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 | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 132 | 130 | 143 | 144 | 139 | 156 | 167 | 157 |
N.S. |
1 | 1.00 | 0.96 | 0.95 | 1.04 | 1.05 | 1.01 | 1.14 | 1.22 | 1.15 |
time (sec) |
N/A | 0.338 | 0.068 | 0.690 | 0.027 | 0.066 | 0.182 | 0.230 | 0.206 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 107 | 103 | 111 | 113 | 105 | 119 | 131 | 121 |
N.S. |
1 | 1.00 | 0.99 | 0.95 | 1.03 | 1.05 | 0.97 | 1.10 | 1.21 | 1.12 |
time (sec) |
N/A | 0.292 | 0.041 | 0.724 | 0.028 | 0.067 | 0.147 | 0.227 | 0.229 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 74 | 76 | 81 | 82 | 71 | 84 | 95 | 85 |
N.S. |
1 | 1.00 | 0.94 | 0.96 | 1.03 | 1.04 | 0.90 | 1.06 | 1.20 | 1.08 |
time (sec) |
N/A | 0.250 | 0.028 | 0.788 | 0.030 | 0.068 | 0.128 | 0.235 | 0.232 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 48 | 49 | 50 | 52 | 44 | 50 | 62 | 51 |
N.S. |
1 | 1.00 | 0.92 | 0.94 | 0.96 | 1.00 | 0.85 | 0.96 | 1.19 | 0.98 |
time (sec) |
N/A | 0.212 | 0.016 | 0.644 | 0.033 | 0.071 | 0.101 | 0.242 | 0.225 | 10.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 45 | 44 | 44 | 75 | 46 | 54 | 40 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 1.00 | 1.00 | 1.70 | 1.05 | 1.23 | 0.91 |
time (sec) |
N/A | 0.211 | 0.019 | 0.740 | 0.026 | 0.074 | 0.451 | 0.213 | 0.215 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 53 | 54 | 53 | 57 | 126 | 55 | 68 | 50 |
N.S. |
1 | 1.00 | 1.04 | 1.06 | 1.04 | 1.12 | 2.47 | 1.08 | 1.33 | 0.98 |
time (sec) |
N/A | 0.224 | 0.023 | 0.648 | 0.033 | 0.074 | 0.410 | 0.241 | 0.206 | 11.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 71 | 75 | 73 | 78 | 185 | 86 | 104 | 58 |
N.S. |
1 | 1.00 | 0.92 | 0.97 | 0.95 | 1.01 | 2.40 | 1.12 | 1.35 | 0.75 |
time (sec) |
N/A | 0.243 | 0.056 | 0.694 | 0.035 | 0.074 | 0.345 | 0.213 | 0.206 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 99 | 102 | 106 | 111 | 233 | 118 | 141 | 121 |
N.S. |
1 | 1.00 | 0.94 | 0.97 | 1.01 | 1.06 | 2.22 | 1.12 | 1.34 | 1.15 |
time (sec) |
N/A | 0.274 | 0.083 | 0.757 | 0.027 | 0.075 | 0.412 | 0.233 | 0.212 | 10.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 133 | 130 | 139 | 144 | 275 | 149 | 179 | 153 |
N.S. |
1 | 1.00 | 0.99 | 0.96 | 1.03 | 1.07 | 2.04 | 1.10 | 1.33 | 1.13 |
time (sec) |
N/A | 0.307 | 0.086 | 0.774 | 0.028 | 0.072 | 0.472 | 0.204 | 0.224 | 10.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 12 | 7 | 11 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.00 | 0.58 | 0.92 | 1.00 | 0.83 |
time (sec) |
N/A | 0.168 | 0.005 | 0.656 | 0.035 | 0.068 | 0.037 | 0.232 | 0.219 | 10.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 16 | 18 | 14 | 18 | 18 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 1.00 | 0.78 | 1.00 | 1.00 | 0.89 |
time (sec) |
N/A | 0.181 | 0.005 | 0.748 | 0.039 | 0.073 | 0.046 | 0.468 | 0.214 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 392 | 317 | 467 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 0.88 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.017 | 2.501 | 1.493 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 278 | 242 | 353 | 0 | 1459 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.09 | 0.95 | 1.38 | 0.00 | 5.72 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.590 | 1.398 | 1.454 | 0.000 | 101.975 | 0.000 | 0.000 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 203 | 184 | 280 | 0 | 1165 | 0 | 0 | 4268 | 0 |
