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 | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 148 | 138 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.620 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 148 | 138 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.620 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 132 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.652 | 21.883 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 132 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.653 | 21.974 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 275 | 231 | 271 | 0 | 725 | 562 | 0 | 0 | 749 |
N.S. |
1 | 0.84 | 0.99 | 0.00 | 2.64 | 2.04 | 0.00 | 0.00 | 2.72 |
time (sec) |
N/A | 0.972 | 11.975 | 0.000 | 0.344 | 0.309 | 0.000 | 0.000 | 21.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 166 | 174 | 174 | 0 | 498 | 313 | 0 | 0 | 480 |
N.S. |
1 | 1.05 | 1.05 | 0.00 | 3.00 | 1.89 | 0.00 | 0.00 | 2.89 |
time (sec) |
N/A | 0.754 | 4.090 | 0.000 | 0.345 | 0.299 | 0.000 | 0.000 | 19.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 116 | 0 | 323 | 165 | 0 | 0 | 105 |
N.S. |
1 | 1.00 | 1.12 | 0.00 | 3.11 | 1.59 | 0.00 | 0.00 | 1.01 |
time (sec) |
N/A | 0.531 | 1.391 | 0.000 | 0.340 | 0.267 | 0.000 | 0.000 | 1.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 132 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.632 | 0.278 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 139 | 144 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.678 | 25.657 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 134 | 139 | 159 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.705 | 33.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 267 | 233 | 183 | 0 | 0 | 205 | 0 | 0 | 368 |
N.S. |
1 | 0.87 | 0.69 | 0.00 | 0.00 | 0.77 | 0.00 | 0.00 | 1.38 |
time (sec) |
N/A | 0.966 | 0.608 | 0.000 | 0.000 | 0.277 | 0.000 | 0.000 | 20.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 191 | 176 | 141 | 0 | 0 | 137 | 0 | 0 | 239 |
N.S. |
1 | 0.92 | 0.74 | 0.00 | 0.00 | 0.72 | 0.00 | 0.00 | 1.25 |
time (sec) |
N/A | 0.741 | 0.416 | 0.000 | 0.000 | 0.280 | 0.000 | 0.000 | 15.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 92 | 0 | 0 | 89 | 0 | 0 | 134 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.78 | 0.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.515 | 0.327 | 0.000 | 0.000 | 0.277 | 0.000 | 0.000 | 14.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 163 | 201 | 310 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.708 | 7.255 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 158 | 196 | 402 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 2.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.628 | 6.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 170 | 209 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.707 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 173 | 211 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.728 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 63 | 63 | 0 | 78 | 898 | 9586 | 64 |
