.453 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 207 | 213 | 192 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.320 | 0.185 | 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 | 184 | 184 | 149 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.233 | 0.085 | 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 | 145 | 145 | 109 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.220 | 0.246 | 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 | 190 | 190 | 181 | 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 | 0.244 | 0.756 | 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 | 221 | 225 | 212 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.317 | 1.136 | 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 | 269 | 270 | 232 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 1.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |