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 | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 318 | 263 | 995 | 0 | 514 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.03 | 0.85 | 3.23 | 0.00 | 1.67 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.721 | 1.697 | 13.033 | 0.000 | 0.112 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 260 | 214 | 827 | 0 | 474 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.04 | 0.86 | 3.32 | 0.00 | 1.90 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.294 | 1.093 | 9.895 | 0.000 | 0.108 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 203 | 177 | 662 | 0 | 437 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.03 | 0.90 | 3.36 | 0.00 | 2.22 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.050 | 0.818 | 8.185 | 0.000 | 0.107 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 231 | 379 | 528 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.04 | 1.71 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 1.906 | 1.852 | 6.645 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 236 | 390 | 960 | 0 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.06 | 1.76 | 4.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 1.883 | 2.477 | 11.468 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 288 | 395 | 1134 | 0 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.07 | 1.46 | 4.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 2.453 | 3.006 | 36.389 | 0.000 | 0.000 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 352 | 434 | 1742 | 0 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.09 | 1.34 | 5.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 3.121 | 4.403 | 109.518 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 257 | 211 | 824 | 0 | 474 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.04 | 0.86 | 3.35 | 0.00 | 1.93 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.347 | 1.278 | 9.910 | 0.000 | 0.108 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 153 | 92 | 275 | 0 | 148 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.11 | 0.67 | 1.99 | 0.00 | 1.07 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.777 | 0.475 | 6.648 | 0.000 | 0.088 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 115 | 81 | 253 | 0 | 138 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 0.77 | 2.41 | 0.00 | 1.31 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.581 | 0.299 | 4.358 | 0.000 | 0.084 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 83 | 69 | 231 | 0 | 128 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.06 | 0.88 | 2.96 | 0.00 | 1.64 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.426 | 0.167 | 2.579 | 0.000 | 0.084 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 137 | 0 | 108 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.96 | 0.00 | 4.70 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.181 | 0.070 | 2.910 | 0.000 | 0.111 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 41 | 158 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.85 | 3.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.350 | 0.174 | 2.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 105 | 157 | 350 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.11 | 1.65 | 3.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.761 | 11.446 | 3.150 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 194 | 408 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 1.44 | 3.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.008 | 1.517 | 4.302 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 155 | 114 | 276 | 0 | 148 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.11 | 0.81 | 1.97 | 0.00 | 1.06 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.766 | 0.448 | 9.655 | 0.000 | 0.100 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 117 | 104 | 253 | 0 | 138 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 0.97 | 2.36 | 0.00 | 1.29 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.567 | 0.376 | 6.080 | 0.000 | 0.084 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 85 | 94 | 231 | 0 | 128 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.06 | 1.18 | 2.89 | 0.00 | 1.60 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.417 | 0.191 | 4.106 | 0.000 | 0.087 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 44 | 138 | 0 | 106 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 1.83 | 5.75 | 0.00 | 4.42 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.185 | 0.078 | 4.174 | 0.000 | 0.081 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 61 | 159 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.22 | 3.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.357 | 0.183 | 3.277 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 108 | 178 | 351 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 1.82 | 3.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.749 | 1.598 | 4.512 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 144 | 237 | 408 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 1.72 | 2.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.005 | 2.358 | 6.430 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 227 | 182 | 665 | 0 | 439 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.06 | 0.85 | 3.09 | 0.00 | 2.04 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.085 | 1.206 | 7.710 | 0.000 | 0.102 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 169 | 137 | 453 | 0 | 398 | 0 | 0 | 34 | 116 |
N.S. |
1 | 1.02 | 0.83 | 2.75 | 0.00 | 2.41 | 0.00 | 0.00 | 0.21 | 0.70 |
time (sec) |
N/A | 0.814 | 0.860 | 4.937 | 0.000 | 0.106 | 0.000 | 0.000 | 0.176 | 45.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 86 | 220 | 0 | 355 | 0 | 0 | 32 | 80 |
N.S. |
1 | 1.00 | 0.70 | 1.80 | 0.00 | 2.91 | 0.00 | 0.00 | 0.26 | 0.66 |
time (sec) |
N/A | 0.583 | 3.685 | 3.132 | 0.000 | 0.092 | 0.000 | 0.000 | 0.170 | 45.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 57 | 0 | 147 | 0 | 0 | 26 | 52 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 2.58 | 0.00 | 0.00 | 0.46 | 0.91 |
time (sec) |
N/A | 0.288 | 0.033 | 0.684 | 0.000 | 0.087 | 0.000 | 0.000 | 0.174 | 46.516 |
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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 58 | 166 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.387 | 0.295 | 1.943 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 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 | 206 | 218 | 310 | 532 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.06 | 1.50 | 2.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.675 | 17.104 | 2.243 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 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 | 268 | 276 | 518 | 710 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.03 | 1.93 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 2.188 | 6.660 | 2.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 326 | 242 | 1285 | 0 | 667 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.74 | 3.94 | 0.00 | 2.05 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.734 | 1.618 | 8.418 | 0.000 | 0.136 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 266 | 197 | 743 | 0 | 608 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.04 | 0.77 | 2.89 | 0.00 | 2.37 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.322 | 1.203 | 7.044 | 0.000 | 0.112 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 200 | 159 | 530 | 0 | 549 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.08 | 0.85 | 2.85 | 0.00 | 2.95 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.937 | 0.941 | 6.153 | 0.000 | 0.108 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 182 | 137 | 373 | 0 | 509 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.07 | 0.81 | 2.19 | 0.00 | 2.99 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.835 | 0.667 | 3.823 | 0.000 | 0.095 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 83 | 217 | 0 | 472 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.78 | 2.05 | 0.00 | 4.45 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.427 | 0.194 | 1.955 | 0.000 | 0.098 | 0.000 | 0.000 | 0.191 | 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 | 176 | 184 | 402 | 376 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.05 | 2.28 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.159 | 5.808 | 4.985 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 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 | 277 | 310 | 441 | 898 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.12 | 1.59 | 3.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 2.444 | 4.306 | 6.796 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 373 | 597 | 1546 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.08 | 1.73 | 4.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 3.023 | 6.704 | 9.