N.S. |
1 | 1.00 | 1.85 | 1.85 | 0.00 | 2.29 | 26.41 | 281.94 | 1.88 |
time (sec) |
N/A | 0.500 | 1.208 | 11.497 | 0.000 | 0.283 | 65.207 | 48.339 | 14.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 67 | 62 | 0 | 77 | 898 | 9587 | 61 |
N.S. |
1 | 1.00 | 1.97 | 1.82 | 0.00 | 2.26 | 26.41 | 281.97 | 1.79 |
time (sec) |
N/A | 0.463 | 7.361 | 13.155 | 0.000 | 0.261 | 65.370 | 48.817 | 13.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 66 | 62 | 0 | 78 | 898 | 9586 | 61 |
N.S. |
1 | 1.00 | 2.00 | 1.88 | 0.00 | 2.36 | 27.21 | 290.48 | 1.85 |
time (sec) |
N/A | 0.468 | 7.131 | 13.326 | 0.000 | 0.274 | 65.469 | 45.410 | 13.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 61 | 65 | 0 | 77 | 898 | 9587 | 64 |
N.S. |
1 | 1.00 | 1.74 | 1.86 | 0.00 | 2.20 | 25.66 | 273.91 | 1.83 |
time (sec) |
N/A | 0.481 | 0.893 | 11.232 | 0.000 | 0.260 | 66.132 | 41.811 | 13.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 37 | 0 | 36 | 0 | 8947 | 36 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.00 | 0.00 | 248.53 | 1.00 |
time (sec) |
N/A | 0.311 | 1.866 | 9.819 | 0.000 | 0.263 | 0.000 | 53.146 | 12.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 38 | 0 | 37 | 0 | 8948 | 37 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.00 | 0.00 | 241.84 | 1.00 |
time (sec) |
N/A | 0.308 | 1.313 | 9.799 | 0.000 | 0.258 | 0.000 | 51.920 | 12.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 87 | 90 | 157 | 105 | 440 | 131 | 300 |
N.S. |
1 | 1.00 | 0.62 | 0.64 | 1.12 | 0.75 | 3.14 | 0.94 | 2.14 |
time (sec) |
N/A | 0.405 | 0.370 | 2.191 | 0.243 | 0.254 | 0.481 | 0.305 | 14.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 77 | 79 | 138 | 91 | 359 | 113 | 256 |
N.S. |
1 | 1.00 | 0.64 | 0.65 | 1.14 | 0.75 | 2.97 | 0.93 | 2.12 |
time (sec) |
N/A | 0.385 | 0.240 | 1.627 | 0.228 | 0.250 | 0.348 | 0.291 | 14.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 106 | 57 | 112 | 77 | 267 | 77 | 292 |
N.S. |
1 | 1.00 | 1.10 | 0.59 | 1.17 | 0.80 | 2.78 | 0.80 | 3.04 |
time (sec) |
N/A | 0.320 | 0.723 | 1.359 | 0.239 | 0.250 | 0.249 | 0.287 | 14.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 54 | 57 | 86 | 63 | 196 | 77 | 250 |
N.S. |
1 | 1.00 | 0.66 | 0.70 | 1.05 | 0.77 | 2.39 | 0.94 | 3.05 |
time (sec) |
N/A | 0.443 | 0.555 | 1.298 | 0.214 | 0.253 | 0.173 | 0.282 | 14.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 74 | 58 | 85 | 92 | 0 | 107 | 212 |
N.S. |
1 | 1.00 | 0.97 | 0.76 | 1.12 | 1.21 | 0.00 | 1.41 | 2.79 |
time (sec) |
N/A | 0.314 | 0.242 | 0.962 | 0.235 | 0.262 | 0.000 | 0.296 | 12.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 77 | 80 | 83 | 111 | 0 | 153 | 226 |
N.S. |
1 | 1.00 | 0.97 | 1.01 | 1.05 | 1.41 | 0.00 | 1.94 | 2.86 |
time (sec) |
N/A | 0.421 | 0.272 | 0.965 | 0.237 | 0.265 | 0.000 | 0.304 | 13.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 142 | 78 | 90 | 152 | 0 | 137 | 220 |
N.S. |
1 | 1.00 | 1.82 | 1.00 | 1.15 | 1.95 | 0.00 | 1.76 | 2.82 |
time (sec) |
N/A | 0.330 | 0.135 | 1.210 | 0.216 | 0.300 | 0.000 | 0.308 | 13.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 141 | 99 | 117 | 175 | 0 | 150 | 245 |
N.S. |
1 | 1.00 | 1.81 | 1.27 | 1.50 | 2.24 | 0.00 | 1.92 | 3.14 |
time (sec) |
N/A | 0.333 | 0.542 | 1.194 | 0.252 | 0.286 | 0.000 | 0.308 | 13.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 210 | 114 | 145 | 166 | 0 | 174 | 244 |
N.S. |
1 | 1.00 | 2.44 | 1.33 | 1.69 | 1.93 | 0.00 | 2.02 | 2.84 |
time (sec) |
N/A | 0.349 | 0.233 | 1.284 | 0.218 | 0.285 | 0.000 | 0.322 | 13.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 107 | 268 | 121 | 175 | 201 | 0 | 174 | 244 |
N.S. |
1 | 1.02 | 2.55 | 1.15 | 1.67 | 1.91 | 0.00 | 1.66 | 2.32 |
time (sec) |
N/A | 0.482 | 0.268 | 1.849 | 0.242 | 0.258 | 0.000 | 0.325 | 12.872 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 306 | 125 | 207 | 240 | 0 | 242 | 340 |
N.S. |
1 | 1.00 | 2.35 | 0.96 | 1.59 | 1.85 | 0.00 | 1.86 | 2.62 |
time (sec) |
N/A | 0.402 | 0.290 | 1.886 | 0.219 | 0.281 | 0.000 | 0.320 | 12.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 211 | 154 | 715 | 248 | 3614 | 156 | 326 |
N.S. |
1 | 1.00 | 1.64 | 1.19 | 5.54 | 1.92 | 28.02 | 1.21 | 2.53 |
time (sec) |
N/A | 0.419 | 3.802 | 1.044 | 0.352 | 0.264 | 22.200 | 0.319 | 16.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 155 | 115 | 543 | 225 | 2290 | 113 | 261 |
N.S. |
1 | 1.00 | 1.50 | 1.12 | 5.27 | 2.18 | 22.23 | 1.10 | 2.53 |
time (sec) |
N/A | 0.392 | 2.187 | 0.934 | 0.323 | 0.269 | 12.943 | 0.312 | 16.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 112 | 85 | 392 | 204 | 1268 | 93 | 178 |
N.S. |
1 | 1.00 | 1.26 | 0.96 | 4.40 | 2.29 | 14.25 | 1.04 | 2.00 |
time (sec) |
N/A | 0.380 | 2.119 | 0.660 | 0.340 | 0.269 | 7.409 | 0.316 | 14.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 107 | 62 | 348 | 156 | 461 | 63 | 110 |
N.S. |
1 | 1.00 | 1.30 | 0.76 | 4.24 | 1.90 | 5.62 | 0.77 | 1.34 |
time (sec) |
N/A | 0.338 | 2.525 | 0.584 | 0.248 | 0.258 | 4.171 | 0.305 | 12.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 61 | 92 | 62 | 387 | 154 | 573 | 79 | 134 |
N.S. |
1 | 1.05 | 1.59 | 1.07 | 6.67 | 2.66 | 9.88 | 1.36 | 2.31 |
time (sec) |
N/A | 0.386 | 1.549 | 0.558 | 0.232 | 0.247 | 2.323 | 0.303 | 12.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 313 | 95 | 433 | 310 | 0 | 99 | 199 |
N.S. |
1 | 1.00 | 3.19 | 0.97 | 4.42 | 3.16 | 0.00 | 1.01 | 2.03 |
time (sec) |
N/A | 0.361 | 6.548 | 0.931 | 0.223 | 0.258 | 0.000 | 0.313 | 14.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 167 | 120 | 519 | 406 | 0 | 146 | 210 |
N.S. |
1 | 1.00 | 1.48 | 1.06 | 4.59 | 3.59 | 0.00 | 1.29 | 1.86 |
