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 | F(-2) | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 262 | 267 | 236 | 0 | 1376 | 0 | 0 | 891 | 0 |
N.S. |
1 | 1.02 | 1.03 | 0.91 | 0.00 | 5.33 | 0.00 | 0.00 | 3.45 | 0.00 |
time (sec) |
N/A | 0.882 | 10.692 | 0.681 | 0.000 | 0.198 | 0.000 | 0.000 | 29.943 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 210 | 205 | 185 | 0 | 1008 | 0 | 0 | 719 | 0 |
N.S. |
1 | 1.07 | 1.05 | 0.94 | 0.00 | 5.14 | 0.00 | 0.00 | 3.67 | 0.00 |
time (sec) |
N/A | 0.785 | 10.510 | 0.650 | 0.000 | 0.148 | 0.000 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 193 | 166 | 156 | 0 | 767 | 0 | 0 | 601 | 0 |
N.S. |
1 | 1.28 | 1.10 | 1.03 | 0.00 | 5.08 | 0.00 | 0.00 | 3.98 | 0.00 |
time (sec) |
N/A | 0.578 | 10.441 | 0.658 | 0.000 | 0.121 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 555 | 176 | 139 | 0 | 684 | 0 | 0 | 530 | 0 |
N.S. |
1 | 4.24 | 1.34 | 1.06 | 0.00 | 5.22 | 0.00 | 0.00 | 4.05 | 0.00 |
time (sec) |
N/A | 1.570 | 0.662 | 0.618 | 0.000 | 0.116 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 146 | 832 | 109 | 0 | 246 | 0 | 658 | 624 | 0 |
N.S. |
1 | 1.42 | 8.08 | 1.06 | 0.00 | 2.39 | 0.00 | 6.39 | 6.06 | 0.00 |
time (sec) |
N/A | 0.437 | 6.379 | 0.661 | 0.000 | 0.091 | 0.000 | 0.761 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 197 | 1953 | 143 | 0 | 339 | 0 | 1345 | 980 | 0 |
N.S. |
1 | 1.21 | 11.98 | 0.88 | 0.00 | 2.08 | 0.00 | 8.25 | 6.01 | 0.00 |
time (sec) |
N/A | 0.502 | 11.885 | 0.695 | 0.000 | 0.088 | 0.000 | 8.721 | 0.548 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 273 | 209 | 173 | 0 | 468 | 0 | 0 | 749 | 0 |
N.S. |
1 | 1.28 | 0.98 | 0.81 | 0.00 | 2.19 | 0.00 | 0.00 | 3.50 | 0.00 |
time (sec) |
N/A | 0.766 | 0.866 | 0.770 | 0.000 | 0.118 | 0.000 | 0.000 | 0.511 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 428 | 377 | 327 | 0 | 2129 | 0 | 610 | 24 | 0 |
N.S. |
1 | 1.29 | 1.14 | 0.98 | 0.00 | 6.41 | 0.00 | 1.84 | 0.07 | 0.00 |
time (sec) |
N/A | 1.132 | 10.950 | 0.764 | 0.000 | 0.238 | 0.000 | 0.198 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 245 | 273 | 258 | 0 | 1635 | 0 | 548 | 22 | 0 |
N.S. |
1 | 0.92 | 1.03 | 0.97 | 0.00 | 6.15 | 0.00 | 2.06 | 0.08 | 0.00 |
time (sec) |
N/A | 0.835 | 10.941 | 0.720 | 0.000 | 0.177 | 0.000 | 0.191 | 200.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 216 | 237 | 221 | 0 | 1745 | 0 | 497 | 2312 | 0 |
N.S. |
1 | 0.99 | 1.08 | 1.01 | 0.00 | 7.97 | 0.00 | 2.27 | 10.56 | 0.00 |
time (sec) |
N/A | 0.726 | 10.886 | 0.717 | 0.000 | 0.152 | 0.000 | 0.179 | 0.896 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 681 | 189 | 195 | 0 | 1538 | 0 | 475 | 2151 | 0 |
N.S. |
1 | 3.80 | 1.06 | 1.09 | 0.00 | 8.59 | 0.00 | 2.65 | 12.02 | 0.00 |
time (sec) |
N/A | 1.881 | 10.786 | 0.641 | 0.000 | 0.154 | 0.000 | 0.167 | 0.355 | 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 | 116 | 143 | 126 | 87 | 0 | 401 | 0 | 388 | 1056 | 0 |
N.S. |
1 | 1.23 | 1.09 | 0.75 | 0.00 | 3.46 | 0.00 | 3.34 | 9.10 | 0.00 |
time (sec) |
N/A | 0.439 | 10.272 | 0.638 | 0.000 | 0.098 | 0.000 | 0.150 | 0.960 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 189 | 173 | 166 | 0 | 562 | 0 | 0 | 1613 | 0 |
N.S. |
1 | 1.15 | 1.05 | 1.01 | 0.00 | 3.41 | 0.00 | 0.00 | 9.78 | 0.00 |