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 440 | 272 | 1688 | 0 | 1008 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 0.62 | 3.87 | 0.00 | 2.31 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 2.553 | 2.529 | 10.676 | 0.000 | 0.178 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 350 | 237 | 1295 | 0 | 922 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 0.69 | 3.75 | 0.00 | 2.67 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.864 | 2.020 | 8.999 | 0.000 | 0.154 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 297 | 188 | 911 | 0 | 835 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.06 | 0.67 | 3.24 | 0.00 | 2.97 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.414 | 1.593 | 7.505 | 0.000 | 0.134 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 272 | 175 | 850 | 0 | 782 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.03 | 0.67 | 3.23 | 0.00 | 2.97 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.264 | 1.461 | 6.306 | 0.000 | 0.111 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 253 | 154 | 746 | 0 | 733 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.04 | 0.63 | 3.07 | 0.00 | 3.02 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.156 | 1.230 | 5.770 | 0.000 | 0.108 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 231 | 158 | 489 | 0 | 662 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.05 | 0.71 | 2.21 | 0.00 | 3.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.085 | 0.973 | 3.045 | 0.000 | 0.107 | 0.000 | 0.000 | 0.173 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 347 | 464 | 849 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.08 | 1.45 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 2.702 | 5.094 | 7.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 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 | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 380 | 414 | 638 | 1324 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.09 | 1.68 | 3.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 3.284 | 6.708 | 8.816 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 308 | 189 | 616 | 0 | 941 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.09 | 0.67 | 2.18 | 0.00 | 3.34 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.466 | 1.493 | 3.065 | 0.000 | 0.128 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 121 | 81 | 231 | 0 | 136 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.09 | 0.73 | 2.08 | 0.00 | 1.23 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.602 | 0.430 | 4.281 | 0.000 | 0.088 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 83 | 70 | 231 | 0 | 128 | 0 | 0 | 34 | 78 |
N.S. |
1 | 1.06 | 0.90 | 2.96 | 0.00 | 1.64 | 0.00 | 0.00 | 0.44 | 1.00 |
time (sec) |
N/A | 0.448 | 0.268 | 2.681 | 0.000 | 0.086 | 0.000 | 0.000 | 0.171 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 43 | 155 | 0 | 108 | 0 | 0 | 32 | 54 |
N.S. |
1 | 1.00 | 0.84 | 3.04 | 0.00 | 2.12 | 0.00 | 0.00 | 0.63 | 1.06 |
time (sec) |
N/A | 0.292 | 0.166 | 1.947 | 0.000 | 0.086 | 0.000 | 0.000 | 0.184 | 44.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 23 | 0 | 54 | 0 | 0 | 26 | 39 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 2.35 | 0.00 | 0.00 | 1.13 | 1.70 |
time (sec) |
N/A | 0.182 | 0.076 | 0.477 | 0.000 | 0.090 | 0.000 | 0.000 | 0.177 | 43.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 138 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.75 | 0.00 | 0.00 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.204 | 0.176 | 1.307 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 110 | 158 | 350 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.09 | 1.56 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.750 | 1.311 | 1.411 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 134 | 195 | 408 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.98 | 1.42 | 2.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.009 | 1.589 | 1.894 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 123 | 102 | 254 | 0 | 136 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.09 | 0.90 | 2.25 | 0.00 | 1.20 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.618 | 0.441 | 4.938 | 0.000 | 0.086 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 85 | 94 | 232 | 0 | 128 | 0 | 0 | 36 | 78 |
N.S. |
1 | 1.06 | 1.18 | 2.90 | 0.00 | 1.60 | 0.00 | 0.00 | 0.45 | 0.98 |
time (sec) |
N/A | 0.436 | 0.314 | 2.717 | 0.000 | 0.084 | 0.000 | 0.000 | 0.183 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 60 | 158 | 0 | 106 | 0 | 0 | 34 | 52 |
N.S. |
1 | 1.00 | 1.13 | 2.98 | 0.00 | 2.00 | 0.00 | 0.00 | 0.64 | 0.98 |
time (sec) |
N/A | 0.303 | 0.180 | 1.886 | 0.000 | 0.087 | 0.000 | 0.000 | 0.195 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 44 | 44 | 0 | 52 | 0 | 0 | 28 | 39 |
N.S. |
1 | 1.00 | 1.83 | 1.83 | 0.00 | 2.17 | 0.00 | 0.00 | 1.17 | 1.62 |
time (sec) |
N/A | 0.187 | 0.089 | 0.483 | 0.000 | 0.081 | 0.000 | 0.000 | 0.176 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 45 | 139 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.80 | 5.56 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.215 | 0.204 | 1.353 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 113 | 179 | 351 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.09 | 1.72 | 3.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.768 | 1.707 | 1.707 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 137 | 236 | 408 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.98 | 1.69 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.002 | 2.185 | 1.990 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 117 | 77 | 290 | 0 | 148 | 0 | 0 | 41 | 87 |