time (sec) |
N/A | 0.615 | 2.327 | 1.125 | 0.246 | 0.276 | 0.000 | 0.321 | 15.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 245 | 148 | 622 | 498 | 0 | 180 | 288 |
N.S. |
1 | 1.00 | 1.78 | 1.07 | 4.51 | 3.61 | 0.00 | 1.30 | 2.09 |
time (sec) |
N/A | 0.447 | 2.896 | 1.091 | 0.268 | 0.283 | 0.000 | 0.327 | 16.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 348 | 174 | 706 | 594 | 0 | 213 | 314 |
N.S. |
1 | 1.00 | 2.27 | 1.14 | 4.61 | 3.88 | 0.00 | 1.39 | 2.05 |
time (sec) |
N/A | 0.464 | 6.595 | 1.170 | 0.286 | 0.269 | 0.000 | 0.324 | 15.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 327 | 336 | 267 | 244 | 406 | 239 | 996 | 309 | 830 |
N.S. |
1 | 1.03 | 0.82 | 0.75 | 1.24 | 0.73 | 3.05 | 0.94 | 2.54 |
time (sec) |
N/A | 1.117 | 2.542 | 1.827 | 0.232 | 0.272 | 0.340 | 0.304 | 16.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 220 | 185 | 172 | 264 | 160 | 571 | 194 | 547 |
N.S. |
1 | 1.03 | 0.87 | 0.81 | 1.24 | 0.75 | 2.68 | 0.91 | 2.57 |
time (sec) |
N/A | 0.754 | 1.636 | 1.125 | 0.231 | 0.269 | 0.228 | 0.301 | 15.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 123 | 104 | 94 | 143 | 84 | 277 | 98 | 134 |
N.S. |
1 | 1.11 | 0.94 | 0.85 | 1.29 | 0.76 | 2.50 | 0.88 | 1.21 |
time (sec) |
N/A | 0.477 | 0.630 | 0.883 | 0.232 | 0.251 | 0.136 | 0.289 | 12.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 45 | 44 | 57 | 43 | 94 | 46 | 100 |
N.S. |
1 | 1.00 | 0.94 | 0.92 | 1.19 | 0.90 | 1.96 | 0.96 | 2.08 |
time (sec) |
N/A | 0.213 | 0.143 | 0.438 | 0.241 | 0.258 | 0.095 | 0.281 | 12.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 109 | 196 | 120 | 0 | 292 | 5508 | 137 | 3074 |
N.S. |
1 | 1.11 | 2.00 | 1.22 | 0.00 | 2.98 | 56.20 | 1.40 | 31.37 |
time (sec) |
N/A | 0.632 | 1.040 | 0.719 | 0.000 | 0.276 | 113.708 | 0.296 | 16.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 155 | 217 | 174 | 0 | 655 | 0 | 197 | 5102 |
N.S. |
1 | 1.25 | 1.75 | 1.40 | 0.00 | 5.28 | 0.00 | 1.59 | 41.15 |
time (sec) |
N/A | 0.739 | 1.902 | 0.837 | 0.000 | 0.294 | 0.000 | 0.298 | 20.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 191 | 345 | 424 | 0 | 967 | 0 | 570 | 554 |
N.S. |
1 | 1.09 | 1.96 | 2.41 | 0.00 | 5.49 | 0.00 | 3.24 | 3.15 |
time (sec) |
N/A | 0.817 | 2.991 | 1.100 | 0.000 | 0.304 | 0.000 | 0.327 | 15.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 464 | 480 | 437 | 324 | 724 | 364 | 1865 | 468 | 1291 |
N.S. |
1 | 1.03 | 0.94 | 0.70 | 1.56 | 0.78 | 4.02 | 1.01 | 2.78 |
time (sec) |
N/A | 1.753 | 2.056 | 2.532 | 0.256 | 0.294 | 0.517 | 0.326 | 15.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 336 | 350 | 296 | 222 | 478 | 245 | 1129 | 306 | 765 |
N.S. |
1 | 1.04 | 0.88 | 0.66 | 1.42 | 0.73 | 3.36 | 0.91 | 2.28 |
time (sec) |
N/A | 1.332 | 0.998 | 1.771 | 0.250 | 0.274 | 0.349 | 0.294 | 15.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 145 | 144 | 135 | 268 | 144 | 571 | 168 | 492 |