time (sec) |
N/A | 0.500 | 10.213 | 0.736 | 0.000 | 0.102 | 0.000 | 0.000 | 99.580 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 282 | 215 | 207 | 0 | 710 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.29 | 0.98 | 0.95 | 0.00 | 3.24 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.793 | 10.505 | 0.800 | 0.000 | 0.101 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 493 | 488 | 702 | 577 | 0 | 1920 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.99 | 1.42 | 1.17 | 0.00 | 3.89 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.575 | 5.854 | 0.565 | 0.000 | 3.418 | 0.000 | 0.000 | 200.038 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 380 | 388 | 625 | 476 | 0 | 1544 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.02 | 1.64 | 1.25 | 0.00 | 4.06 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.289 | 4.579 | 0.558 | 0.000 | 2.524 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 355 | 560 | 275 | 0 | 1216 | 0 | 0 | 699 | 0 |
N.S. |
1 | 1.22 | 1.92 | 0.95 | 0.00 | 4.18 | 0.00 | 0.00 | 2.40 | 0.00 |
time (sec) |
N/A | 0.973 | 3.804 | 0.642 | 0.000 | 0.700 | 0.000 | 0.000 | 10.785 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 263 | 499 | 180 | 0 | 932 | 0 | 0 | 570 | 0 |
N.S. |
1 | 1.20 | 2.28 | 0.82 | 0.00 | 4.26 | 0.00 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.816 | 3.180 | 0.668 | 0.000 | 0.291 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 204 | 191 | 133 | 0 | 722 | 0 | 0 | 477 | 0 |
N.S. |
1 | 1.23 | 1.15 | 0.80 | 0.00 | 4.35 | 0.00 | 0.00 | 2.87 | 0.00 |
time (sec) |
N/A | 0.631 | 0.504 | 0.684 | 0.000 | 0.208 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 185 | 443 | 148 | 0 | 685 | 0 | 0 | 466 | 0 |
N.S. |
1 | 1.26 | 3.01 | 1.01 | 0.00 | 4.66 | 0.00 | 0.00 | 3.17 | 0.00 |
time (sec) |
N/A | 0.624 | 2.430 | 0.702 | 0.000 | 0.193 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 904 | 174 | 135 | 0 | 698 | 0 | 0 | 471 | 0 |
N.S. |
1 | 6.37 | 1.23 | 0.95 | 0.00 | 4.92 | 0.00 | 0.00 | 3.32 | 0.00 |
time (sec) |
N/A | 2.131 | 0.579 | 0.730 | 0.000 | 0.197 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 168 | 421 | 132 | 0 | 327 | 0 | 372 | 507 | 0 |
N.S. |
1 | 1.22 | 3.05 | 0.96 | 0.00 | 2.37 | 0.00 | 2.70 | 3.67 | 0.00 |
time (sec) |
N/A | 0.482 | 2.033 | 0.819 | 0.000 | 0.087 | 0.000 | 0.141 | 0.408 | 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 | 220 | 199 | 209 | 157 | 0 | 448 | 0 | 600 | 631 | 0 |
N.S. |
1 | 0.90 | 0.95 | 0.71 | 0.00 | 2.04 | 0.00 | 2.73 | 2.87 | 0.00 |
time (sec) |
N/A | 0.515 | 0.755 | 0.870 | 0.000 | 0.086 | 0.000 | 0.135 | 0.512 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 282 | 238 | 235 | 0 | 1356 | 0 | 2074 | 24 | 0 |
N.S. |
1 | 1.09 | 0.92 | 0.91 | 0.00 | 5.24 | 0.00 | 8.01 | 0.09 | 0.00 |
time (sec) |
N/A | 0.590 | 10.588 | 1.304 | 0.000 | 0.112 | 0.000 | 0.213 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 150 | 188 | 97 | 206 | 256 | 204 | 134 | 177 | 0 |
N.S. |
1 | 0.93 | 1.16 | 0.60 | 1.27 | 1.58 | 1.26 | 0.83 | 1.09 | 0.00 |
time (sec) |
N/A | 0.516 | 0.085 | 0.497 | 0.031 | 0.090 | 0.491 | 0.152 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 118 | 125 | 80 | 160 | 209 | 180 | 106 | 137 | 0 |