N.S. |
1 | 1.06 | 0.96 | 1.47 | 0.00 | 6.10 | 0.00 | 0.00 | 22.35 | 0.00 |
time (sec) |
N/A | 0.443 | 0.944 | 1.366 | 0.000 | 9.429 | 0.000 | 0.000 | 0.517 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 158 | 175 | 236 | 0 | 992 | 0 | 0 | 3976 | 0 |
N.S. |
1 | 1.04 | 1.15 | 1.55 | 0.00 | 6.53 | 0.00 | 0.00 | 26.16 | 0.00 |
time (sec) |
N/A | 0.354 | 1.217 | 1.582 | 0.000 | 0.680 | 0.000 | 0.000 | 0.447 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 170 | 157 | 413 | 0 | 2218 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.02 | 0.94 | 2.47 | 0.00 | 13.28 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.416 | 0.747 | 1.404 | 0.000 | 39.785 | 0.000 | 0.000 | 0.493 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 324 | 142 | 249 | 0 | 1020 | 0 | 197 | 203 | 0 |
N.S. |
1 | 2.08 | 0.91 | 1.60 | 0.00 | 6.54 | 0.00 | 1.26 | 1.30 | 0.00 |
time (sec) |
N/A | 0.597 | 0.854 | 1.526 | 0.000 | 0.268 | 0.000 | 0.203 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 420 | 223 | 288 | 0 | 1217 | 0 | 432 | 377 | 0 |
N.S. |
1 | 1.94 | 1.03 | 1.33 | 0.00 | 5.63 | 0.00 | 2.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.682 | 1.595 | 1.537 | 0.000 | 0.478 | 0.000 | 1.220 | 0.505 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 544 | 293 | 368 | 0 | 1507 | 0 | 844 | 25 | 0 |
N.S. |
1 | 1.83 | 0.98 | 1.23 | 0.00 | 5.06 | 0.00 | 2.83 | 0.08 | 0.00 |
time (sec) |
N/A | 0.819 | 2.798 | 1.842 | 0.000 | 1.088 | 0.000 | 0.277 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 635 | 675 | 662 | 890 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.06 | 1.04 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.516 | 11.466 | 1.480 | 0.000 | 0.000 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 461 | 495 | 443 | 664 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.07 | 0.96 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.049 | 11.012 | 1.424 | 0.000 | 0.000 | 0.000 | 0.000 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 364 | 324 | 500 | 0 | 0 | 0 | 0 | 10332 | 0 |
N.S. |
1 | 1.07 | 0.96 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 30.48 | 0.00 |
time (sec) |
N/A | 0.826 | 2.869 | 1.504 | 0.000 | 0.000 | 0.000 | 0.000 | 25.089 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 271 | 247 | 383 | 0 | 1523 | 0 | 0 | 9833 | 0 |
N.S. |
1 | 1.08 | 0.98 | 1.52 | 0.00 | 6.04 | 0.00 | 0.00 | 39.02 | 0.00 |
time (sec) |
N/A | 0.601 | 2.338 | 1.388 | 0.000 | 110.405 | 0.000 | 0.000 | 1.058 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 318 | 223 | 793 | 0 | 0 | 0 | 0 | 562 | 0 |
N.S. |
1 | 1.26 | 0.88 | 3.15 | 0.00 | 0.00 | 0.00 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 0.744 | 1.511 | 1.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.522 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 516 | 210 | 406 | 0 | 0 | 0 | 0 | 513 | 0 |
N.S. |
1 | 2.23 | 0.91 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 2.22 | 0.00 |
time (sec) |