N.S. |
1 | 0.87 | 0.87 | 0.81 | 1.61 | 0.87 | 3.44 | 1.01 | 2.96 |
time (sec) |
N/A | 0.615 | 0.426 | 1.158 | 0.240 | 0.261 | 0.229 | 0.284 | 14.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 83 | 106 | 70 | 114 | 70 | 199 | 85 | 91 |
N.S. |
1 | 0.88 | 1.13 | 0.74 | 1.21 | 0.74 | 2.12 | 0.90 | 0.97 |
time (sec) |
N/A | 0.302 | 0.223 | 0.750 | 0.216 | 0.270 | 0.136 | 0.280 | 12.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 185 | 177 | 235 | 0 | 452 | 0 | 305 | 7371 |
N.S. |
1 | 1.08 | 1.04 | 1.37 | 0.00 | 2.64 | 0.00 | 1.78 | 43.11 |
time (sec) |
N/A | 1.045 | 0.451 | 0.737 | 0.000 | 0.292 | 0.000 | 0.294 | 20.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 213 | 192 | 251 | 0 | 731 | 0 | 480 | 8706 |
N.S. |
1 | 1.08 | 0.97 | 1.27 | 0.00 | 3.69 | 0.00 | 2.42 | 43.97 |
time (sec) |
N/A | 1.158 | 5.631 | 1.040 | 0.000 | 0.318 | 0.000 | 0.302 | 22.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 255 | 226 | 431 | 0 | 1483 | 0 | 678 | 8632 |
N.S. |
1 | 1.19 | 1.05 | 2.00 | 0.00 | 6.90 | 0.00 | 3.15 | 40.15 |
time (sec) |
N/A | 1.242 | 5.895 | 1.020 | 0.000 | 0.331 | 0.000 | 0.328 | 22.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 604 | 628 | 528 | 384 | 1056 | 432 | 2878 | 559 | 1395 |
N.S. |
1 | 1.04 | 0.87 | 0.64 | 1.75 | 0.72 | 4.76 | 0.93 | 2.31 |
time (sec) |
N/A | 2.561 | 3.053 | 2.718 | 0.228 | 0.298 | 0.716 | 0.335 | 16.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 463 | 485 | 355 | 268 | 704 | 299 | 1804 | 374 | 976 |
N.S. |
1 | 1.05 | 0.77 | 0.58 | 1.52 | 0.65 | 3.90 | 0.81 | 2.11 |
time (sec) |
N/A | 2.029 | 1.589 | 2.096 | 0.254 | 0.288 | 0.504 | 0.316 | 16.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 163 | 156 | 167 | 398 | 178 | 960 | 212 | 550 |
N.S. |
1 | 0.81 | 0.78 | 0.83 | 1.98 | 0.89 | 4.78 | 1.05 | 2.74 |
time (sec) |
N/A | 0.698 | 0.598 | 1.658 | 0.217 | 0.266 | 0.330 | 0.298 | 14.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 101 | 120 | 87 | 171 | 93 | 371 | 112 | 330 |
N.S. |
1 | 0.80 | 0.94 | 0.69 | 1.35 | 0.73 | 2.92 | 0.88 | 2.60 |
time (sec) |
N/A | 0.362 | 0.344 | 1.086 | 0.288 | 0.268 | 0.199 | 0.279 | 14.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 269 | 233 | 378 | 0 | 627 | 0 | 597 | 10256 |
N.S. |
1 | 1.09 | 0.95 | 1.54 | 0.00 | 2.55 | 0.00 | 2.43 | 41.69 |
time (sec) |
N/A | 1.694 | 1.764 | 1.041 | 0.000 | 0.300 | 0.000 | 0.307 | 22.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 295 | 244 | 406 | 0 | 1027 | 0 | 571 | 11993 |
N.S. |
1 | 1.04 | 0.86 | 1.43 | 0.00 | 3.63 | 0.00 | 2.02 | 42.38 |
time (sec) |
N/A | 1.745 | 5.947 | 1.671 | 0.000 | 0.333 | 0.000 | 0.309 | 24.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 305 | 330 | 830 | 586 | 0 | 1670 | 0 | 953 | 13891 |
N.S. |
1 | 1.08 | 2.72 | 1.92 | 0.00 | 5.48 | 0.00 | 3.12 | 45.54 |
time (sec) |
N/A | 1.833 | 7.176 | 2.056 | 0.000 | 0.343 | 0.000 | 0.345 | 25.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 788 | 337 | 1124 | 470 | 14644 | 460 | 839 |
