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 | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 288 | 146 | 156 | 712 | 144 | 0 | 0 | 141 | 348 |
N.S. |
1 | 1.05 | 0.53 | 0.57 | 2.59 | 0.52 | 0.00 | 0.00 | 0.51 | 1.27 |
time (sec) |
N/A | 1.525 | 0.820 | 14.030 | 0.237 | 0.090 | 0.000 | 0.000 | 0.326 | 28.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 245 | 124 | 136 | 619 | 126 | 0 | 0 | 141 | 316 |
N.S. |
1 | 1.07 | 0.54 | 0.60 | 2.71 | 0.55 | 0.00 | 0.00 | 0.62 | 1.39 |
time (sec) |
N/A | 1.302 | 0.791 | 13.928 | 0.266 | 0.096 | 0.000 | 0.000 | 0.342 | 31.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 202 | 102 | 116 | 527 | 107 | 0 | 0 | 141 | 259 |
N.S. |
1 | 1.12 | 0.56 | 0.64 | 2.91 | 0.59 | 0.00 | 0.00 | 0.78 | 1.43 |
time (sec) |
N/A | 1.087 | 0.635 | 14.001 | 0.228 | 0.087 | 0.000 | 0.000 | 0.336 | 32.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 160 | 80 | 94 | 436 | 88 | 0 | 0 | 141 | 197 |
N.S. |
1 | 1.19 | 0.60 | 0.70 | 3.25 | 0.66 | 0.00 | 0.00 | 1.05 | 1.47 |
time (sec) |
N/A | 0.914 | 0.402 | 14.018 | 0.341 | 0.090 | 0.000 | 0.000 | 0.338 | 1.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 149 | 106 | 148 | 1462 | 130 | 0 | 0 | 141 | 0 |
N.S. |
1 | 1.03 | 0.73 | 1.02 | 10.08 | 0.90 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.891 | 0.469 | 14.372 | 0.369 | 0.104 | 0.000 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 147 | 107 | 197 | 1801 | 119 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.01 | 0.73 | 1.35 | 12.34 | 0.82 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.900 | 0.380 | 21.621 | 0.508 | 0.136 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 121 | 190 | 1884 | 133 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.00 | 0.79 | 1.24 | 12.31 | 0.87 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.898 | 0.492 | 21.783 | 0.614 | 0.141 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 197 | 139 | 207 | 3023 | 153 | 0 | 0 | 141 | 0 |
N.S. |
1 | 0.98 | 0.70 | 1.04 | 15.12 | 0.76 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 1.093 | 0.978 | 18.295 | 0.667 | 0.137 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 240 | 156 | 227 | 8901 | 171 | 0 | 0 | 141 | 0 |
N.S. |
1 | 0.97 | 0.63 | 0.92 | 36.04 | 0.69 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 1.297 | 1.588 | 18.608 | 1.125 | 0.169 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 342 | 171 | 172 | 763 | 176 | 0 | 0 | 219 | 789 |
N.S. |
1 | 1.06 | 0.53 | 0.53 | 2.37 | 0.55 | 0.00 | 0.00 | 0.68 | 2.45 |
time (sec) |
N/A | 1.919 | 1.451 | 3.695 | 0.203 | 0.098 | 0.000 | 0.000 | 0.443 | 30.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 299 | 147 | 152 | 672 | 156 | 0 | 0 | 219 | 751 |
N.S. |
1 | 1.09 | 0.53 | 0.55 | 2.44 | 0.57 | 0.00 | 0.00 | 0.80 | 2.73 |
time (sec) |
N/A | 1.694 | 1.252 | 3.142 | 0.246 | 0.094 | 0.000 | 0.000 | 0.448 | 31.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 256 | 126 | 132 | 579 | 135 | 0 | 0 | 219 | 617 |
N.S. |
1 | 1.12 | 0.55 | 0.58 | 2.54 | 0.59 | 0.00 | 0.00 | 0.96 | 2.71 |
time (sec) |
N/A | 1.450 | 0.969 | 3.124 | 0.226 | 0.095 | 0.000 | 0.000 | 0.446 | 54.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 212 | 104 | 112 | 488 | 114 | 0 | 0 | 219 | 579 |
N.S. |
1 | 1.17 | 0.57 | 0.62 | 2.70 | 0.63 | 0.00 | 0.00 | 1.21 | 3.20 |
time (sec) |
N/A | 1.241 | 0.795 | 3.138 | 0.227 | 0.093 | 0.000 | 0.000 | 0.451 | 50.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 201 | 130 | 169 | 1713 | 162 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.05 | 0.68 | 0.88 | 8.92 | 0.84 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 1.202 | 0.946 | 3.285 | 0.413 | 0.107 | 0.000 | 0.000 | 0.440 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 198 | 130 | 234 | 2780 | 166 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.03 | 0.67 | 1.21 | 14.40 | 0.86 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 1.248 | 0.819 | 3.352 | 0.531 | 0.132 | 0.000 | 0.000 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 199 | 126 | 223 | 0 | 147 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.01 | 0.64 | 1.13 | 0.00 | 0.74 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 1.272 | 0.679 | 21.979 | 0.000 | 0.132 | 0.000 | 0.000 | 0.379 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 206 | 141 | 215 | 3071 | 163 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.03 | 0.70 | 1.08 | 15.36 | 0.82 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 1.238 | 1.106 | 22.112 | 0.674 | 0.135 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 251 | 157 | 229 | 9390 | 183 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.02 | 0.64 | 0.93 | 38.02 | 0.74 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 1.452 | 1.908 | 18.713 | 1.048 | 0.173 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 294 | 179 | 249 | 10042 | 203 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.00 | 0.61 | 0.85 | 34.16 | 0.69 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 1.681 | 3.192 | 18.750 | 0.905 | 0.177 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 336 | 272 | 265 | 0 | 198 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.14 | 0.92 | 0.90 | 0.00 | 0.67 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.998 | 10.768 | 14.137 | 0.000 | 0.121 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 281 | 250 | 245 | 0 | 181 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.12 | 1.00 | 0.98 | 0.00 | 0.72 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.540 | 8.060 | 13.984 | 0.000 | 0.126 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 226 | 1719 | 225 | 0 | 164 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.09 | 8.30 | 1.09 | 0.00 | 0.79 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.207 | 8.216 | 13.907 | 0.000 | 0.139 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 171 | 617 | 204 | 0 | 143 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.06 | 3.81 | 1.26 | 0.00 | 0.88 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.894 | 7.030 | 13.919 | 0.000 | 0.119 | 0.000 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 120 | 203 | 177 | 0 | 110 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.01 | 1.71 | 1.49 | 0.00 | 0.92 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.618 | 1.788 | 13.872 | 0.000 | 0.110 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 121 | 102 | 138 | 1221 | 96 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.86 | 0.73 | 0.99 | 8.72 | 0.69 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.746 | 0.253 | 13.897 | 1.108 | 0.851 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 171 | 467 | 196 | 0 | 168 | 0 | 0 | 99 | 0 |
N.S. |
1 | 0.94 | 2.58 | 1.08 | 0.00 | 0.93 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.015 | 2.881 | 18.007 | 0.000 | 1.100 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 224 | 412 | 239 | 0 | 194 | 0 | 0 | 107 | 0 |
N.S. |
1 | 0.97 | 1.79 | 1.04 | 0.00 | 0.84 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 1.340 | 2.629 | 17.965 | 0.000 | 2.081 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 183 | 143 | 281 | 0 | 208 | 0 | 0 | 120 | 0 |
N.S. |
1 | 0.95 | 0.74 | 1.46 | 0.00 | 1.08 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.198 | 0.528 | 24.218 | 0.000 | 13.760 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 344 | 2966 | 285 | 0 | 237 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.09 | 9.36 | 0.90 | 0.00 | 0.75 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.060 | 10.089 | 14.485 | 0.000 | 0.127 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 289 | 2166 | 265 | 0 | 220 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.07 | 8.02 | 0.98 | 0.00 | 0.81 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.640 | 8.256 | 14.642 | 0.000 | 0.116 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 234 | 981 | 245 | 0 | 197 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.05 | 4.40 | 1.10 | 0.00 | 0.88 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 1.260 | 7.088 | 14.528 | 0.000 | 0.114 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 179 | 443 | 199 | 0 | 163 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.02 | 2.52 | 1.13 | 0.00 | 0.93 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.940 | 5.159 | 14.268 | 0.000 | 0.115 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 128 | 191 | 192 | 0 | 144 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.01 | 1.50 | 1.51 | 0.00 | 1.13 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.656 | 2.273 | 14.322 | 0.000 | 0.116 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 171 | 243 | 256 | 0 | 203 | 0 | 0 | 131 | 0 |
N.S. |
1 | 0.92 | 1.31 | 1.38 | 0.00 | 1.10 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 1.051 | 3.396 | 10.754 | 0.000 | 2.778 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 226 | 836 | 284 | 0 | 246 | 0 | 0 | 143 | 0 |
N.S. |
1 | 0.95 | 3.53 | 1.20 | 0.00 | 1.04 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 1.438 | 8.213 | 18.250 | 0.000 | 3.690 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 344 | 261 | 325 | 0 | 266 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.09 | 0.82 | 1.03 | 0.00 | 0.84 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 2.010 | 13.436 | 14.802 | 0.000 | 0.129 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 289 | 1152 | 305 | 0 | 246 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.07 | 4.27 | 1.13 | 0.00 | 0.91 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.646 | 10.009 | 14.653 | 0.000 | 0.122 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 234 | 732 | 261 | 0 | 210 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.05 | 3.28 | 1.17 | 0.00 | 0.94 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 1.289 | 7.396 | 14.311 | 0.000 | 0.119 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 183 | 162 | 244 | 0 | 207 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.04 | 0.92 | 1.39 | 0.00 | 1.18 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.931 | 3.237 | 14.450 | 0.000 | 0.121 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 181 | 474 | 238 | 0 | 205 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.04 | 2.72 | 1.37 | 0.00 | 1.18 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.944 | 6.475 | 10.821 | 0.000 | 0.139 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 226 | 264 | 288 | 0 | 277 | 0 | 0 | 179 | 0 |