N.S. |
1 | 0.93 | 0.98 | 0.63 | 1.26 | 1.65 | 1.42 | 0.83 | 1.08 | 0.00 |
time (sec) |
N/A | 0.449 | 0.110 | 0.482 | 0.027 | 0.089 | 0.476 | 0.131 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 75 | 108 | 75 | 115 | 158 | 151 | 80 | 99 | 0 |
N.S. |
1 | 0.82 | 1.17 | 0.82 | 1.25 | 1.72 | 1.64 | 0.87 | 1.08 | 0.00 |
time (sec) |
N/A | 0.345 | 0.057 | 0.434 | 0.040 | 0.089 | 0.563 | 0.142 | 0.195 | 0.000 |
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 | 55 | 55 | 91 | 46 | 75 | 119 | 122 | 59 | 64 | 77 |
N.S. |
1 | 1.00 | 1.65 | 0.84 | 1.36 | 2.16 | 2.22 | 1.07 | 1.16 | 1.40 |
time (sec) |
N/A | 0.309 | 0.044 | 0.431 | 0.030 | 0.081 | 0.377 | 0.155 | 0.198 | 9.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 74 | 49 | 49 | 117 | 0 | 59 | 55 | 50 |
N.S. |
1 | 1.00 | 1.42 | 0.94 | 0.94 | 2.25 | 0.00 | 1.13 | 1.06 | 0.96 |
time (sec) |
N/A | 0.312 | 0.020 | 0.424 | 0.031 | 0.093 | 0.000 | 0.173 | 0.210 | 9.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 35 | 32 | 62 | 35 | 0 | 76 | 64 | 33 |
N.S. |
1 | 1.00 | 0.61 | 0.56 | 1.09 | 0.61 | 0.00 | 1.33 | 1.12 | 0.58 |
time (sec) |
N/A | 0.329 | 0.013 | 0.421 | 0.036 | 0.076 | 0.000 | 0.146 | 0.261 | 9.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 89 | 56 | 49 | 106 | 58 | 0 | 133 | 106 | 56 |
N.S. |
1 | 0.99 | 0.62 | 0.54 | 1.18 | 0.64 | 0.00 | 1.48 | 1.18 | 0.62 |
time (sec) |
N/A | 0.382 | 0.016 | 0.433 | 0.034 | 0.085 | 0.000 | 0.121 | 0.209 | 9.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 121 | 76 | 66 | 152 | 82 | 0 | 191 | 148 | 113 |
N.S. |
1 | 0.97 | 0.61 | 0.53 | 1.22 | 0.66 | 0.00 | 1.53 | 1.18 | 0.90 |
time (sec) |
N/A | 0.447 | 0.018 | 0.464 | 0.051 | 0.077 | 0.000 | 0.341 | 0.212 | 9.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 153 | 95 | 83 | 198 | 106 | 0 | 251 | 188 | 146 |
N.S. |
1 | 0.96 | 0.59 | 0.52 | 1.24 | 0.66 | 0.00 | 1.57 | 1.18 | 0.91 |
time (sec) |
N/A | 0.510 | 0.194 | 0.473 | 0.031 | 0.082 | 0.000 | 0.161 | 0.209 | 9.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 207 | 244 | 160 | 368 | 416 | 323 | 217 | 321 | 0 |
N.S. |
1 | 0.83 | 0.98 | 0.64 | 1.48 | 1.67 | 1.30 | 0.87 | 1.29 | 0.00 |
time (sec) |
N/A | 0.748 | 0.874 | 0.623 | 0.035 | 0.089 | 0.543 | 0.125 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 175 | 184 | 132 | 294 | 341 | 282 | 175 | 256 | 0 |
N.S. |
1 | 0.87 | 0.91 | 0.65 | 1.46 | 1.69 | 1.40 | 0.87 | 1.27 | 0.00 |
time (sec) |
N/A | 0.648 | 0.782 | 0.537 | 0.039 | 0.090 | 0.498 | 0.152 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 147 | 153 | 104 | 220 | 264 | 240 | 134 | 193 | 0 |
N.S. |
1 | 0.95 | 0.99 | 0.67 | 1.42 | 1.70 | 1.55 | 0.86 | 1.25 | 0.00 |
time (sec) |
N/A | 0.519 | 0.552 | 0.507 | 0.048 | 0.090 | 0.592 | 0.136 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 109 | 79 | 154 | 191 | 185 | 96 | 135 | 0 |
N.S. |
1 | 1.05 | 1.01 | 0.73 | 1.43 | 1.77 | 1.71 | 0.89 | 1.25 | 0.00 |
time (sec) |
N/A | 0.447 | 0.126 | 0.488 | 0.041 | 0.098 | 0.506 | 0.161 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 92 | 102 | 74 | 103 | 173 | 0 | 90 | 122 | 0 |
N.S. |
1 | 1.12 | 1.24 | 0.90 | 1.26 | 2.11 | 0.00 | 1.10 | 1.49 | 0.00 |
time (sec) |