N.S. |
1 | 1.00 | 3.58 | 1.53 | 5.11 | 2.14 | 66.56 | 2.09 | 3.81 |
time (sec) |
N/A | 0.702 | 7.016 | 0.865 | 0.316 | 0.279 | 3.875 | 0.291 | 14.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 137 | 200 | 193 | 606 | 303 | 5763 | 214 | 297 |
N.S. |
1 | 0.96 | 1.40 | 1.35 | 4.24 | 2.12 | 40.30 | 1.50 | 2.08 |
time (sec) |
N/A | 0.467 | 6.462 | 0.629 | 0.295 | 0.260 | 2.041 | 0.286 | 16.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 69 | 126 | 81 | 256 | 154 | 1307 | 151 | 122 |
N.S. |
1 | 1.03 | 1.88 | 1.21 | 3.82 | 2.30 | 19.51 | 2.25 | 1.82 |
time (sec) |
N/A | 0.544 | 0.441 | 0.652 | 0.299 | 0.257 | 1.042 | 0.288 | 13.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 79 | 42 | 78 | 66 | 109 | 38 | 35 |
N.S. |
1 | 1.00 | 2.26 | 1.20 | 2.23 | 1.89 | 3.11 | 1.09 | 1.00 |
time (sec) |
N/A | 0.265 | 0.134 | 0.346 | 0.276 | 0.258 | 0.557 | 0.294 | 13.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 107 | 148 | 94 | 0 | 595 | 0 | 110 | 154 |
N.S. |
1 | 1.06 | 1.47 | 0.93 | 0.00 | 5.89 | 0.00 | 1.09 | 1.52 |
time (sec) |
N/A | 0.440 | 4.393 | 0.768 | 0.000 | 0.278 | 0.000 | 0.294 | 13.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 189 | 209 | 197 | 0 | 1538 | 0 | 425 | 437 |
N.S. |
1 | 1.04 | 1.15 | 1.09 | 0.00 | 8.50 | 0.00 | 2.35 | 2.41 |
time (sec) |
N/A | 0.697 | 2.931 | 1.110 | 0.000 | 0.305 | 0.000 | 0.335 | 15.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 302 | 313 | 482 | 0 | 3303 | 0 | 727 | 1076 |
N.S. |
1 | 1.07 | 1.11 | 1.70 | 0.00 | 11.67 | 0.00 | 2.57 | 3.80 |
time (sec) |
N/A | 1.076 | 3.278 | 2.488 | 0.000 | 0.366 | 0.000 | 0.382 | 17.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 234 | 547 | 340 | 1382 | 584 | 14612 | 472 | 663 |
N.S. |
1 | 1.03 | 2.40 | 1.49 | 6.06 | 2.56 | 64.09 | 2.07 | 2.91 |
time (sec) |
N/A | 0.866 | 2.414 | 1.052 | 0.361 | 0.271 | 7.600 | 0.319 | 17.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 138 | 338 | 193 | 831 | 375 | 5358 | 264 | 365 |
N.S. |
1 | 1.05 | 2.56 | 1.46 | 6.30 | 2.84 | 40.59 | 2.00 | 2.77 |
time (sec) |
N/A | 0.998 | 1.328 | 0.794 | 0.319 | 0.266 | 4.014 | 0.311 | 16.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 180 | 110 | 454 | 208 | 1062 | 133 | 94 |
N.S. |
1 | 1.05 | 2.12 | 1.29 | 5.34 | 2.45 | 12.49 | 1.56 | 1.11 |
time (sec) |
N/A | 0.568 | 1.400 | 0.582 | 0.310 | 0.267 | 2.109 | 0.307 | 14.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 43 | 60 | 214 | 117 | 372 | 64 | 97 |
N.S. |
1 | 0.98 | 0.66 | 0.92 | 3.29 | 1.80 | 5.72 | 0.98 | 1.49 |
time (sec) |
N/A | 0.288 | 0.041 | 0.472 | 0.211 | 0.249 | 1.121 | 0.290 | 13.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 165 | 229 | 159 | 0 | 1285 | 0 | 249 | 302 |
N.S. |
1 | 1.09 | 1.51 | 1.05 | 0.00 | 8.45 | 0.00 | 1.64 | 1.99 |
time (sec) |
N/A | 0.723 | 2.632 | 1.104 | 0.000 | 0.296 | 0.000 | 0.310 | 14.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 288 | 313 | 263 | 0 | 3123 | 0 | 411 | 844 |
N.S. |
1 | 1.05 | 1.14 | 0.96 | 0.00 | 11.36 | 0.00 | 1.49 | 3.07 |
time (sec) |
N/A | 1.162 | 7.005 | 1.867 | 0.000 | 0.363 | 0.000 | 0.337 | 16.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 386 | 417 | 1257 | 547 | 0 | 4997 | 0 | 911 | 1686 |
N.S. |
1 | 1.08 | 3.26 | 1.42 | 0.00 | 12.95 | 0.00 | 2.36 | 4.37 |
time (sec) |
N/A | 1.645 | 10.899 | 4.518 | 0.000 | 0.453 | 0.000 | 0.371 | 17.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 237 | 366 | 349 | 1682 | 649 | 11456 | 567 | 593 |
N.S. |
1 | 1.05 | 1.63 | 1.55 | 7.48 | 2.88 | 50.92 | 2.52 | 2.64 |
time (sec) |
N/A | 1.604 | 6.898 | 1.072 | 0.342 | 0.272 | 14.033 | 0.317 | 16.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 164 | 174 | 514 | 240 | 1132 | 432 | 3468 | 362 | 286 |
N.S. |
1 | 1.06 | 3.13 | 1.46 | 6.90 | 2.63 | 21.15 | 2.21 | 1.74 |
time (sec) |
N/A | 1.025 | 0.812 | 0.734 | 0.320 | 0.261 | 7.853 | 0.312 | 16.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 129 | 176 | 139 | 733 | 271 | 1819 | 210 | 245 |
N.S. |
1 | 1.02 | 1.39 | 1.09 | 5.77 | 2.13 | 14.32 | 1.65 | 1.93 |
time (sec) |
N/A | 0.608 | 1.718 | 0.655 | 0.226 | 0.251 | 4.366 | 0.315 | 14.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 99 | 63 | 95 | 387 | 190 | 1015 | 122 | 150 |
N.S. |
1 | 0.97 | 0.62 | 0.93 | 3.79 | 1.86 | 9.95 | 1.20 | 1.47 |
time (sec) |
N/A | 0.391 | 0.058 | 0.565 | 0.302 | 0.239 | 2.371 | 0.291 | 13.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 258 | 502 | 252 | 0 | 2292 | 0 | 553 | 591 |
N.S. |
1 | 1.13 | 2.19 | 1.10 | 0.00 | 10.01 | 0.00 | 2.41 | 2.58 |
time (sec) |
N/A | 1.207 | 4.747 | 1.516 | 0.000 | 0.333 | 0.000 | 0.317 | 17.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 381 | 409 | 1253 | 355 | 0 | 4486 | 0 | 743 | 1349 |
N.S. |
1 | 1.07 | 3.29 | 0.93 | 0.00 | 11.77 | 0.00 | 1.95 | 3.54 |
time (sec) |
N/A | 1.789 | 12.275 | 2.897 | 0.000 | 0.421 | 0.000 | 0.347 | 17.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 508 | 551 | 548 | 639 | 0 | 7283 | 0 | 1224 | 2387 |
N.S. |
1 | 1.08 | 1.08 | 1.26 | 0.00 | 14.34 | 0.00 | 2.41 | 4.70 |
time (sec) |
N/A | 2.341 | 8.637 | 6.115 | 0.000 | 0.559 | 0.000 | 0.433 | 19.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 256 | 235 | 305 | 242 | 0 | 467 | 0 | 550 | 0 |
N.S. |
1 | 0.92 | 1.19 | 0.95 | 0.00 | 1.82 | 0.00 | 2.15 | 0.00 |
time (sec) |
N/A | 1.044 | 1.298 | 2.190 | 0.000 | 0.271 | 0.000 | 0.397 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 187 | 176 | 161 | 0 | 306 | 0 | 348 | 0 |
N.S. |
1 | 0.97 | 0.92 | 0.84 | 0.00 | 1.59 | 0.00 | 1.81 | 0.00 |
time (sec) |
N/A | 0.771 | 0.841 | 1.763 | 0.000 | 0.277 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 129 | 117 | 102 | 0 | 175 | 0 | 186 | 0 |
N.S. |
1 | 1.09 | 0.99 | 0.86 | 0.00 | 1.48 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.637 | 0.740 | 1.540 | 0.000 | 0.267 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 82 | 58 | 0 | 85 | 0 | 85 | 0 |
N.S. |
1 | 1.00 | 1.32 | 0.94 | 0.00 | 1.37 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 0.292 | 0.147 | 0.931 | 0.000 | 0.272 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 903 | 139 | 0 | 651 | 0 | 125 | 0 |
N.S. |
1 | 1.00 | 9.03 | 1.39 | 0.00 | 6.51 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.483 | 6.754 | 0.696 | 0.000 | 0.715 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 901 | 274 | 0 | 1012 | 0 | 212 | 0 |
N.S. |
1 | 1.00 | 7.15 | 2.17 | 0.00 | 8.03 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.533 | 7.018 | 0.838 | 0.000 | 0.848 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 186 | 967 | 628 | 0 | 1750 | 0 | 422 | 0 |
N.S. |
1 | 0.97 | 5.04 | 3.27 | 0.00 | 9.11 | 0.00 | 2.20 | 0.00 |
time (sec) |
N/A | 0.743 | 8.527 | 1.091 | 0.000 | 1.291 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 374 | 316 | 390 | 312 | 0 | 637 | 0 | 755 | 0 |
N.S. |
1 | 0.84 | 1.04 | 0.83 | 0.00 | 1.70 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 1.531 | 4.337 | 2.475 | 0.000 | 0.296 | 0.000 | 0.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 268 | 267 | 207 | 0 | 430 | 0 | 497 | 0 |
N.S. |
1 | 0.91 | 0.91 | 0.70 | 0.00 | 1.46 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 1.242 | 2.915 | 2.044 | 0.000 | 0.280 | 0.000 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 163 | 144 | 150 | 0 | 257 | 0 | 285 | 0 |
N.S. |
1 | 0.99 | 0.87 | 0.91 | 0.00 | 1.56 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.818 | 2.348 | 1.821 | 0.000 | 0.269 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 99 | 101 | 77 | 0 | 137 | 0 | 139 | 0 |
N.S. |
1 | 0.98 | 1.00 | 0.76 | 0.00 | 1.36 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.395 | 1.087 | 1.217 | 0.000 | 0.255 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 159 | 898 | 292 | 0 | 880 | 0 | 274 | 0 |
N.S. |
1 | 1.04 | 5.87 | 1.91 | 0.00 | 5.75 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.840 | 3.347 | 1.058 | 0.000 | 0.848 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 199 | 922 | 592 | 0 | 1428 | 0 | 364 | 0 |
N.S. |
1 | 1.04 | 4.83 | 3.10 | 0.00 | 7.48 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.922 | 9.590 | 0.967 | 0.000 | 0.996 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 229 | 957 | 896 | 0 | 2208 | 0 | 624 | 0 |
N.S. |
1 | 1.04 | 4.33 | 4.05 | 0.00 | 9.99 | 0.00 | 2.82 | 0.00 |
time (sec) |
N/A | 0.998 | 10.840 | 1.344 | 0.000 | 1.494 | 0.000 | 0.356 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 534 | 420 | 1565 | 374 | 0 | 863 | 0 | 1014 | 0 |
N.S. |
1 | 0.79 | 2.93 | 0.70 | 0.00 | 1.62 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 2.162 | 8.546 | 168.510 | 0.000 | 0.308 | 0.000 | 0.553 | 0.000 |