N.S. |
1 | 1.05 | 0.69 | 2.61 | 0.00 | 1.33 | 0.00 | 0.00 | 0.37 | 0.78 |
time (sec) |
N/A | 0.511 | 0.652 | 13.720 | 0.000 | 0.092 | 0.000 | 0.000 | 0.179 | 42.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 89 | 66 | 262 | 0 | 137 | 0 | 0 | 39 | 80 |
N.S. |
1 | 1.02 | 0.76 | 3.01 | 0.00 | 1.57 | 0.00 | 0.00 | 0.45 | 0.92 |
time (sec) |
N/A | 0.402 | 0.305 | 9.101 | 0.000 | 0.091 | 0.000 | 0.000 | 0.191 | 42.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 62 | 53 | 229 | 0 | 125 | 0 | 0 | 30 | 53 |
N.S. |
1 | 1.02 | 0.87 | 3.75 | 0.00 | 2.05 | 0.00 | 0.00 | 0.49 | 0.87 |
time (sec) |
N/A | 0.365 | 0.170 | 5.710 | 0.000 | 0.087 | 0.000 | 0.000 | 0.173 | 42.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 152 | 0 | 107 | 0 | 0 | 32 | 33 |
N.S. |
1 | 1.00 | 1.00 | 4.34 | 0.00 | 3.06 | 0.00 | 0.00 | 0.91 | 0.94 |
time (sec) |
N/A | 0.279 | 0.125 | 3.107 | 0.000 | 0.080 | 0.000 | 0.000 | 0.170 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 58 | 51 | 150 | 0 | 156 | 0 | 0 | 41 | 60 |
N.S. |
1 | 1.02 | 0.89 | 2.63 | 0.00 | 2.74 | 0.00 | 0.00 | 0.72 | 1.05 |
time (sec) |
N/A | 0.365 | 0.219 | 2.978 | 0.000 | 0.085 | 0.000 | 0.000 | 0.189 | 43.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 65 | 397 | 0 | 175 | 0 | 0 | 41 | 87 |
N.S. |
1 | 1.02 | 0.78 | 4.78 | 0.00 | 2.11 | 0.00 | 0.00 | 0.49 | 1.05 |
time (sec) |
N/A | 0.395 | 0.519 | 4.571 | 0.000 | 0.094 | 0.000 | 0.000 | 0.193 | 44.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 95 | 502 | 0 | 188 | 0 | 0 | 41 | 87 |
N.S. |
1 | 1.02 | 0.86 | 4.52 | 0.00 | 1.69 | 0.00 | 0.00 | 0.37 | 0.78 |
time (sec) |
N/A | 0.484 | 0.413 | 5.762 | 0.000 | 0.090 | 0.000 | 0.000 | 0.178 | 44.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 158 | 113 | 398 | 0 | 195 | 0 | 0 | 67 | 135 |
N.S. |
1 | 0.99 | 0.71 | 2.49 | 0.00 | 1.22 | 0.00 | 0.00 | 0.42 | 0.84 |
time (sec) |
N/A | 0.750 | 1.325 | 24.645 | 0.000 | 0.097 | 0.000 | 0.000 | 0.197 | 45.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 130 | 98 | 362 | 0 | 180 | 0 | 0 | 65 | 128 |
N.S. |
1 | 0.96 | 0.73 | 2.68 | 0.00 | 1.33 | 0.00 | 0.00 | 0.48 | 0.95 |
time (sec) |
N/A | 0.624 | 1.053 | 13.934 | 0.000 | 0.096 | 0.000 | 0.000 | 0.174 | 44.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 102 | 79 | 357 | 0 | 162 | 0 | 0 | 56 | 102 |
N.S. |
1 | 1.01 | 0.78 | 3.53 | 0.00 | 1.60 | 0.00 | 0.00 | 0.55 | 1.01 |
time (sec) |
N/A | 0.533 | 0.679 | 9.211 | 0.000 | 0.090 | 0.000 | 0.000 | 0.185 | 44.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 64 | 283 | 0 | 147 | 0 | 0 | 56 | 76 |
N.S. |
1 | 1.00 | 0.89 | 3.93 | 0.00 | 2.04 | 0.00 | 0.00 | 0.78 | 1.06 |
time (sec) |
N/A | 0.411 | 0.951 | 6.473 | 0.000 | 0.087 | 0.000 | 0.000 | 0.170 | 44.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 62 | 202 | 0 | 178 | 0 | 0 | 58 | 81 |
N.S. |
1 | 1.00 | 0.91 | 2.97 | 0.00 | 2.62 | 0.00 | 0.00 | 0.85 | 1.19 |
time (sec) |
N/A | 0.413 | 0.737 | 5.557 | 0.000 | 0.086 | 0.000 | 0.000 | 0.177 | 44.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 96 | 73 | 420 | 0 | 198 | 0 | 0 | 67 | 108 |
N.S. |
1 | 1.01 | 0.77 | 4.42 | 0.00 | 2.08 | 0.00 | 0.00 | 0.71 | 1.14 |
time (sec) |
N/A | 0.533 | 1.097 | 5.902 | 0.000 | 0.088 | 0.000 | 0.000 | 0.174 | 43.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 126 | 124 | 633 | 0 | 223 | 0 | 0 | 67 | 113 |
N.S. |
1 | 0.93 | 0.92 | 4.69 | 0.00 | 1.65 | 0.00 | 0.00 | 0.50 | 0.84 |
time (sec) |
N/A | 0.625 | 0.842 | 7.648 | 0.000 | 0.095 | 0.000 | 0.000 | 0.168 | 43.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 186 | 137 | 470 | 0 | 227 | 0 | 0 | 91 | 178 |
N.S. |
1 | 0.96 | 0.71 | 2.42 | 0.00 | 1.17 | 0.00 | 0.00 | 0.47 | 0.92 |
time (sec) |
N/A | 0.823 | 1.662 | 19.987 | 0.000 | 0.102 | 0.000 | 0.000 | 0.198 | 41.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 158 | 110 | 421 | 0 | 205 | 0 | 0 | 82 | 146 |
N.S. |
1 | 0.99 | 0.69 | 2.65 | 0.00 | 1.29 | 0.00 | 0.00 | 0.52 | 0.92 |
time (sec) |
N/A | 0.798 | 1.319 | 15.119 | 0.000 | 0.097 | 0.000 | 0.000 | 0.194 | 36.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 117 | 84 | 412 | 0 | 185 | 0 | 0 | 82 | 125 |
N.S. |
1 | 1.01 | 0.72 | 3.55 | 0.00 | 1.59 | 0.00 | 0.00 | 0.71 | 1.08 |
time (sec) |
N/A | 0.656 | 0.947 | 9.650 | 0.000 | 0.096 | 0.000 | 0.000 | 0.187 | 42.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 127 | 86 | 303 | 0 | 214 | 0 | 0 | 82 | 124 |
N.S. |
1 | 1.02 | 0.69 | 2.44 | 0.00 | 1.73 | 0.00 | 0.00 | 0.66 | 1.00 |
time (sec) |
N/A | 0.674 | 0.998 | 8.671 | 0.000 | 0.096 | 0.000 | 0.000 | 0.188 | 42.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 121 | 85 | 558 | 0 | 222 | 0 | 0 | 84 | 128 |