N/A | 0.453 | 0.252 | 0.490 | 0.032 | 0.085 | 0.000 | 0.136 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 1 | 100 | 70 | 97 | 176 | 0 | 118 | 114 | 0 |
N.S. |
1 | 0.01 | 1.11 | 0.78 | 1.08 | 1.96 | 0.00 | 1.31 | 1.27 | 0.00 |
time (sec) |
N/A | 0.246 | 0.157 | 0.501 | 0.030 | 0.084 | 0.000 | 0.374 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 138 | 68 | 63 | 136 | 73 | 0 | 167 | 149 | 75 |
N.S. |
1 | 1.34 | 0.66 | 0.61 | 1.32 | 0.71 | 0.00 | 1.62 | 1.45 | 0.73 |
time (sec) |
N/A | 0.518 | 0.168 | 0.492 | 0.034 | 0.077 | 0.000 | 0.246 | 0.198 | 9.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 172 | 100 | 91 | 208 | 109 | 0 | 258 | 215 | 141 |
N.S. |
1 | 1.04 | 0.61 | 0.55 | 1.26 | 0.66 | 0.00 | 1.56 | 1.30 | 0.85 |
time (sec) |
N/A | 0.579 | 0.213 | 0.510 | 0.033 | 0.087 | 0.000 | 1.416 | 0.201 | 9.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 204 | 130 | 119 | 282 | 148 | 0 | 351 | 282 | 188 |
N.S. |
1 | 1.03 | 0.65 | 0.60 | 1.42 | 0.74 | 0.00 | 1.76 | 1.42 | 0.94 |
time (sec) |
N/A | 0.659 | 0.238 | 0.534 | 0.042 | 0.085 | 0.000 | 0.125 | 0.225 | 8.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 217 | 469 | 125 | 0 | 696 | 0 | 0 | 334 | 0 |
N.S. |
1 | 1.29 | 2.79 | 0.74 | 0.00 | 4.14 | 0.00 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 0.638 | 3.638 | 0.633 | 0.000 | 0.132 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 156 | 431 | 95 | 0 | 534 | 0 | 0 | 237 | 0 |
N.S. |
1 | 1.36 | 3.75 | 0.83 | 0.00 | 4.64 | 0.00 | 0.00 | 2.06 | 0.00 |
time (sec) |
N/A | 0.485 | 3.478 | 0.641 | 0.000 | 0.102 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 104 | 380 | 69 | 0 | 432 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.20 | 4.37 | 0.79 | 0.00 | 4.97 | 0.00 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.430 | 1.985 | 0.547 | 0.000 | 0.101 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 68 | 92 | 42 | 0 | 129 | 0 | 58 | 101 | 0 |
N.S. |
1 | 1.31 | 1.77 | 0.81 | 0.00 | 2.48 | 0.00 | 1.12 | 1.94 | 0.00 |
time (sec) |
N/A | 0.308 | 0.134 | 0.539 | 0.000 | 0.087 | 0.000 | 0.138 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 104 | 110 | 79 | 0 | 216 | 0 | 89 | 168 | 0 |
N.S. |
1 | 1.33 | 1.41 | 1.01 | 0.00 | 2.77 | 0.00 | 1.14 | 2.15 | 0.00 |
time (sec) |
N/A | 0.371 | 0.238 | 0.575 | 0.000 | 0.080 | 0.000 | 0.128 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 151 | 132 | 109 | 0 | 300 | 0 | 145 | 263 | 0 |
N.S. |
1 | 1.29 | 1.13 | 0.93 | 0.00 | 2.56 | 0.00 | 1.24 | 2.25 | 0.00 |
time (sec) |
N/A | 0.450 | 0.359 | 0.627 | 0.000 | 0.089 | 0.000 | 0.148 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 205 | 167 | 130 | 0 | 405 | 0 | 235 | 372 | 0 |
N.S. |
1 | 1.23 | 1.01 | 0.78 | 0.00 | 2.44 | 0.00 | 1.42 | 2.24 | 0.00 |
time (sec) |
N/A | 0.542 | 0.440 | 0.635 | 0.000 | 0.088 | 0.000 | 0.385 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 236 | 199 | 179 | 0 | 1151 | 0 | 0 | 873 | 0 |
N.S. |
1 | 1.32 | 1.11 | 1.00 | 0.00 | 6.43 | 0.00 | 0.00 | 4.88 | 0.00 |
time (sec) |
N/A | 0.670 | 10.635 | 0.705 | 0.000 | 0.166 | 0.000 | 0.000 | 0.321 | 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 | 132 | 187 | 175 | 146 | 0 | 851 | 0 | 0 | 709 | 0 |
N.S. |
1 | 1.42 | 1.33 | 1.11 | 0.00 | 6.45 | 0.00 | 0.00 | 5.37 | 0.00 |
time (sec) |