N.S. |
1 | 0.97 | 1.13 | 1.23 | 0.00 | 1.18 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 1.419 | 4.444 | 10.823 | 0.000 | 6.012 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 283 | 929 | 354 | 0 | 313 | 0 | 0 | 179 | 0 |
N.S. |
1 | 0.99 | 3.25 | 1.24 | 0.00 | 1.09 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.869 | 8.580 | 18.576 | 0.000 | 7.653 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 344 | 267 | 355 | 0 | 295 | 0 | 0 | 151 | 0 |
N.S. |
1 | 1.09 | 0.84 | 1.12 | 0.00 | 0.93 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 2.079 | 11.326 | 14.835 | 0.000 | 0.136 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 289 | 802 | 311 | 0 | 260 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.07 | 2.97 | 1.15 | 0.00 | 0.96 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.697 | 8.023 | 14.576 | 0.000 | 0.124 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 238 | 180 | 294 | 0 | 257 | 0 | 0 | 135 | 0 |
N.S. |
1 | 1.07 | 0.81 | 1.32 | 0.00 | 1.15 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.297 | 3.344 | 14.662 | 0.000 | 0.120 | 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 | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 236 | 179 | 288 | 0 | 255 | 0 | 0 | 195 | 0 |
N.S. |
1 | 1.07 | 0.81 | 1.30 | 0.00 | 1.15 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.289 | 3.320 | 10.747 | 0.000 | 0.123 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 236 | 561 | 284 | 0 | 257 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.07 | 2.54 | 1.29 | 0.00 | 1.16 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 1.288 | 6.769 | 10.689 | 0.000 | 0.126 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 281 | 281 | 352 | 0 | 338 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 0.00 | 1.20 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 1.781 | 6.226 | 10.820 | 0.000 | 7.398 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 338 | 1017 | 422 | 0 | 379 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.02 | 3.05 | 1.27 | 0.00 | 1.14 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 2.254 | 9.332 | 18.941 | 0.000 | 13.106 | 0.000 | 0.000 | 0.215 | 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 | 180 | 170 | 132 | 636 | 0 | 235 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.94 | 0.73 | 3.53 | 0.00 | 1.31 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.859 | 2.955 | 104.357 | 0.000 | 0.092 | 0.000 | 0.000 | 0.268 | 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 | 143 | 142 | 104 | 401 | 0 | 205 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.99 | 0.73 | 2.80 | 0.00 | 1.43 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.822 | 1.681 | 103.412 | 0.000 | 0.086 | 0.000 | 0.000 | 0.267 | 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 | 111 | 85 | 246 | 0 | 153 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.00 | 0.77 | 2.22 | 0.00 | 1.38 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.692 | 2.374 | 7.162 | 0.000 | 0.084 | 0.000 | 0.000 | 0.248 | 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 | 115 | 118 | 90 | 326 | 0 | 156 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.03 | 0.78 | 2.83 | 0.00 | 1.36 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.721 | 1.437 | 8.527 | 0.000 | 0.087 | 0.000 | 0.000 | 0.197 | 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 | 148 | 147 | 108 | 371 | 0 | 184 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.99 | 0.73 | 2.51 | 0.00 | 1.24 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.817 | 1.751 | 11.535 | 0.000 | 0.097 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 174 | 125 | 413 | 0 | 203 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.97 | 0.69 | 2.29 | 0.00 | 1.13 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.921 | 2.420 | 14.925 | 0.000 | 0.103 | 0.000 | 0.000 | 0.194 | 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 | 221 | 206 | 171 | 723 | 0 | 286 | 0 | 0 | 115 | 0 |
N.S. |
1 | 0.93 | 0.77 | 3.27 | 0.00 | 1.29 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 1.421 | 4.377 | 516.694 | 0.000 | 0.093 | 0.000 | 0.000 | 0.309 | 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 | 177 | 178 | 125 | 650 | 0 | 247 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.01 | 0.71 | 3.67 | 0.00 | 1.40 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.215 | 7.041 | 527.681 | 0.000 | 0.093 | 0.000 | 0.000 | 0.318 | 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 | 161 | 164 | 124 | 405 | 0 | 208 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.02 | 0.77 | 2.52 | 0.00 | 1.29 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 1.130 | 6.398 | 9.130 | 0.000 | 0.092 | 0.000 | 0.000 | 0.276 | 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 | 171 | 174 | 128 | 487 | 0 | 226 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.02 | 0.75 | 2.85 | 0.00 | 1.32 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 1.166 | 6.719 | 12.226 | 0.000 | 0.091 | 0.000 | 0.000 | 0.224 | 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 | 213 | 202 | 161 | 548 | 0 | 254 | 0 | 0 | 115 | 0 |