N/A | 0.966 | 1.412 | 1.537 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 672 | 253 | 356 | 0 | 0 | 0 | 0 | 649 | 0 |
N.S. |
1 | 2.61 | 0.98 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 2.53 | 0.00 |
time (sec) |
N/A | 1.095 | 1.717 | 1.605 | 0.000 | 0.000 | 0.000 | 0.000 | 0.533 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 835 | 289 | 402 | 0 | 1591 | 0 | 916 | 25 | 0 |
N.S. |
1 | 2.99 | 1.04 | 1.44 | 0.00 | 5.70 | 0.00 | 3.28 | 0.09 | 0.00 |
time (sec) |
N/A | 1.290 | 2.497 | 1.546 | 0.000 | 1.484 | 0.000 | 0.335 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 982 | 384 | 526 | 0 | 2011 | 0 | 1853 | 25 | 0 |
N.S. |
1 | 2.35 | 0.92 | 1.26 | 0.00 | 4.82 | 0.00 | 4.44 | 0.06 | 0.00 |
time (sec) |
N/A | 1.439 | 5.220 | 1.691 | 0.000 | 5.220 | 0.000 | 0.411 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 577 | 1154 | 522 | 702 | 0 | 2575 | 0 | 3046 | 1597 | 0 |
N.S. |
1 | 2.00 | 0.90 | 1.22 | 0.00 | 4.46 | 0.00 | 5.28 | 2.77 | 0.00 |
time (sec) |
N/A | 1.624 | 9.165 | 1.984 | 0.000 | 11.921 | 0.000 | 0.560 | 3.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 327 | 254 | 337 | 0 | 0 | 0 | 0 | 5414 | 0 |
N.S. |
1 | 1.11 | 0.86 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 18.41 | 0.00 |
time (sec) |
N/A | 1.104 | 1.686 | 1.681 | 0.000 | 0.000 | 0.000 | 0.000 | 7.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 235 | 198 | 269 | 0 | 1685 | 0 | 0 | 4867 | 0 |
N.S. |
1 | 1.07 | 0.90 | 1.23 | 0.00 | 7.69 | 0.00 | 0.00 | 22.22 | 0.00 |
time (sec) |
N/A | 0.659 | 1.928 | 1.536 | 0.000 | 161.776 | 0.000 | 0.000 | 1.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 167 | 147 | 230 | 0 | 1306 | 0 | 0 | 4437 | 0 |
N.S. |
1 | 1.06 | 0.94 | 1.46 | 0.00 | 8.32 | 0.00 | 0.00 | 28.26 | 0.00 |
time (sec) |
N/A | 0.364 | 1.445 | 1.434 | 0.000 | 11.804 | 0.000 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 134 | 190 | 0 | 1034 | 0 | 0 | 4099 | 0 |
N.S. |
1 | 1.00 | 1.08 | 1.53 | 0.00 | 8.34 | 0.00 | 0.00 | 33.06 | 0.00 |
time (sec) |
N/A | 0.272 | 0.698 | 1.407 | 0.000 | 0.748 | 0.000 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 92 | 157 | 0 | 343 | 0 | 71 | 3755 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.99 | 0.00 | 4.34 | 0.00 | 0.90 | 47.53 | 0.00 |
time (sec) |
N/A | 0.199 | 0.408 | 1.455 | 0.000 | 0.125 | 0.000 | 0.238 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 135 | 194 | 0 | 1047 | 0 | 0 | 243 | 0 |
N.S. |
1 | 1.00 | 1.07 | 1.54 | 0.00 | 8.31 | 0.00 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 0.321 | 0.713 | 1.371 | 0.000 | 0.227 | 0.000 | 0.000 | 0.477 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 196 | 192 | 237 | 0 | 1340 | 0 | 191 | 431 | 0 |
N.S. |
1 | 1.21 | 1.19 | 1.46 | 0.00 | 8.27 | 0.00 | 1.18 | 2.66 | 0.00 |
time (sec) |
N/A | 0.389 | 1.291 | 1.599 | 0.000 | 0.505 | 0.000 | 0.259 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 309 | 232 | 278 | 0 | 1737 | 0 | 399 | 756 | 0 |
N.S. |
1 | 1.39 | 1.04 | 1.25 | 0.00 | 7.79 | 0.00 | 1.79 | 3.39 | 0.00 |
time (sec) |