N/A | 0.534 | 0.833 | 0.621 | 0.000 | 0.118 | 0.000 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 104 | 590 | 73 | 0 | 297 | 0 | 379 | 293 | 0 |
N.S. |
1 | 1.22 | 6.94 | 0.86 | 0.00 | 3.49 | 0.00 | 4.46 | 3.45 | 0.00 |
time (sec) |
N/A | 0.393 | 4.574 | 0.563 | 0.000 | 0.096 | 0.000 | 0.287 | 0.223 | 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 | 97 | 117 | 137 | 83 | 0 | 344 | 0 | 0 | 518 | 0 |
N.S. |
1 | 1.21 | 1.41 | 0.86 | 0.00 | 3.55 | 0.00 | 0.00 | 5.34 | 0.00 |
time (sec) |
N/A | 0.412 | 0.364 | 0.589 | 0.000 | 0.091 | 0.000 | 0.000 | 0.206 | 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 | 145 | 177 | 157 | 132 | 0 | 488 | 0 | 739 | 712 | 0 |
N.S. |
1 | 1.22 | 1.08 | 0.91 | 0.00 | 3.37 | 0.00 | 5.10 | 4.91 | 0.00 |
time (sec) |
N/A | 0.491 | 0.804 | 0.671 | 0.000 | 0.095 | 0.000 | 0.476 | 0.267 | 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 | 207 | 232 | 204 | 174 | 0 | 646 | 0 | 1082 | 1291 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.84 | 0.00 | 3.12 | 0.00 | 5.23 | 6.24 | 0.00 |
time (sec) |
N/A | 0.607 | 1.180 | 0.698 | 0.000 | 0.096 | 0.000 | 6.882 | 0.467 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 306 | 260 | 214 | 0 | 787 | 0 | 0 | 1494 | 0 |
N.S. |
1 | 1.09 | 0.93 | 0.76 | 0.00 | 2.80 | 0.00 | 0.00 | 5.32 | 0.00 |
time (sec) |
N/A | 0.724 | 1.793 | 0.706 | 0.000 | 0.108 | 0.000 | 0.000 | 1.813 | 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 | 207 | 232 | 204 | 174 | 0 | 646 | 0 | 1082 | 1291 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.84 | 0.00 | 3.12 | 0.00 | 5.23 | 6.24 | 0.00 |
time (sec) |
N/A | 0.598 | 0.135 | 0.632 | 0.000 | 0.096 | 0.000 | 6.860 | 0.508 | 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 | 207 | 232 | 204 | 174 | 0 | 646 | 0 | 1082 | 1291 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.84 | 0.00 | 3.12 | 0.00 | 5.23 | 6.24 | 0.00 |
time (sec) |
N/A | 0.652 | 0.004 | 0.590 | 0.000 | 0.102 | 0.000 | 8.533 | 0.481 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 232 | 204 | 174 | 0 | 646 | 0 | 0 | 1291 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.84 | 0.00 | 3.12 | 0.00 | 0.00 | 6.24 | 0.00 |
time (sec) |
N/A | 0.717 | 0.003 | 0.499 | 0.000 | 0.097 | 0.000 | 0.000 | 0.459 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 232 | 204 | 174 | 0 | 646 | 0 | 0 | 1291 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.84 | 0.00 | 3.12 | 0.00 | 0.00 | 6.24 | 0.00 |
time (sec) |
N/A | 0.777 | 0.004 | 0.458 | 0.000 | 0.105 | 0.000 | 0.000 | 0.463 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 122 | 125 | 125 | 163 | 260 | 0 | 135 | 152 | 0 |
N.S. |
1 | 1.01 | 1.03 | 1.03 | 1.35 | 2.15 | 0.00 | 1.12 | 1.26 | 0.00 |
time (sec) |
N/A | 0.593 | 0.096 | 0.465 | 0.039 | 0.107 | 0.000 | 0.156 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 84 | 103 | 68 | 115 | 205 | 0 | 107 | 122 | 0 |
N.S. |
1 | 1.02 | 1.26 | 0.83 | 1.40 | 2.50 | 0.00 | 1.30 | 1.49 | 0.00 |
time (sec) |
N/A | 0.395 | 0.062 | 0.658 | 0.038 | 0.095 | 0.000 | 0.143 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 77 | 63 | 65 | 166 | 0 | 80 | 83 | 64 |
N.S. |
1 | 1.00 | 1.28 | 1.05 | 1.08 | 2.77 | 0.00 | 1.33 | 1.38 | 1.07 |
time (sec) |
N/A | 0.321 | 0.027 | 0.552 | 0.032 | 0.107 | 0.000 | 0.206 | 0.256 | 9.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 33 | 30 | 30 | 55 | 44 | 0 | 33 | 68 | 31 |
N.S. |
1 | 0.69 | 0.62 | 0.62 | 1.15 | 0.92 | 0.00 | 0.69 | 1.42 | 0.65 |
time (sec) |
N/A | 0.251 | 0.009 | 0.423 | 0.032 | 0.093 | 0.000 | 0.224 | 0.187 | 9.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 60 | 54 | 49 | 96 | 69 | 0 | 0 | 93 | 62 |
N.S. |
1 | 0.70 | 0.63 | 0.57 | 1.12 | 0.80 | 0.00 | 0.00 | 1.08 | 0.72 |
time (sec) |
N/A | 0.314 | 0.013 | 0.590 | 0.028 | 0.080 | 0.000 | 0.000 | 0.200 | 9.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 92 | 75 | 66 | 142 | 94 | 0 | 0 | 124 | 87 |
N.S. |
1 | 0.75 | 0.61 | 0.54 | 1.16 | 0.77 | 0.00 | 0.00 | 1.02 | 0.71 |
time (sec) |
N/A | 0.372 | 0.017 | 0.454 | 0.033 | 0.087 | 0.000 | 0.000 | 0.200 | 9.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 124 | 94 | 83 | 188 | 118 | 0 | 0 | 154 | 161 |
N.S. |
1 | 0.79 | 0.60 | 0.53 | 1.20 | 0.75 | 0.00 | 0.00 | 0.98 | 1.03 |
time (sec) |
N/A | 0.434 | 0.019 | 0.520 | 0.029 | 0.086 | 0.000 | 0.000 | 0.200 | 9.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 256 | 246 | 170 | 377 | 503 | 0 | 245 | 326 | 0 |
N.S. |
1 | 1.01 | 0.97 | 0.67 | 1.48 | 1.98 | 0.00 | 0.96 | 1.28 | 0.00 |
time (sec) |
N/A | 1.377 | 0.859 | 0.698 | 0.037 | 0.095 | 0.000 | 0.144 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 197 | 181 | 139 | 299 | 420 | 0 | 204 | 275 | 0 |
N.S. |
1 | 0.96 | 0.88 | 0.68 | 1.46 | 2.05 | 0.00 | 1.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.956 | 0.705 | 0.592 | 0.037 | 0.128 | 0.000 | 0.146 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 136 | 151 | 115 | 225 | 337 | 0 | 162 | 226 | 0 |
N.S. |
1 | 0.86 | 0.96 | 0.73 | 1.42 | 2.13 | 0.00 | 1.03 | 1.43 | 0.00 |
time (sec) |
N/A | 0.614 | 0.455 | 0.555 | 0.030 | 0.208 | 0.000 | 0.234 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 105 | 125 | 144 | 267 | 0 | 122 | 172 | 0 |
N.S. |
1 | 1.00 | 1.17 | 1.39 | 1.60 | 2.97 | 0.00 | 1.36 | 1.91 | 0.00 |
time (sec) |
N/A | 0.422 | 0.198 | 0.540 | 0.043 | 0.209 | 0.000 | 0.135 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 103 | 100 | 82 | 110 | 243 | 0 | 88 | 148 | 96 |
N.S. |
1 | 1.13 | 1.10 | 0.90 | 1.21 | 2.67 | 0.00 | 0.97 | 1.63 | 1.05 |
time (sec) |
N/A | 0.430 | 0.164 | 0.816 | 0.038 | 0.154 | 0.000 | 0.143 | 0.235 | 9.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 105 | 67 | 63 | 124 | 85 | 0 | 0 | 149 | 81 |
N.S. |
1 | 1.07 | 0.68 | 0.64 | 1.27 | 0.87 | 0.00 | 0.00 | 1.52 | 0.83 |
time (sec) |
N/A | 0.468 | 0.209 | 0.526 | 0.044 | 0.104 | 0.000 | 0.000 | 0.191 | 9.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 143 | 100 | 91 | 193 | 121 | 0 | 0 | 184 | 121 |
N.S. |
1 | 0.88 | 0.61 | 0.56 | 1.18 | 0.74 | 0.00 | 0.00 | 1.13 | 0.74 |
time (sec) |
N/A | 0.525 | 0.216 | 0.519 | 0.038 | 0.138 | 0.000 | 0.000 | 0.206 | 9.520 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 175 | 131 | 121 | 267 | 159 | 0 | 0 | 234 | 217 |
N.S. |
1 | 0.89 | 0.67 | 0.62 | 1.36 | 0.81 | 0.00 | 0.00 | 1.19 | 1.11 |
time (sec) |
N/A | 0.585 | 0.252 | 0.572 | 0.034 | 0.117 | 0.000 | 0.000 | 0.203 | 9.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 202 | 160 | 149 | 341 | 197 | 0 | 0 | 283 | 261 |
N.S. |