N.S. |
1 | 0.95 | 0.76 | 2.57 | 0.00 | 1.19 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.413 | 7.430 | 16.744 | 0.000 | 0.102 | 0.000 | 0.000 | 0.200 | 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 | 295 | 277 | 225 | 917 | 0 | 364 | 0 | 0 | 149 | 0 |
N.S. |
1 | 0.94 | 0.76 | 3.11 | 0.00 | 1.23 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.990 | 6.150 | 2342.573 | 0.000 | 0.108 | 0.000 | 0.000 | 0.389 | 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 | 244 | 248 | 192 | 970 | 0 | 326 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.02 | 0.79 | 3.98 | 0.00 | 1.34 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.717 | 12.903 | 2639.665 | 0.000 | 0.102 | 0.000 | 0.000 | 0.363 | 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 | 239 | 238 | 166 | 886 | 0 | 298 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.00 | 0.69 | 3.71 | 0.00 | 1.25 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.709 | 11.342 | 2609.825 | 0.000 | 0.100 | 0.000 | 0.000 | 0.365 | 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 | 237 | 241 | 172 | 641 | 0 | 270 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.02 | 0.73 | 2.70 | 0.00 | 1.14 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 1.693 | 10.849 | 13.826 | 0.000 | 0.106 | 0.000 | 0.000 | 0.329 | 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 | 245 | 253 | 180 | 664 | 0 | 295 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.03 | 0.73 | 2.71 | 0.00 | 1.20 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.715 | 10.787 | 20.325 | 0.000 | 0.101 | 0.000 | 0.000 | 0.221 | 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 | 295 | 281 | 219 | 745 | 0 | 332 | 0 | 0 | 149 | 0 |
N.S. |
1 | 0.95 | 0.74 | 2.53 | 0.00 | 1.13 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 2.001 | 11.297 | 24.900 | 0.000 | 0.124 | 0.000 | 0.000 | 0.201 | 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 | 210 | 224 | 225 | 441 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.07 | 1.07 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.954 | 13.654 | 15.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 125 | 300 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.99 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.097 | 3.630 | 5.154 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 76 | 217 | 0 | 0 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.806 | 1.686 | 4.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 126 | 220 | 295 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.85 | 1.48 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.009 | 21.565 | 6.437 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 203 | 542 | 822 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.03 | 2.75 | 4.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.550 | 7.804 | 8.743 | 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(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 389 | 735 | 1005 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.96 | 1.81 | 2.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 3.160 | 7.565 | 42.842 | 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 | B | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 306 | 681 | 856 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.97 | 2.16 | 2.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.397 | 7.324 | 7.309 | 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 | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 252 | 639 | 721 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.97 | 2.46 | 2.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.819 | 7.229 | 6.513 | 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 | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 247 | 626 | 808 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.96 | 2.43 | 3.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.755 | 7.194 | 6.849 | 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 | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 275 | 655 | 849 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.97 | 2.31 | 2.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.955 | 7.399 | 9.047 | 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 | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 350 | 701 | 1066 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.96 | 1.93 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.565 | 7.514 | 11.371 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 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 | 480 | 476 | 844 | 1975 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.99 | 1.76 | 4.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 3.625 | 7.829 | 9.565 | 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 | A | B | F(-1) | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 403 | 797 | 1744 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.97 | 4.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.819 | 7.387 | 7.690 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 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 | 402 | 397 | 784 | 1850 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.99 | 1.95 | 4.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 2.691 | 7.450 | 8.786 | 0.000 | 0.000 | 0.000 | 0.000 | 0.262 | 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 | 400 | 397 | 786 | 1937 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.99 | 1.96 | 4.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 2.791 | 7.571 | 6.892 | 0.000 | 0.000 | 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 | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 428 | 820 | 1977 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 1.92 | 4.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 3.030 | 7.845 | 11.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 519 | 865 | 2195 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 1.66 | 4.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 3.894 | 8.026 | 13.546 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 47 | 214 | 0 | 91 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.73 | 3.34 | 0.00 | 1.42 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.343 | 0.090 | 2.661 | 0.000 | 0.087 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 46 | 183 | 0 | 76 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.77 | 3.05 | 0.00 | 1.27 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.356 | 0.067 | 1.881 | 0.000 | 0.080 | 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 | 37 | 37 | 37 | 134 | 0 | 53 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.62 | 0.00 | 1.43 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.265 | 0.054 | 1.737 | 0.000 | 0.082 | 0.000 | 0.000 | 0.190 | 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 | 37 | 37 | 37 | 134 | 0 | 59 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.62 | 0.00 | 1.59 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.266 | 0.061 | 2.832 | 0.000 | 0.083 | 0.000 | 0.000 | 0.198 | 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 | 64 | 64 | 50 | 180 | 0 | 71 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.78 | 2.81 | 0.00 | 1.11 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.348 | 0.065 | 4.204 | 0.000 | 0.085 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 56 | 203 | 0 | 77 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.88 | 3.17 | 0.00 | 1.20 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.347 | 0.103 | 5.862 | 0.000 | 0.092 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 471 | 3321 | 2095 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 7.02 | 4.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 2.303 | 25.964 | 56.475 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 390 | 380 | 2899 | 1515 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.97 | 7.43 | 3.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.632 | 22.664 | 44.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 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 | 324 | 306 | 346 | 1036 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.94 | 1.07 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.198 | 16.252 | 34.799 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 372 | 635 | 667 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.91 | 1.55 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.378 | 18.162 | 27.329 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 412 | 787 | 666 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.93 | 1.77 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.782 | 20.167 | 21.931 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 533 | 492 | 1121 | 1145 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.92 | 2.10 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 2.209 | 20.043 | 20.662 | 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 | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 620 | 584 | 1533 | 1656 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.94 | 2.47 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.948 | 16.489 | 27.438 | 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 | B | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 562 | 554 | 3739 | 2693 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.99 | 6.65 | 4.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 2.870 | 28.805 | 70.526 | 0.000 | 0.000 | 0.000 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 465 | 3318 | 2095 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.98 | 7.01 | 4.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 2.260 | 26.477 | 60.625 | 0.000 | 0.000 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 393 | 380 | 2931 | 1631 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.97 | 7.46 | 4.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.757 | 23.951 | 43.641 | 0.000 | 0.000 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 441 | 5981 | 1371 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.92 | 12.49 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.963 | 26.428 | 15.346 | 0.000 | 0.000 | 0.000 | 0.000 | 0.304 | 0.000 |