N/A | 0.499 | 2.369 | 1.558 | 0.000 | 1.422 | 0.000 | 0.260 | 0.497 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 314 | 288 | 815 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.15 | 1.05 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.927 | 11.740 | 1.539 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 253 | 229 | 615 | 0 | 4811 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.15 | 1.04 | 2.80 | 0.00 | 21.87 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.539 | 1.223 | 1.493 | 0.000 | 35.399 | 0.000 | 0.000 | 200.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 191 | 498 | 0 | 1351 | 0 | 461 | 25 | 0 |
N.S. |
1 | 1.00 | 1.22 | 3.19 | 0.00 | 8.66 | 0.00 | 2.96 | 0.16 | 0.00 |
time (sec) |
N/A | 0.343 | 0.995 | 1.412 | 0.000 | 0.342 | 0.000 | 0.264 | 200.058 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 180 | 438 | 0 | 1320 | 0 | 444 | 23 | 0 |
N.S. |
1 | 1.00 | 1.20 | 2.92 | 0.00 | 8.80 | 0.00 | 2.96 | 0.15 | 0.00 |
time (sec) |
N/A | 0.320 | 0.946 | 1.356 | 0.000 | 0.358 | 0.000 | 0.278 | 200.054 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 190 | 400 | 0 | 1349 | 0 | 461 | 22 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.58 | 0.00 | 8.70 | 0.00 | 2.97 | 0.14 | 0.00 |
time (sec) |
N/A | 0.300 | 1.229 | 1.353 | 0.000 | 0.359 | 0.000 | 0.274 | 200.057 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 248 | 230 | 493 | 0 | 4819 | 0 | 0 | 3348 | 0 |
N.S. |
1 | 1.14 | 1.06 | 2.26 | 0.00 | 22.11 | 0.00 | 0.00 | 15.36 | 0.00 |
time (sec) |
N/A | 0.510 | 1.871 | 1.411 | 0.000 | 2.012 | 0.000 | 0.000 | 5.604 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 386 | 332 | 649 | 0 | 6396 | 0 | 757 | 4729 | 0 |
N.S. |
1 | 1.39 | 1.20 | 2.34 | 0.00 | 23.09 | 0.00 | 2.73 | 17.07 | 0.00 |
time (sec) |
N/A | 0.642 | 2.412 | 1.517 | 0.000 | 4.883 | 0.000 | 0.307 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 498 | 520 | 478 | 1448 | 0 | 4618 | 0 | 8448 | 25 | 0 |
N.S. |
1 | 1.04 | 0.96 | 2.91 | 0.00 | 9.27 | 0.00 | 16.96 | 0.05 | 0.00 |
time (sec) |
N/A | 1.147 | 12.059 | 1.522 | 0.000 | 1.208 | 0.000 | 0.517 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 446 | 412 | 1131 | 0 | 4600 | 0 | 8382 | 25 | 0 |
N.S. |
1 | 1.07 | 0.99 | 2.71 | 0.00 | 11.03 | 0.00 | 20.10 | 0.06 | 0.00 |
time (sec) |
N/A | 0.722 | 12.200 | 1.467 | 0.000 | 1.301 | 0.000 | 0.480 | 200.063 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 371 | 356 | 936 | 0 | 4636 | 0 | 8210 | 25 | 0 |
N.S. |
1 | 1.06 | 1.02 | 2.68 | 0.00 | 13.28 | 0.00 | 23.52 | 0.07 | 0.00 |
time (sec) |
N/A | 0.611 | 12.042 | 1.494 | 0.000 | 1.248 | 0.000 | 0.489 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 345 | 304 | 839 | 0 | 4596 | 0 | 8378 | 23 | 0 |
N.S. |
1 | 1.13 | 0.99 | 2.74 | 0.00 | 15.02 | 0.00 | 27.38 | 0.08 | 0.00 |
time (sec) |
N/A | 0.534 | 10.501 | 1.381 | 0.000 | 1.403 | 0.000 | 0.467 | 200.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 350 | 309 | 766 | 0 | 4612 | 0 | 8447 | 22 | 0 |
N.S. |
1 | 1.14 | 1.01 | 2.50 | 0.00 | 15.02 | 0.00 | 27.51 | 0.07 | 0.00 |
time (sec) |
N/A | 0.544 | 10.523 | 1.444 | 0.000 | 1.362 | 0.000 | 0.497 | 200.050 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 515 | 477 | 459 | 953 | 0 | 16795 | 0 | 0 | 13522 | 0 |
N.S. |
1 | 0.93 | 0.89 | 1.85 | 0.00 | 32.61 | 0.00 | 0.00 | 26.26 | 0.00 |
time (sec) |
N/A | 0.873 | 11.658 | 1.417 | 0.000 | 19.054 | 0.000 | 0.000 | 6.129 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 628 | 705 | 654 | 1239 | 0 | 20807 | 0 | 10475 | 17328 | 0 |
N.S. |
1 | 1.12 | 1.04 | 1.97 | 0.00 | 33.13 | 0.00 | 16.68 | 27.59 | 0.00 |
time (sec) |
N/A | 1.096 | 12.692 | 1.678 | 0.000 | 38.371 | 0.000 | 0.580 | 0.383 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 551 | 635 | 488 | 1071 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.15 | 0.89 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.417 | 12.879 | 1.970 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 337 | 298 | 638 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.88 | 0.78 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.875 | 22.143 | 1.942 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 212 | 284 | 238 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.98 | 1.31 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.607 | 23.112 | 2.803 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 419 | 550 | 424 | 819 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.31 | 1.01 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.217 | 25.239 | 3.957 | 0.000 | 0.000 | 0.000 | 0.000 | 200.050 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 102 | 78 | 68 | 75 | 134 | 88 | 71 | 238 | 84 |
N.S. |
1 | 1.13 | 0.87 | 0.76 | 0.83 | 1.49 | 0.98 | 0.79 | 2.64 | 0.93 |
time (sec) |
N/A | 0.275 | 0.074 | 2.589 | 0.112 | 0.077 | 0.107 | 0.256 | 0.298 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 33 | 22 | 20 | 32 | 32 | 31 | 20 | 33 | 20 |
N.S. |
1 | 1.10 | 0.73 | 0.67 | 1.07 | 1.07 | 1.03 | 0.67 | 1.10 | 0.67 |
time (sec) |
N/A | 0.180 | 0.013 | 1.392 | 0.024 | 0.072 | 0.051 | 0.207 | 0.281 | 11.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 490 | 498 | 627 | 594 | 0 | 5507 | 0 | 1200 | 25 | 13879 |
N.S. |
1 | 1.02 | 1.28 | 1.21 | 0.00 | 11.24 | 0.00 | 2.45 | 0.05 | 28.32 |
time (sec) |
N/A | 7.965 | 3.195 | 1.763 | 0.000 | 0.652 | 0.000 | 0.334 | 200.041 | 13.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 404 | 465 | 497 | 0 | 4245 | 0 | 1074 | 25 | 11143 |
N.S. |
1 | 1.02 | 1.17 | 1.25 | 0.00 | 10.69 | 0.00 | 2.71 | 0.06 | 28.07 |
time (sec) |
N/A | 4.118 | 2.467 | 1.677 | 0.000 | 0.360 | 0.000 | 0.328 | 200.033 | 12.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 321 | 375 | 425 | 0 | 2966 | 0 | 897 | 25 | 8171 |
N.S. |
1 | 1.02 | 1.19 | 1.34 | 0.00 | 9.39 | 0.00 | 2.84 | 0.08 | 25.86 |
time (sec) |
N/A | 2.001 | 1.579 | 1.577 | 0.000 | 0.173 | 0.000 | 0.296 | 200.033 | 11.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 293 | 341 | 325 | 0 | 1721 | 0 | 758 | 1844 | 5664 |
N.S. |
1 | 1.02 | 1.19 | 1.13 | 0.00 | 6.00 | 0.00 | 2.64 | 6.43 | 19.74 |
time (sec) |
N/A | 1.082 | 1.540 | 1.552 | 0.000 | 0.113 | 0.000 | 0.303 | 6.896 | 12.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 233 | 252 | 222 | 0 | 715 | 0 | 445 | 1369 | 709 |
N.S. |
1 | 1.18 | 1.27 | 1.12 | 0.00 | 3.61 | 0.00 | 2.25 | 6.91 | 3.58 |
time (sec) |
N/A | 0.378 | 0.988 | 1.415 | 0.000 | 0.086 | 0.000 | 0.282 | 0.482 | 11.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 283 | 266 | 291 | 0 | 2443 | 0 | 719 | 25 | 10894 |
N.S. |
1 | 1.03 | 0.97 | 1.06 | 0.00 | 8.88 | 0.00 | 2.61 | 0.09 | 39.61 |
time (sec) |
N/A | 0.930 | 1.549 | 1.522 | 0.000 | 0.324 | 0.000 | 0.290 | 200.041 | 15.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 371 | 337 | 373 | 0 | 4857 | 0 | 776 | 25 | 19887 |
N.S. |
1 | 1.12 | 1.02 | 1.13 | 0.00 | 14.72 | 0.00 | 2.35 | 0.08 | 60.26 |
time (sec) |
N/A | 2.459 | 1.886 | 1.659 | 0.000 | 5.452 | 0.000 | 0.328 | 200.040 | 14.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 550 | 433 | 489 | 0 | 7422 | 0 | 1043 | 25 | 33838 |
N.S. |
1 | 1.19 | 0.94 | 1.06 | 0.00 | 16.06 | 0.00 | 2.26 | 0.05 | 73.24 |
time (sec) |
N/A | 2.088 | 2.763 | 1.746 | 0.000 | 78.988 | 0.000 | 0.329 | 200.024 | 15.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 650 | 659 | 901 | 762 | 0 | 14340 | 0 | 1612 | 25 | 31485 |
N.S. |
1 | 1.01 | 1.39 | 1.17 | 0.00 | 22.06 | 0.00 | 2.48 | 0.04 | 48.44 |
time (sec) |
N/A | 2.114 | 5.201 | 1.951 | 0.000 | 12.640 | 0.000 | 0.392 | 200.036 | 15.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 581 | 589 | 755 | 680 | 0 | 11459 | 0 | 1397 | 25 | 25497 |
N.S. |
1 | 1.01 | 1.30 | 1.17 | 0.00 | 19.72 | 0.00 | 2.40 | 0.04 | 43.88 |
time (sec) |
N/A | 8.063 | 4.477 | 1.869 | 0.000 | 6.579 | 0.000 | 0.352 | 200.043 | 15.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 441 | 447 | 537 | 541 | 0 | 8530 | 0 | 1195 | 25 | 19465 |
N.S. |
1 | 1.01 | 1.22 | 1.23 | 0.00 | 19.34 | 0.00 | 2.71 | 0.06 | 44.14 |
time (sec) |
N/A | 1.598 | 2.883 | 1.760 | 0.000 | 2.450 | 0.000 | 0.371 | 200.039 | 13.785 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 386 | 493 | 485 | 0 | 5572 | 0 | 986 | 23 | 13841 |
N.S. |
1 | 1.03 | 1.31 | 1.29 | 0.00 | 14.82 | 0.00 | 2.62 | 0.06 | 36.81 |
time (sec) |
N/A | 0.899 | 3.096 | 1.610 | 0.000 | 0.883 | 0.000 | 0.306 | 200.035 | 13.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 300 | 364 | 345 | 0 | 2770 | 0 | 797 | 2819 | 8334 |
N.S. |
1 | 0.93 | 1.13 | 1.07 | 0.00 | 8.60 | 0.00 | 2.48 | 8.75 | 25.88 |
time (sec) |
N/A | 0.607 | 1.996 | 1.556 | 0.000 | 0.266 | 0.000 | 0.290 | 0.567 | 14.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 348 | 371 | 370 | 0 | 5164 | 0 | 833 | 25 | 20897 |
N.S. |
1 | 1.02 | 1.09 | 1.09 | 0.00 | 15.19 | 0.00 | 2.45 | 0.07 | 61.46 |
time (sec) |
N/A | 1.166 | 2.113 | 1.931 | 0.000 | 4.070 | 0.000 | 0.327 | 200.029 | 18.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 417 | 416 | 409 | 0 | 8650 | 0 | 890 | 25 | 29890 |
N.S. |
1 | 1.11 | 1.11 | 1.09 | 0.00 | 23.01 | 0.00 | 2.37 | 0.07 | 79.49 |
time (sec) |
N/A | 1.708 | 2.560 | 1.662 | 0.000 | 18.955 | 0.000 | 0.358 | 200.043 | 17.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 529 | 626 | 560 | 509 | 0 | 14414 | 0 | 1129 | 25 | 44649 |
N.S. |
1 | 1.18 | 1.06 | 0.96 | 0.00 | 27.25 | 0.00 | 2.13 | 0.05 | 84.40 |
time (sec) |
N/A | 2.536 | 4.271 | 1.855 | 0.000 | 169.419 | 0.000 | 0.332 | 200.032 | 17.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 389 | 689 | 988 | 0 | 1719 | 5372 | 948 | 23 | 0 |
N.S. |
1 | 0.75 | 1.32 | 1.90 | 0.00 | 3.30 | 10.31 | 1.82 | 0.04 | 0.00 |
time (sec) |
N/A | 0.795 | 5.765 | 1.383 | 0.000 | 0.243 | 0.923 | 0.273 | 200.038 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 268 | 446 | 610 | 0 | 1151 | 2742 | 602 | 23 | 0 |
N.S. |
1 | 0.81 | 1.35 | 1.84 | 0.00 | 3.48 | 8.28 | 1.82 | 0.07 | 0.00 |
time (sec) |