1 | 0.89 | 0.70 | 0.65 | 1.50 | 0.86 | 0.00 | 0.00 | 1.24 | 1.14 |
time (sec) |
N/A | 0.654 | 0.347 | 0.579 | 0.043 | 0.153 | 0.000 | 0.000 | 0.197 | 9.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 0 | 180 | 157 | 531 | 511 | 0 | 341 | 406 | 0 |
N.S. |
1 | 0.00 | 0.89 | 0.78 | 2.63 | 2.53 | 0.00 | 1.69 | 2.01 | 0.00 |
time (sec) |
N/A | 0.000 | 0.557 | 0.598 | 0.043 | 0.142 | 0.000 | 0.160 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 33 | 145 | 120 | 410 | 399 | 0 | 298 | 304 | 0 |
N.S. |
1 | 0.27 | 1.19 | 0.98 | 3.36 | 3.27 | 0.00 | 2.44 | 2.49 | 0.00 |
time (sec) |
N/A | 0.285 | 0.486 | 0.622 | 0.048 | 0.143 | 0.000 | 0.209 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 0 | 111 | 112 | 295 | 309 | 0 | 235 | 219 | 0 |
N.S. |
1 | 0.00 | 1.03 | 1.04 | 2.73 | 2.86 | 0.00 | 2.18 | 2.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.213 | 0.510 | 0.039 | 0.127 | 0.000 | 0.257 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 66 | 68 | 205 | 94 | 0 | 0 | 216 | 82 |
N.S. |
1 | 1.00 | 1.02 | 1.05 | 3.15 | 1.45 | 0.00 | 0.00 | 3.32 | 1.26 |
time (sec) |
N/A | 0.324 | 0.171 | 0.497 | 0.037 | 0.104 | 0.000 | 0.000 | 0.192 | 9.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 78 | 95 | 94 | 203 | 129 | 0 | 110 | 264 | 111 |
N.S. |
1 | 0.46 | 0.56 | 0.56 | 1.20 | 0.76 | 0.00 | 0.65 | 1.56 | 0.66 |
time (sec) |
N/A | 0.329 | 0.188 | 0.553 | 0.035 | 0.125 | 0.000 | 0.185 | 0.253 | 9.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 143 | 130 | 128 | 250 | 171 | 0 | 0 | 299 | 162 |
N.S. |
1 | 0.76 | 0.70 | 0.68 | 1.34 | 0.91 | 0.00 | 0.00 | 1.60 | 0.87 |
time (sec) |
N/A | 0.550 | 0.344 | 0.517 | 0.036 | 0.122 | 0.000 | 0.000 | 0.217 | 9.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 178 | 161 | 156 | 324 | 208 | 0 | 0 | 351 | 294 |
N.S. |
1 | 0.75 | 0.68 | 0.66 | 1.36 | 0.87 | 0.00 | 0.00 | 1.47 | 1.24 |
time (sec) |
N/A | 0.596 | 0.329 | 0.560 | 0.039 | 0.131 | 0.000 | 0.000 | 0.214 | 9.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 210 | 188 | 184 | 400 | 247 | 0 | 0 | 400 | 378 |
N.S. |
1 | 0.73 | 0.65 | 0.64 | 1.38 | 0.85 | 0.00 | 0.00 | 1.38 | 1.31 |
time (sec) |
N/A | 0.677 | 0.385 | 0.551 | 0.037 | 0.124 | 0.000 | 0.000 | 0.218 | 9.794 |
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 | 199 | 227 | 160 | 306 | 0 | 372 | 0 | 341 | 215 | 0 |
N.S. |
1 | 1.14 | 0.80 | 1.54 | 0.00 | 1.87 | 0.00 | 1.71 | 1.08 | 0.00 |
time (sec) |
N/A | 0.971 | 0.172 | 0.438 | 0.000 | 0.133 | 0.000 | 0.225 | 0.182 | 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 | 185 | 172 | 168 | 167 | 0 | 539 | 0 | 378 | 220 | 0 |
N.S. |
1 | 0.93 | 0.91 | 0.90 | 0.00 | 2.91 | 0.00 | 2.04 | 1.19 | 0.00 |
time (sec) |
N/A | 0.631 | 0.337 | 0.582 | 0.000 | 0.138 | 0.000 | 0.252 | 0.179 | 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 | 144 | 128 | 129 | 151 | 0 | 422 | 0 | 278 | 150 | 0 |
N.S. |
1 | 0.89 | 0.90 | 1.05 | 0.00 | 2.93 | 0.00 | 1.93 | 1.04 | 0.00 |
time (sec) |
N/A | 0.501 | 0.182 | 0.539 | 0.000 | 0.131 | 0.000 | 0.180 | 0.251 | 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 | 109 | 107 | 103 | 110 | 0 | 337 | 0 | 210 | 102 | 0 |
N.S. |
1 | 0.98 | 0.94 | 1.01 | 0.00 | 3.09 | 0.00 | 1.93 | 0.94 | 0.00 |
time (sec) |
N/A | 0.407 | 0.096 | 0.528 | 0.000 | 0.132 | 0.000 | 0.164 | 0.225 | 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 | 102 | 99 | 89 | 103 | 0 | 294 | 0 | 204 | 87 | 0 |
N.S. |
1 | 0.97 | 0.87 | 1.01 | 0.00 | 2.88 | 0.00 | 2.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.390 | 0.075 | 0.536 | 0.000 | 0.138 | 0.000 | 0.142 | 0.274 | 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 | 155 | 157 | 146 | 211 | 0 | 967 | 0 | 373 | 261 | 0 |
N.S. |
1 | 1.01 | 0.94 | 1.36 | 0.00 | 6.24 | 0.00 | 2.41 | 1.68 | 0.00 |
time (sec) |
N/A | 0.504 | 0.225 | 0.560 | 0.000 | 0.176 | 0.000 | 0.318 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 210 | 194 | 189 | 0 | 1294 | 0 | 218 | 393 | 0 |
N.S. |
1 | 1.02 | 0.94 | 0.92 | 0.00 | 6.28 | 0.00 | 1.06 | 1.91 | 0.00 |
time (sec) |
N/A | 0.651 | 0.456 | 0.757 | 0.000 | 0.296 | 0.000 | 1.013 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 280 | 254 | 231 | 0 | 1640 | 0 | 269 | 556 | 0 |
N.S. |
1 | 0.99 | 0.90 | 0.82 | 0.00 | 5.80 | 0.00 | 0.95 | 1.96 | 0.00 |
time (sec) |
N/A | 0.800 | 0.816 | 0.703 | 0.000 | 0.480 | 0.000 | 0.590 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 358 | 328 | 286 | 0 | 2013 | 0 | 401 | 721 | 0 |
N.S. |
1 | 0.98 | 0.89 | 0.78 | 0.00 | 5.49 | 0.00 | 1.09 | 1.96 | 0.00 |
time (sec) |
N/A | 0.938 | 0.767 | 0.847 | 0.000 | 1.126 | 0.000 | 0.651 | 0.220 | 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 | 41 | 74 | 46 | 52 | 0 | 134 | 0 | 52 | 90 | 0 |
N.S. |
1 | 1.80 | 1.12 | 1.27 | 0.00 | 3.27 | 0.00 | 1.27 | 2.20 | 0.00 |
time (sec) |
N/A | 0.336 | 0.046 | 0.537 | 0.000 | 0.127 | 0.000 | 0.147 | 0.212 | 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 | 376 | 374 | 310 | 571 | 0 | 517 | 0 | 0 | 873 | 0 |
N.S. |
1 | 0.99 | 0.82 | 1.52 | 0.00 | 1.38 | 0.00 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.818 | 16.309 | 1.554 | 0.000 | 0.185 | 0.000 | 0.000 | 3.144 | 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 | 296 | 293 | 238 | 427 | 0 | 425 | 0 | 0 | 487 | 0 |
N.S. |
1 | 0.99 | 0.80 | 1.44 | 0.00 | 1.44 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.659 | 12.117 | 1.276 | 0.000 | 0.141 | 0.000 | 0.000 | 1.835 | 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 | 209 | 233 | 208 | 352 | 0 | 356 | 0 | 0 | 469 | 0 |
N.S. |
1 | 1.11 | 1.00 | 1.68 | 0.00 | 1.70 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.542 | 9.087 | 0.640 | 0.000 | 0.114 | 0.000 | 0.000 | 1.509 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 231 | 160 | 280 | 0 | 356 | 0 | 0 | 40 | 0 |
N.S. |
1 | 2.57 | 1.78 | 3.11 | 0.00 | 3.96 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.619 | 5.283 | 1.490 | 0.000 | 0.084 | 0.000 | 0.000 | 0.791 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 243 | 186 | 277 | 0 | 379 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.15 | 0.88 | 1.31 | 0.00 | 1.79 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.626 | 9.375 | 2.068 | 0.000 | 0.103 | 0.000 | 0.000 | 1.569 | 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 | 304 | 356 | 221 | 501 | 0 | 482 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.17 | 0.73 | 1.65 | 0.00 | 1.59 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.788 | 11.612 | 2.243 | 0.000 | 0.115 | 0.000 | 0.000 | 2.963 | 0.000 |