N.S. |
1 | 1.01 | 0.71 | 4.65 | 0.00 | 1.85 | 0.00 | 0.00 | 0.70 | 1.07 |
time (sec) |
N/A | 0.678 | 1.836 | 8.036 | 0.000 | 0.101 | 0.000 | 0.000 | 0.177 | 43.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 141 | 125 | 711 | 0 | 244 | 0 | 0 | 93 | 156 |
N.S. |
1 | 0.95 | 0.84 | 4.77 | 0.00 | 1.64 | 0.00 | 0.00 | 0.62 | 1.05 |
time (sec) |
N/A | 0.802 | 1.569 | 8.999 | 0.000 | 0.097 | 0.000 | 0.000 | 0.180 | 44.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 182 | 177 | 820 | 0 | 270 | 0 | 0 | 93 | 147 |
N.S. |
1 | 0.94 | 0.91 | 4.23 | 0.00 | 1.39 | 0.00 | 0.00 | 0.48 | 0.76 |
time (sec) |
N/A | 0.826 | 1.543 | 11.183 | 0.000 | 0.100 | 0.000 | 0.000 | 0.177 | 44.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 123 | 158 | 552 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.10 | 1.41 | 4.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.906 | 12.352 | 6.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 79 | 81 | 227 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 1.08 | 3.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.552 | 10.697 | 4.536 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 48 | 188 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.91 | 3.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.379 | 0.289 | 3.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 150 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.17 | 0.00 | 0.00 | 0.00 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.222 | 0.268 | 1.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 195 | 354 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 2.53 | 4.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.580 | 3.303 | 3.960 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 138 | 210 | 425 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.08 | 1.64 | 3.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.208 | 4.773 | 5.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 235 | 266 | 1070 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.96 | 1.09 | 4.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.572 | 2.157 | 18.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 182 | 251 | 815 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.98 | 1.36 | 4.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.111 | 2.121 | 18.247 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 156 | 194 | 794 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.96 | 1.19 | 4.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.020 | 3.656 | 5.810 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 136 | 229 | 713 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.92 | 1.55 | 4.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.995 | 4.390 | 5.636 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 150 | 238 | 612 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 0.96 | 1.52 | 3.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.074 | 4.033 | 3.227 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 205 | 278 | 847 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.94 | 1.28 | 3.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.502 | 3.044 | 6.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 261 | 294 | 981 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.93 | 1.05 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 2.093 | 3.899 | 7.523 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 348 | 354 | 2194 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.01 | 1.02 | 6.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 2.284 | 3.631 | 82.396 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 287 | 309 | 1935 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.02 | 1.10 | 6.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.755 | 3.257 | 82.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 272 | 284 | 1914 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.03 | 1.08 | 7.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.694 | 2.440 | 80.740 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 250 | 272 | 1836 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.02 | 1.11 | 7.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.555 | 2.302 | 7.688 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 241 | 291 | 1736 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.96 | 1.16 | 6.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.587 | 3.255 | 6.628 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 261 | 301 | 1176 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 1.15 | 4.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.774 | 3.140 | 3.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |