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 | C | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 142 | 91 | 200 | 170 | 216 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.63 | 1.05 | 2.30 | 1.95 | 2.48 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.684 | 0.005 | 0.219 | 0.050 | 0.091 | 0.000 | 0.000 | 0.612 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 106 | 66 | 166 | 138 | 168 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.68 | 1.05 | 2.63 | 2.19 | 2.67 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.537 | 0.004 | 0.085 | 0.053 | 0.099 | 0.000 | 0.000 | 0.648 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 71 | 47 | 122 | 98 | 112 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.58 | 1.04 | 2.71 | 2.18 | 2.49 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.367 | 0.003 | 0.075 | 0.042 | 0.089 | 0.000 | 0.000 | 0.685 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 10 | 10 | 12 | 10 | 35 | 12 | 8 | 12 | 25 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 3.50 | 1.20 | 0.80 | 1.20 | 2.50 | 1.20 |
time (sec) |
N/A | 0.207 | 0.279 | 0.025 | 0.277 | 0.076 | 0.433 | 0.112 | 0.665 | 2.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 10 | 10 | 12 | 10 | 46 | 12 | 10 | 12 | 45 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 4.60 | 1.20 | 1.00 | 1.20 | 4.50 | 1.20 |
time (sec) |
N/A | 0.211 | 0.700 | 0.018 | 0.188 | 0.087 | 0.439 | 0.112 | 0.638 | 2.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 131 | 222 | 198 | 146 | 632 | 0 | 0 | 307 | 0 |
N.S. |
1 | 1.51 | 2.55 | 2.28 | 1.68 | 7.26 | 0.00 | 0.00 | 3.53 | 0.00 |
time (sec) |
N/A | 1.041 | 0.615 | 0.056 | 0.123 | 0.103 | 0.000 | 0.000 | 0.597 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 96 | 117 | 156 | 108 | 453 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.48 | 1.80 | 2.40 | 1.66 | 6.97 | 0.00 | 0.00 | 3.31 | 0.00 |
time (sec) |
N/A | 0.729 | 0.962 | 0.066 | 0.119 | 0.101 | 0.000 | 0.000 | 0.570 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 46 | 50 | 115 | 189 | 107 | 98 | 127 | 48 |
N.S. |
1 | 1.13 | 1.48 | 1.61 | 3.71 | 6.10 | 3.45 | 3.16 | 4.10 | 1.55 |
time (sec) |
N/A | 0.437 | 0.086 | 0.107 | 0.084 | 0.098 | 0.641 | 0.124 | 0.554 | 2.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 12 | 69 | 14 | 10 | 14 | 48 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 5.75 | 1.17 | 0.83 | 1.17 | 4.00 | 1.17 |
time (sec) |
N/A | 0.367 | 0.130 | 0.023 | 0.136 | 0.078 | 0.500 | 0.123 | 0.705 | 2.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 12 | 91 | 14 | 12 | 14 | 221 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 7.58 | 1.17 | 1.00 | 1.17 | 18.42 | 1.17 |
time (sec) |
N/A | 0.276 | 0.704 | 0.020 | 0.169 | 0.095 | 0.449 | 0.121 | 0.724 | 2.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 266 | 422 | 375 | 302 | 1985 | 0 | 0 | 776 | 0 |
N.S. |
1 | 1.49 | 2.36 | 2.09 | 1.69 | 11.09 | 0.00 | 0.00 | 4.34 | 0.00 |
time (sec) |
N/A | 1.514 | 2.132 | 0.089 | 0.103 | 0.123 | 0.000 | 0.000 | 0.557 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 168 | 314 | 246 | 226 | 1467 | 0 | 0 | 583 | 0 |
N.S. |
1 | 1.47 | 2.75 | 2.16 | 1.98 | 12.87 | 0.00 | 0.00 | 5.11 | 0.00 |
time (sec) |
N/A | 0.941 | 2.127 | 0.066 | 0.106 | 0.131 | 0.000 | 0.000 | 0.668 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 112 | 131 | 164 | 149 | 975 | 0 | 0 | 376 | 0 |
N.S. |
1 | 1.37 | 1.60 | 2.00 | 1.82 | 11.89 | 0.00 | 0.00 | 4.59 | 0.00 |
time (sec) |
N/A | 0.544 | 0.943 | 0.054 | 0.091 | 0.122 | 0.000 | 0.000 | 0.757 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 12 | 144 | 14 | 10 | 14 | 111 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 12.00 | 1.17 | 0.83 | 1.17 | 9.25 | 1.17 |
time (sec) |
N/A | 0.331 | 0.256 | 0.029 | 0.252 | 0.077 | 0.564 | 0.139 | 0.629 | 2.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 12 | 175 | 14 | 12 | 14 | 660 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 14.58 | 1.17 | 1.00 | 1.17 | 55.00 | 1.17 |
time (sec) |
N/A | 0.367 | 0.201 | 0.024 | 0.201 | 0.087 | 0.525 | 0.139 | 0.678 | 2.272 |
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 | 169 | 179 | 244 | 165 | 183 | 304 | 864 | 188 | 195 | 223 |
N.S. |
1 | 1.06 | 1.44 | 0.98 | 1.08 | 1.80 | 5.11 | 1.11 | 1.15 | 1.32 |
time (sec) |
N/A | 1.206 | 0.630 | 0.223 | 0.300 | 0.086 | 0.739 | 0.120 | 0.523 | 2.674 |
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 | 122 | 127 | 169 | 103 | 124 | 192 | 522 | 119 | 125 | 186 |
N.S. |
1 | 1.04 | 1.39 | 0.84 | 1.02 | 1.57 | 4.28 | 0.98 | 1.02 | 1.52 |
time (sec) |
N/A | 0.752 | 0.396 | 0.155 | 0.141 | 0.092 | 0.641 | 0.122 | 0.583 | 2.516 |
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 | 74 | 78 | 81 | 46 | 72 | 101 | 250 | 62 | 67 | 76 |
N.S. |
1 | 1.05 | 1.09 | 0.62 | 0.97 | 1.36 | 3.38 | 0.84 | 0.91 | 1.03 |
time (sec) |
N/A | 0.361 | 0.484 | 0.168 | 0.151 | 0.096 | 0.569 | 0.121 | 0.547 | 2.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 122 | 61 | 48 | 75 | 0 | 48 | 30 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.39 | 0.31 | 0.48 | 0.00 | 0.31 | 0.19 | 0.00 |
time (sec) |
N/A | 0.774 | 0.433 | 0.160 | 0.282 | 0.119 | 0.000 | 0.121 | 0.562 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 168 | 206 | 91 | 56 | 216 | 0 | 321 | 129 | 0 |
N.S. |
1 | 1.06 | 1.30 | 0.57 | 0.35 | 1.36 | 0.00 | 2.02 | 0.81 | 0.00 |
time (sec) |
N/A | 0.804 | 0.619 | 0.187 | 0.637 | 0.098 | 0.000 | 0.146 | 0.578 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 219 | 265 | 210 | 68 | 342 | 0 | 175 | 265 | 0 |
N.S. |
1 | 1.04 | 1.26 | 1.00 | 0.32 | 1.62 | 0.00 | 0.83 | 1.26 | 0.00 |
time (sec) |
N/A | 0.997 | 0.814 | 0.211 | 0.859 | 0.099 | 0.000 | 0.118 | 0.634 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 230 | 420 | 273 | 297 | 571 | 2193 | 368 | 385 | 266 |
N.S. |
1 | 1.00 | 1.83 | 1.19 | 1.29 | 2.48 | 9.53 | 1.60 | 1.67 | 1.16 |
time (sec) |
N/A | 0.915 | 1.942 | 0.339 | 0.533 | 0.100 | 1.047 | 0.123 | 0.750 | 2.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 207 | 163 | 191 | 359 | 1353 | 217 | 229 | 164 |
N.S. |
1 | 1.00 | 1.22 | 0.96 | 1.12 | 2.11 | 7.96 | 1.28 | 1.35 | 0.96 |
time (sec) |
N/A | 0.633 | 1.531 | 0.266 | 0.681 | 0.090 | 0.875 | 0.125 | 0.615 | 2.639 |
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 | 133 | 133 | 114 | 74 | 107 | 190 | 700 | 103 | 111 | 88 |
N.S. |
1 | 1.00 | 0.86 | 0.56 | 0.80 | 1.43 | 5.26 | 0.77 | 0.83 | 0.66 |
time (sec) |
N/A | 0.673 | 0.967 | 0.175 | 0.207 | 0.113 | 0.812 | 0.120 | 0.528 | 2.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 297 | 199 | 106 | 81 | 137 | 0 | 77 | 53 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.36 | 0.27 | 0.46 | 0.00 | 0.26 | 0.18 | 0.00 |
time (sec) |
N/A | 1.127 | 0.740 | 0.182 | 1.594 | 0.098 | 0.000 | 0.119 | 0.626 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 420 | 420 | 442 | 164 | 100 | 615 | 0 | 585 | 249 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.39 | 0.24 | 1.46 | 0.00 | 1.39 | 0.59 | 0.00 |
time (sec) |
N/A | 1.162 | 1.579 | 0.219 | 1.841 | 0.091 | 0.000 | 0.152 | 0.760 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 336 | 615 | 379 | 406 | 844 | 3918 | 548 | 575 | 374 |
N.S. |
1 | 1.00 | 1.83 | 1.13 | 1.21 | 2.51 | 11.66 | 1.63 | 1.71 | 1.11 |
time (sec) |
N/A | 0.698 | 3.021 | 0.424 | 2.512 | 0.095 | 1.348 | 0.132 | 0.567 | 2.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 246 | 371 | 223 | 254 | 532 | 2443 | 315 | 333 | 234 |
N.S. |
1 | 1.00 | 1.51 | 0.91 | 1.03 | 2.16 | 9.93 | 1.28 | 1.35 | 0.95 |
time (sec) |
N/A | 0.632 | 2.051 | 0.432 | 2.776 | 0.110 | 1.174 | 0.127 | 0.695 | 2.540 |
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 | 183 | 182 | 185 | 102 | 138 | 286 | 1287 | 142 | 153 | 127 |
N.S. |
1 | 0.99 | 1.01 | 0.56 | 0.75 | 1.56 | 7.03 | 0.78 | 0.84 | 0.69 |
time (sec) |
N/A | 0.761 | 1.118 | 0.217 | 1.003 | 0.085 | 1.098 | 0.127 | 0.611 | 2.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 437 | 312 | 151 | 114 | 195 | 0 | 104 | 76 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.35 | 0.26 | 0.45 | 0.00 | 0.24 | 0.17 | 0.00 |
time (sec) |
N/A | 2.790 | 0.879 | 0.228 | 3.771 | 0.099 | 0.000 | 0.126 | 0.636 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 692 | 692 | 796 | 239 | 140 | 1162 | 0 | 841 | 373 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.35 | 0.20 | 1.68 | 0.00 | 1.22 | 0.54 | 0.00 |
time (sec) |
N/A | 2.265 | 2.462 | 0.280 | 13.502 | 0.112 | 0.000 | 0.164 | 0.694 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 122 | 37 | 44 | 22 | 5342 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 6.10 | 1.85 | 2.20 | 1.10 | 267.10 | 1.10 |
time (sec) |
N/A | 0.375 | 27.681 | 0.061 | 0.396 | 0.080 | 4.346 | 0.152 | 0.882 | 2.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 18 | 18 | 20 | 18 | 68 | 20 | 24 | 20 | 84 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 3.78 | 1.11 | 1.33 | 1.11 | 4.67 | 1.11 |
time (sec) |
N/A | 0.293 | 16.443 | 0.040 | 0.193 | 0.088 | 2.788 | 0.125 | 0.710 | 2.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 115 | 0 | 0 | 148 | 0 | 0 | 201 | 0 |
N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 1.68 | 0.00 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.589 | 0.825 | 0.000 | 0.000 | 0.124 | 0.000 | 0.000 | 0.490 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 162 | 0 | 0 | 248 | 0 | 0 | 352 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.647 | 1.155 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.568 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 223 | 228 | 0 | 0 | 345 | 0 | 0 | 505 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 1.55 | 0.00 | 0.00 | 2.26 | 0.00 |
time (sec) |
N/A | 0.580 | 1.319 | 0.000 | 0.000 | 0.089 | 0.000 | 0.000 | 0.637 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 311 | 766 | 419 | 488 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.00 | 2.34 | 5.76 | 3.15 | 3.67 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.520 | 0.139 | 0.166 | 0.174 | 0.132 | 0.000 | 0.000 | 0.643 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 172 | 465 | 240 | 303 | 0 | 0 | 164 | 0 |
N.S. |
1 | 1.00 | 1.70 | 4.60 | 2.38 | 3.00 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.438 | 0.074 | 0.115 | 0.270 | 0.099 | 0.000 | 0.000 | 0.656 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 79 | 201 | 0 | 156 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 1.05 | 2.68 | 0.00 | 2.08 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.337 | 0.014 | 0.080 | 0.000 | 0.101 | 0.000 | 0.000 | 0.623 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 18 | 18 | 20 | 18 | 78 | 20 | 15 | 20 | 62 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.33 | 1.11 | 0.83 | 1.11 | 3.44 | 1.11 |
time (sec) |
N/A | 0.215 | 3.761 | 0.043 | 0.287 | 0.074 | 0.919 | 0.121 | 0.588 | 2.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 18 | 18 | 20 | 18 | 131 | 31 | 17 | 20 | 168 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 7.28 | 1.72 | 0.94 | 1.11 | 9.33 | 1.11 |
time (sec) |
N/A | 0.215 | 24.738 | 0.040 | 0.188 | 0.090 | 2.977 | 0.174 | 0.610 | 2.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 843 | 1425 | 781 | 3239 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.11 | 5.26 | 2.88 | 11.95 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.825 | 3.219 | 0.310 | 0.195 | 0.152 | 0.000 | 0.000 | 0.742 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 473 | 825 | 494 | 1854 | 0 | 0 | 1288 | 0 |
N.S. |
1 | 1.00 | 2.26 | 3.95 | 2.36 | 8.87 | 0.00 | 0.00 | 6.16 | 0.00 |
time (sec) |
N/A | 0.906 | 4.585 | 0.262 | 0.180 | 0.123 | 0.000 | 0.000 | 0.679 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 218 | 318 | 244 | 851 | 0 | 0 | 592 | 0 |
N.S. |
1 | 1.00 | 1.72 | 2.50 | 1.92 | 6.70 | 0.00 | 0.00 | 4.66 | 0.00 |
time (sec) |
N/A | 0.682 | 6.807 | 0.220 | 0.358 | 0.122 | 0.000 | 0.000 | 0.739 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 226 | 36 | 17 | 22 | 258 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 11.30 | 1.80 | 0.85 | 1.10 | 12.90 | 1.10 |
time (sec) |
N/A | 0.396 | 29.278 | 0.123 | 0.411 | 0.087 | 1.443 | 0.157 | 0.853 | 2.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 375 | 47 | 19 | 22 | 803 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 18.75 | 2.35 | 0.95 | 1.10 | 40.15 | 1.10 |
time (sec) |
N/A | 0.331 | 22.584 | 0.116 | 0.812 | 0.107 | 2.443 | 0.271 | 0.782 | 2.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 556 | 556 | 2043 | 2823 | 1531 | 11137 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.67 | 5.08 | 2.75 | 20.03 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.693 | 7.900 | 0.538 | 0.442 | 0.279 | 0.000 | 0.000 | 16.487 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 392 | 392 | 585 | 1586 | 997 | 6356 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.49 | 4.05 | 2.54 | 16.21 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.036 | 4.855 | 0.397 | 0.374 | 0.164 | 0.000 | 0.000 | 0.659 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 259 | 318 | 651 | 528 | 2907 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.51 | 2.04 | 11.22 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.680 | 7.475 | 0.299 | 0.175 | 0.151 | 0.000 | 0.000 | 0.728 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 644 | 52 | 17 | 22 | 793 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 32.20 | 2.60 | 0.85 | 1.10 | 39.65 | 1.10 |
time (sec) |
N/A | 0.241 | 36.609 | 0.316 | 1.492 | 0.097 | 1.920 | 0.231 | 0.905 | 2.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 1144 | 63 | 19 | 22 | 2588 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 57.20 | 3.15 | 0.95 | 1.10 | 129.40 | 1.10 |
time (sec) |
N/A | 0.239 | 40.489 | 0.241 | 1.455 | 0.107 | 3.311 | 0.553 | 1.023 | 2.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 200 | 247 | 1158 | 521 | 730 | 0 | 0 | 566 | 0 |
N.S. |
1 | 0.95 | 1.18 | 5.51 | 2.48 | 3.48 | 0.00 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 1.609 | 1.018 | 0.221 | 0.252 | 0.134 | 0.000 | 0.000 | 0.766 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 155 | 200 | 735 | 332 | 492 | 0 | 0 | 389 | 0 |
N.S. |
1 | 0.99 | 1.28 | 4.71 | 2.13 | 3.15 | 0.00 | 0.00 | 2.49 | 0.00 |
time (sec) |
N/A | 1.253 | 0.687 | 0.158 | 0.380 | 0.104 | 0.000 | 0.000 | 0.695 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 112 | 152 | 357 | 0 | 300 | 0 | 0 | 214 | 0 |
N.S. |
1 | 1.04 | 1.41 | 3.31 | 0.00 | 2.78 | 0.00 | 0.00 | 1.98 | 0.00 |
time (sec) |
N/A | 0.544 | 0.674 | 0.115 | 0.000 | 0.104 | 0.000 | 0.000 | 0.625 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 117 | 27 | 17 | 22 | 271 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 5.85 | 1.35 | 0.85 | 1.10 | 13.55 | 1.10 |
time (sec) |
N/A | 0.248 | 4.937 | 0.062 | 0.502 | 0.094 | 1.196 | 0.113 | 0.657 | 2.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 202 | 51 | 19 | 22 | 937 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 10.10 | 2.55 | 0.95 | 1.10 | 46.85 | 1.10 |
time (sec) |
N/A | 0.247 | 8.795 | 0.056 | 0.758 | 0.099 | 1.908 | 0.189 | 0.753 | 2.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 638 | 638 | 659 | 2444 | 1056 | 6171 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 3.83 | 1.66 | 9.67 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.545 | 5.008 | 0.282 | 0.655 | 0.269 | 0.000 | 0.000 | 0.716 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 475 | 475 | 519 | 1470 | 751 | 3702 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.09 | 3.09 | 1.58 | 7.79 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.909 | 3.207 | 0.213 | 1.031 | 0.166 | 0.000 | 0.000 | 0.572 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 214 | 244 | 620 | 0 | 1797 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.24 | 3.16 | 0.00 | 9.17 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.839 | 2.519 | 0.136 | 0.000 | 0.159 | 0.000 | 0.000 | 0.621 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 472 | 55 | 19 | 22 | 2595 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 23.60 | 2.75 | 0.95 | 1.10 | 129.75 | 1.10 |
time (sec) |
N/A | 0.245 | 29.894 | 0.072 | 1.724 | 0.093 | 1.820 | 0.155 | 0.853 | 2.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 20 | 20 | 22 | 20 | 789 | 96 | 20 | 22 | 8964 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 39.45 | 4.80 | 1.00 | 1.10 | 448.20 | 1.10 |
time (sec) |
N/A | 0.244 | 25.677 | 0.066 | 4.820 | 0.096 | 3.321 | 0.313 | 0.824 | 3.384 |