N/A | 0.479 | 2.706 | 1.287 | 0.000 | 0.185 | 0.862 | 0.269 | 200.053 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 178 | 254 | 316 | 0 | 689 | 1175 | 329 | 775 | 0 |
N.S. |
1 | 0.90 | 1.28 | 1.60 | 0.00 | 3.48 | 5.93 | 1.66 | 3.91 | 0.00 |
time (sec) |
N/A | 0.318 | 1.376 | 1.137 | 0.000 | 0.127 | 0.808 | 0.235 | 2.739 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 148 | 128 | 128 | 0 | 341 | 343 | 156 | 317 | 199 |
N.S. |
1 | 1.09 | 0.94 | 0.94 | 0.00 | 2.51 | 2.52 | 1.15 | 2.33 | 1.46 |
time (sec) |
N/A | 0.273 | 0.565 | 1.185 | 0.000 | 0.149 | 0.394 | 0.223 | 0.728 | 11.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 364 | 324 | 500 | 0 | 0 | 0 | 0 | 10332 | 0 |
N.S. |
1 | 1.07 | 0.96 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 30.48 | 0.00 |
time (sec) |
N/A | 0.848 | 0.237 | 1.372 | 0.000 | 0.000 | 0.000 | 0.000 | 35.858 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 311 | 304 | 709 | 0 | 2135 | 0 | 0 | 1343 | 0 |
N.S. |
1 | 1.05 | 1.03 | 2.40 | 0.00 | 7.21 | 0.00 | 0.00 | 4.54 | 0.00 |
time (sec) |
N/A | 0.672 | 11.011 | 1.451 | 0.000 | 112.282 | 0.000 | 0.000 | 0.594 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 294 | 507 | 1235 | 0 | 3719 | 0 | 973 | 3154 | 0 |
N.S. |
1 | 1.02 | 1.76 | 4.29 | 0.00 | 12.91 | 0.00 | 3.38 | 10.95 | 0.00 |
time (sec) |
N/A | 0.565 | 12.040 | 1.541 | 0.000 | 104.095 | 0.000 | 0.426 | 0.595 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 432 | 685 | 2195 | 0 | 0 | 0 | 2470 | 6174 | 0 |
N.S. |
1 | 1.18 | 1.87 | 5.98 | 0.00 | 0.00 | 0.00 | 6.73 | 16.82 | 0.00 |
time (sec) |
N/A | 0.835 | 13.440 | 1.593 | 0.000 | 0.000 | 0.000 | 4.508 | 1.797 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 440 | 580 | 605 | 8161 | 0 | 0 | 0 | 0 | 10533 | 0 |
N.S. |
1 | 1.32 | 1.38 | 18.55 | 0.00 | 0.00 | 0.00 | 0.00 | 23.94 | 0.00 |
time (sec) |
N/A | 1.066 | 14.364 | 1.690 | 0.000 | 0.000 | 0.000 | 0.000 | 17.555 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 321 | 274 | 10265 | 0 | 4824 | 0 | 9517 | 7687 | 0 |
N.S. |
1 | 1.10 | 0.94 | 35.03 | 0.00 | 16.46 | 0.00 | 32.48 | 26.24 | 0.00 |
time (sec) |
N/A | 0.470 | 11.705 | 1.861 | 0.000 | 43.121 | 0.000 | 1.413 | 96.498 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 425 | 357 | 15588 | 0 | 8120 | 0 | 15909 | 23 | 0 |
N.S. |
1 | 1.03 | 0.86 | 37.65 | 0.00 | 19.61 | 0.00 | 38.43 | 0.06 | 0.00 |
time (sec) |
N/A | 0.641 | 12.474 | 2.304 | 0.000 | 114.285 | 0.000 | 13.009 | 200.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 606 | 566 | 705 | 26119 | 0 | 0 | 0 | 24842 | 23 | 0 |
N.S. |
1 | 0.93 | 1.16 | 43.10 | 0.00 | 0.00 | 0.00 | 40.99 | 0.04 | 0.00 |
time (sec) |
N/A | 0.875 | 16.129 | 2.663 | 0.000 | 0.000 | 0.000 | 7.907 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 652 | 0 | 1390 | 1177 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.00 | 2.13 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 33.792 | 5.758 | 0.000 | 0.000 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 723 | 0 | 7762 | 1344 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.00 | 10.74 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 35.376 | 11.750 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 599 | 642 | 5357 | 1125 | 0 | 588 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.07 | 8.94 | 1.88 | 0.00 | 0.98 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.499 | 35.119 | 4.637 | 0.000 | 0.095 | 0.000 | 0.000 | 200.052 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 528 | 707 | 925 | 0 | 486 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.06 | 1.43 | 1.86 | 0.00 | 0.98 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.916 | 32.477 | 4.244 | 0.000 | 0.100 | 0.000 | 0.000 | 200.060 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 423 | 447 | 602 | 807 | 0 | 418 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.06 | 1.42 | 1.91 | 0.00 | 0.99 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.624 | 27.869 | 2.306 | 0.000 | 0.090 | 0.000 | 0.000 | 200.049 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 188 | 365 | 746 | 0 | 359 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 2.05 | 4.19 | 0.00 | 2.02 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.286 | 21.793 | 1.370 | 0.000 | 0.087 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 575 | 363 | 638 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.42 | 0.90 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.108 | 23.448 | 2.401 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 623 | 824 | 1292 | 820 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.32 | 2.07 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.477 | 32.881 | 4.276 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 719 | 1462 | 6774 | 1205 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 2.03 | 9.42 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.959 | 35.077 | 6.621 | 0.000 | 0.000 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 509 | 545 | 707 | 913 | 0 | 485 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.07 | 1.39 | 1.79 | 0.00 | 0.95 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.913 | 33.222 | 5.533 | 0.000 | 0.088 | 0.000 | 0.000 | 200.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 426 | 453 | 934 | 812 | 0 | 415 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.06 | 2.19 | 1.91 | 0.00 | 0.97 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.642 | 31.027 | 4.338 | 0.000 | 0.078 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 385 | 804 | 459 | 0 | 356 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.05 | 2.20 | 1.26 | 0.00 | 0.98 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.506 | 27.169 | 3.026 | 0.000 | 0.073 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 189 | 308 | 287 | 0 | 128 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 1.72 | 1.60 | 0.00 | 0.72 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.312 | 22.689 | 2.838 | 0.000 | 0.070 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 387 | 482 | 313 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.74 | 2.17 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.738 | 24.000 | 4.217 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 630 | 829 | 1381 | 827 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.32 | 2.19 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.465 | 33.337 | 5.971 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |