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 | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 22 | 20 | 30 | 19 | 35 | 17 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.91 | 1.36 | 0.86 | 1.59 | 0.77 |
time (sec) |
N/A | 0.206 | 0.024 | 0.786 | 0.312 | 0.250 | 0.121 | 0.267 | 12.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 44 | 81 | 76 | 81 | 75 | 93 | 53 |
N.S. |
1 | 0.00 | 1.52 | 2.79 | 2.62 | 2.79 | 2.59 | 3.21 | 1.83 |
time (sec) |
N/A | 0.000 | 0.323 | 94.410 | 0.488 | 0.249 | 2.001 | 1.614 | 13.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 23 | 28 | 25 | 25 | 31 | 44 | 0 |
N.S. |
1 | 0.00 | 0.77 | 0.93 | 0.83 | 0.83 | 1.03 | 1.47 | 0.00 |
time (sec) |
N/A | 0.000 | 0.701 | 1.048 | 0.228 | 0.243 | 0.124 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 49 | 28 | 27 | 21 | 31 | 29 | 33 | 21 |
N.S. |
1 | 2.04 | 1.17 | 1.12 | 0.88 | 1.29 | 1.21 | 1.38 | 0.88 |
time (sec) |
N/A | 0.201 | 3.663 | 1.409 | 0.232 | 0.247 | 0.097 | 0.271 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 56 | 41 | 54 | 52 | 37 | 54 | 50 | 49 |
N.S. |
1 | 2.80 | 2.05 | 2.70 | 2.60 | 1.85 | 2.70 | 2.50 | 2.45 |
time (sec) |
N/A | 0.027 | 0.029 | 0.315 | 0.191 | 0.260 | 0.073 | 0.267 | 11.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 51 | 49 | 36 | 39 | 39 | 39 | 39 | 35 |
N.S. |
1 | 2.04 | 1.96 | 1.44 | 1.56 | 1.56 | 1.56 | 1.56 | 1.40 |
time (sec) |
N/A | 0.010 | 0.013 | 0.178 | 0.201 | 0.269 | 0.025 | 0.268 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 36 | 26 | 26 | 25 | 24 | 25 | 16 |
N.S. |
1 | 0.00 | 1.50 | 1.08 | 1.08 | 1.04 | 1.00 | 1.04 | 0.67 |
time (sec) |
N/A | 0.000 | 4.642 | 0.419 | 0.341 | 0.263 | 0.115 | 0.292 | 12.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 23 | 98 | 24 | 19 | 24 | 15 |
N.S. |
1 | 0.00 | 1.00 | 1.28 | 5.44 | 1.33 | 1.06 | 1.33 | 0.83 |
time (sec) |
N/A | 0.000 | 0.027 | 0.260 | 0.390 | 0.282 | 11.232 | 0.979 | 12.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 7 | 6 | 6 | 8 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.64 | 0.55 | 0.55 | 0.73 | 0.55 | 0.55 |
time (sec) |
N/A | 0.001 | 0.009 | 0.123 | 0.205 | 0.249 | 0.033 | 0.261 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 22 | 71 | 24 | 24 | 0 | 28 |
N.S. |
1 | 0.00 | 0.88 | 0.92 | 2.96 | 1.00 | 1.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.000 | 0.338 | 0.774 | 0.407 | 0.267 | 0.582 | 0.000 | 13.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 22 | 0 | 27 | 24 | 0 | 21 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 0.00 | 1.08 | 0.96 | 0.00 | 0.84 |
time (sec) |
N/A | 0.000 | 0.885 | 0.625 | 0.000 | 0.266 | 0.121 | 0.000 | 12.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 41 | 25 | 34 | 38 | 28 | 24 | 27 | 27 |
N.S. |
1 | 1.78 | 1.09 | 1.48 | 1.65 | 1.22 | 1.04 | 1.17 | 1.17 |
time (sec) |
N/A | 0.197 | 0.058 | 0.099 | 0.239 | 0.268 | 0.095 | 0.296 | 12.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 25 | 24 | 34 | 34 | 29 | 25 | 78 |
N.S. |
1 | 0.00 | 1.19 | 1.14 | 1.62 | 1.62 | 1.38 | 1.19 | 3.71 |
time (sec) |
N/A | 0.000 | 0.204 | 1.313 | 0.328 | 0.250 | 0.275 | 0.334 | 12.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 34 | 28 | 31 | 26 | 34 | 0 | 34 | 27 |
N.S. |
1 | 1.21 | 1.00 | 1.11 | 0.93 | 1.21 | 0.00 | 1.21 | 0.96 |
time (sec) |
N/A | 0.696 | 0.209 | 0.127 | 0.452 | 0.246 | 0.000 | 0.371 | 13.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 1473 | 38 | 46 | 1589 | 41 | 58 | 50 | 0 |
N.S. |
1 | 52.61 | 1.36 | 1.64 | 56.75 | 1.46 | 2.07 | 1.79 | 0.00 |
time (sec) |
N/A | 1.797 | 0.071 | 0.472 | 0.348 | 0.248 | 1.133 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 154 | 1045 | 807 | 274 | 279 | 0 | 399 |
N.S. |
1 | 0.00 | 5.50 | 37.32 | 28.82 | 9.79 | 9.96 | 0.00 | 14.25 |
time (sec) |
N/A | 0.000 | 15.481 | 0.267 | 1.349 | 0.289 | 2.894 | 0.000 | 16.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 51 | 27 | 26 | 25 | 25 | 22 | 25 | 28 |
N.S. |
1 | 2.04 | 1.08 | 1.04 | 1.00 | 1.00 | 0.88 | 1.00 | 1.12 |
time (sec) |
N/A | 0.079 | 0.086 | 0.108 | 0.215 | 0.269 | 0.086 | 0.268 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 14 | 15 | 13 | 14 | 14 | 14 | 14 | 12 |
N.S. |
1 | 1.17 | 1.25 | 1.08 | 1.17 | 1.17 | 1.17 | 1.17 | 1.00 |
time (sec) |
N/A | 0.003 | 0.000 | 0.076 | 0.201 | 0.235 | 0.022 | 0.257 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 21 | 21 | 18 | 17 | 17 | 24 | 22 | 17 |
N.S. |
1 | 1.24 | 1.24 | 1.06 | 1.00 | 1.00 | 1.41 | 1.29 | 1.00 |
time (sec) |
N/A | 0.221 | 0.102 | 1.135 | 0.220 | 0.314 | 0.123 | 0.280 | 13.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 53 | 47 | 44 | 40 | 34 | 49 | 213 |
N.S. |
1 | 0.00 | 1.61 | 1.42 | 1.33 | 1.21 | 1.03 | 1.48 | 6.45 |
time (sec) |
N/A | 0.000 | 0.667 | 0.577 | 0.247 | 0.243 | 0.088 | 0.285 | 13.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 29 | 21 | 27 | 27 | 22 | 27 | 20 |
N.S. |
1 | 1.12 | 1.12 | 0.81 | 1.04 | 1.04 | 0.85 | 1.04 | 0.77 |
time (sec) |
N/A | 0.019 | 0.033 | 0.131 | 0.204 | 0.249 | 0.055 | 0.263 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 16 | 25 | 15 | 24 | 24 | 46 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.56 | 0.94 | 1.50 | 1.50 | 2.88 | 1.50 |
time (sec) |
N/A | 0.000 | 0.212 | 0.276 | 0.308 | 0.260 | 0.140 | 0.270 | 12.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 14 | 13 | 60 | 14 | 0 | 14 |
N.S. |
1 | 0.00 | 1.00 | 0.74 | 0.68 | 3.16 | 0.74 | 0.00 | 0.74 |
time (sec) |
N/A | 0.000 | 0.143 | 0.331 | 0.306 | 0.252 | 0.188 | 0.000 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 11 | 11 | 12 | 11 | 11 | 10 | 11 | 7 |
N.S. |
1 | 0.69 | 0.69 | 0.75 | 0.69 | 0.69 | 0.62 | 0.69 | 0.44 |
time (sec) |
N/A | 0.002 | 0.001 | 0.023 | 0.194 | 0.240 | 0.039 | 0.281 | 12.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 12 | 12 | 13 | 19 | 16 | 14 | 19 | 12 |
N.S. |
1 | 0.92 | 0.92 | 1.00 | 1.46 | 1.23 | 1.08 | 1.46 | 0.92 |
time (sec) |
N/A | 0.005 | 0.002 | 0.161 | 0.212 | 0.243 | 0.039 | 0.276 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 98 | 37 | 93 | 99 | 130 | 102 | 132 | 86 |
N.S. |
1 | 3.63 | 1.37 | 3.44 | 3.67 | 4.81 | 3.78 | 4.89 | 3.19 |
time (sec) |
N/A | 1.553 | 0.337 | 4.199 | 0.328 | 0.274 | 0.225 | 0.343 | 13.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 20 | 397 | 37 | 30 | 29 | 54 | 27 |
N.S. |
1 | 0.00 | 0.95 | 18.90 | 1.76 | 1.43 | 1.38 | 2.57 | 1.29 |
time (sec) |
N/A | 0.000 | 0.571 | 1.225 | 0.350 | 0.247 | 1.016 | 1.375 | 15.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 26 | 45 | 25 | 24 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.88 | 1.04 | 1.00 | 1.04 | 1.04 |
time (sec) |
N/A | 0.014 | 0.014 | 0.125 | 0.190 | 0.252 | 0.074 | 0.261 | 12.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 20 | 29 | 54 | 28 | 27 | 28 | 30 |
N.S. |
1 | 0.83 | 0.83 | 1.21 | 2.25 | 1.17 | 1.12 | 1.17 | 1.25 |
time (sec) |
N/A | 0.065 | 0.039 | 0.900 | 0.335 | 0.255 | 0.087 | 0.316 | 13.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 34 | 52 | 118 | 43 | 41 | 151 | 64 |
N.S. |
1 | 0.00 | 1.06 | 1.62 | 3.69 | 1.34 | 1.28 | 4.72 | 2.00 |
time (sec) |
N/A | 0.000 | 0.200 | 31.997 | 89.969 | 0.254 | 0.806 | 0.575 | 13.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 28 | 23 | 27 | 28 | 24 | 27 | 22 |
N.S. |
1 | 0.91 | 1.22 | 1.00 | 1.17 | 1.22 | 1.04 | 1.17 | 0.96 |
time (sec) |
N/A | 0.018 | 0.018 | 0.766 | 0.200 | 0.231 | 0.090 | 0.266 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 37 | 222 | 37 | 39 | 31 | 78 | 37 |
N.S. |
1 | 0.00 | 1.12 | 6.73 | 1.12 | 1.18 | 0.94 | 2.36 | 1.12 |
time (sec) |
N/A | 0.000 | 0.317 | 0.071 | 0.274 | 0.294 | 12.496 | 1.039 | 13.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 22 | 25 | 20 | 78 | 24 | 0 | 21 |
N.S. |
1 | 0.00 | 1.22 | 1.39 | 1.11 | 4.33 | 1.33 | 0.00 | 1.17 |
time (sec) |
N/A | 0.000 | 5.079 | 1.605 | 0.315 | 0.293 | 0.721 | 0.000 | 13.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 24 | 23 | 41 | 20 | 63 | 34 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.96 | 1.71 | 0.83 | 2.62 | 1.42 |
time (sec) |
N/A | 0.000 | 1.149 | 0.270 | 0.251 | 0.261 | 0.101 | 0.286 | 13.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 21 | 22 | 21 | 21 | 22 | 0 | 25 |
N.S. |
1 | 1.08 | 0.81 | 0.85 | 0.81 | 0.81 | 0.85 | 0.00 | 0.96 |
time (sec) |
N/A | 0.174 | 1.178 | 0.199 | 0.317 | 0.245 | 0.179 | 0.000 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 63 | 20 | 22 | 21 | 20 | 15 | 20 | 20 |
N.S. |
1 | 2.86 | 0.91 | 1.00 | 0.95 | 0.91 | 0.68 | 0.91 | 0.91 |
time (sec) |
N/A | 0.029 | 0.360 | 0.082 | 0.261 | 0.247 | 0.093 | 0.271 | 12.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 52 | 45 | 37 | 37 | 41 | 44 | 44 |
N.S. |
1 | 0.00 | 2.00 | 1.73 | 1.42 | 1.42 | 1.58 | 1.69 | 1.69 |
time (sec) |
N/A | 0.000 | 0.242 | 1.062 | 0.237 | 0.247 | 0.179 | 0.283 | 12.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 52 | 52 | 83 | 83 | 65 | 51 | 0 |
N.S. |
1 | 0.00 | 2.36 | 2.36 | 3.77 | 3.77 | 2.95 | 2.32 | 0.00 |
time (sec) |
N/A | 0.000 | 1.000 | 2.703 | 0.312 | 0.256 | 0.491 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 21 | 15 | 13 | 13 | 13 | 8 | 14 | 13 |
N.S. |
1 | 0.81 | 0.58 | 0.50 | 0.50 | 0.50 | 0.31 | 0.54 | 0.50 |
time (sec) |
N/A | 0.004 | 0.004 | 0.116 | 0.190 | 0.233 | 0.036 | 0.279 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 22 | 55 | 21 | 19 | 21 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 2.50 | 0.95 | 0.86 | 0.95 | 1.00 |
time (sec) |
N/A | 0.349 | 0.182 | 0.400 | 0.274 | 0.247 | 0.157 | 0.280 | 12.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 46 | 34 | 34 | 33 | 33 | 29 | 33 | 30 |
N.S. |
1 | 1.53 | 1.13 | 1.13 | 1.10 | 1.10 | 0.97 | 1.10 | 1.00 |
time (sec) |
N/A | 0.012 | 0.044 | 0.179 | 0.193 | 0.243 | 0.046 | 0.280 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 12 | 12 | 12 | 14 | 15 | 12 | 14 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 1.00 | 1.07 | 0.86 | 1.00 | 0.79 |
time (sec) |
N/A | 0.004 | 0.002 | 0.081 | 0.188 | 0.239 | 0.035 | 0.276 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 37 | 36 | 48 | 134 | 107 | 49 | 51 | 95 |
N.S. |
1 | 1.42 | 1.38 | 1.85 | 5.15 | 4.12 | 1.88 | 1.96 | 3.65 |
time (sec) |
N/A | 0.498 | 0.370 | 1.249 | 0.311 | 0.256 | 0.132 | 0.307 | 12.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | C | B | A | A | F | B |
verified |
N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 82 | 39 | 15 | 20 | 0 | 20 |
N.S. |
1 | 0.00 | 0.00 | 3.42 | 1.62 | 0.62 | 0.83 | 0.00 | 0.83 |
time (sec) |
N/A | 0.000 | 0.000 | 2.015 | 0.322 | 0.251 | 0.220 | 0.000 | 12.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 13 | 8 | 8 | 12 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.53 | 0.53 | 0.80 | 0.53 | 0.53 |
time (sec) |
N/A | 0.005 | 0.014 | 0.135 | 0.276 | 0.256 | 0.046 | 0.263 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 112 | 112 | 113 | 147 | 91 | 87 | 112 | 112 |
N.S. |
1 | 5.33 | 5.33 | 5.38 | 7.00 | 4.33 | 4.14 | 5.33 | 5.33 |
time (sec) |
N/A | 0.118 | 0.039 | 0.067 | 0.191 | 0.255 | 0.092 | 0.283 | 12.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 90 | 23 | 32 | 76 | 30 | 65 | 37 | 32 |
N.S. |
1 | 4.50 | 1.15 | 1.60 | 3.80 | 1.50 | 3.25 | 1.85 | 1.60 |
time (sec) |
N/A | 0.494 | 0.250 | 1.110 | 0.243 | 0.246 | 0.854 | 0.274 | 12.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 18 | 25 | 18 | 66 | 27 | 14 | 27 | 22 |
N.S. |
1 | 0.78 | 1.09 | 0.78 | 2.87 | 1.17 | 0.61 | 1.17 | 0.96 |
time (sec) |
N/A | 0.236 | 0.176 | 0.435 | 0.287 | 0.249 | 0.087 | 0.292 | 12.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 20 | 13 | 12 | 18 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.54 | 1.00 | 0.92 | 1.38 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.169 | 0.072 | 0.544 | 0.227 | 0.232 | 0.040 | 0.284 | 12.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 20 | 19 | 21 | 15 | 43 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.86 | 0.95 | 0.68 | 1.95 | 0.86 |
time (sec) |
N/A | 0.015 | 0.032 | 0.263 | 0.196 | 0.259 | 0.049 | 0.279 | 11.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 14 | 15 | 14 | 14 | 12 | 14 | 82 |
N.S. |
1 | 0.00 | 0.88 | 0.94 | 0.88 | 0.88 | 0.75 | 0.88 | 5.12 |
time (sec) |
N/A | 0.000 | 0.251 | 0.809 | 0.239 | 0.254 | 0.086 | 0.293 | 12.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 28 | 19 | 16 | 21 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.33 | 0.90 | 0.76 | 1.00 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.017 | 0.014 | 0.233 | 0.203 | 0.247 | 0.071 | 0.272 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 26 | 26 | 16 | 18 | 18 | 20 | 22 | 15 |
N.S. |
1 | 1.53 | 1.53 | 0.94 | 1.06 | 1.06 | 1.18 | 1.29 | 0.88 |
time (sec) |
N/A | 0.029 | 0.013 | 0.184 | 0.191 | 0.251 | 0.052 | 0.269 | 12.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 20 | 24 | 19 | 20 | 68 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 1.04 | 0.83 | 0.87 | 2.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.821 | 1.306 | 0.348 | 0.241 | 0.229 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 16 | 14 | 11 | 11 | 15 | 13 | 8 |
N.S. |
1 | 0.90 | 0.76 | 0.67 | 0.52 | 0.52 | 0.71 | 0.62 | 0.38 |
time (sec) |
N/A | 0.003 | 0.001 | 1.044 | 0.193 | 0.248 | 0.032 | 0.280 | 12.693 |
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 | 27 | 29 | 29 | 49 | 25 | 43 | 49 | 46 | 47 |
N.S. |
1 | 1.07 | 1.07 | 1.81 | 0.93 | 1.59 | 1.81 | 1.70 | 1.74 |
time (sec) |
N/A | 1.183 | 0.111 | 0.485 | 0.225 | 0.256 | 0.386 | 0.456 | 12.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 16 | 16 | 12 | 16 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.23 | 1.23 | 0.92 | 1.23 | 1.08 |
time (sec) |
N/A | 0.003 | 0.002 | 0.094 | 0.196 | 0.237 | 0.019 | 0.277 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | B | F(-1) | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 25 | 26 | 48 | 0 | 0 | 26 |
N.S. |
1 | 0.00 | 0.00 | 0.83 | 0.87 | 1.60 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.000 | 0.000 | 0.846 | 0.451 | 0.259 | 0.000 | 0.000 | 13.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 41 | 41 | 57 | 36 | 37 | 63 | 57 |
N.S. |
1 | 0.00 | 1.32 | 1.32 | 1.84 | 1.16 | 1.19 | 2.03 | 1.84 |
time (sec) |
N/A | 0.000 | 0.146 | 1.261 | 0.404 | 0.243 | 0.167 | 0.487 | 13.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 160 | 76 | 87 | 128 | 72 | 100 | 97 | 94 |
N.S. |
1 | 6.96 | 3.30 | 3.78 | 5.57 | 3.13 | 4.35 | 4.22 | 4.09 |
time (sec) |
N/A | 0.146 | 0.135 | 0.404 | 0.201 | 0.265 | 0.141 | 0.288 | 13.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 1192 | 1517 | 1403 | 2015 | 1856 | 0 | 1904 | 13908 |
N.S. |
1 | 42.57 | 54.18 | 50.11 | 71.96 | 66.29 | 0.00 | 68.00 | 496.71 |
time (sec) |
N/A | 16.660 | 2.759 | 3.091 | 0.290 | 0.294 | 0.000 | 0.345 | 45.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 36 | 47 | 45 | 45 | 41 | 49 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.42 | 1.36 | 1.36 | 1.24 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 4.136 | 0.174 | 0.279 | 0.253 | 0.225 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 22245 | 42 | 35 | 0 | 2231 | 0 |
N.S. |
1 | 1.00 | 1.00 | 767.07 | 1.45 | 1.21 | 0.00 | 76.93 | 0.00 |
time (sec) |
N/A | 70.709 | 0.485 | 2.785 | 0.417 | 0.264 | 0.000 | 7.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 13 | 13 | 13 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 0.87 | 0.87 | 0.87 | 0.80 | 0.80 | 0.53 | 0.80 | 0.80 |
time (sec) |
N/A | 0.014 | 0.009 | 0.920 | 0.200 | 0.256 | 0.065 | 0.279 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 21 | 20 | 20 | 0 | 20 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.091 | 19.219 | 0.229 | 0.249 | 0.000 | 0.386 | 11.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 23 | 7 | 22 | 24 | 27 | 28 | 23 |
N.S. |
1 | 0.96 | 0.92 | 0.28 | 0.88 | 0.96 | 1.08 | 1.12 | 0.92 |
time (sec) |
N/A | 0.254 | 0.037 | 0.154 | 0.231 | 0.244 | 0.108 | 0.281 | 11.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 28 | 34 | 36 | 34 | 38 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.17 | 1.42 | 1.50 | 1.42 | 1.58 | 0.00 |
time (sec) |
N/A | 0.000 | 5.057 | 2.374 | 0.323 | 0.252 | 0.162 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 80 | 27 | 36 | 156 | 35 | 36 | 40 | 23 |
N.S. |
1 | 2.58 | 0.87 | 1.16 | 5.03 | 1.13 | 1.16 | 1.29 | 0.74 |
time (sec) |
N/A | 0.171 | 0.450 | 0.151 | 0.207 | 0.256 | 0.069 | 0.283 | 10.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 18 | 15 | 14 | 14 | 10 | 0 | 13 |
N.S. |
1 | 0.82 | 0.82 | 0.68 | 0.64 | 0.64 | 0.45 | 0.00 | 0.59 |
time (sec) |
N/A | 0.041 | 0.024 | 0.129 | 0.252 | 0.237 | 0.075 | 0.000 | 11.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 41 | 45 | 51 | 25 | 37 | 41 | 38 |
N.S. |
1 | 0.00 | 1.86 | 2.05 | 2.32 | 1.14 | 1.68 | 1.86 | 1.73 |
time (sec) |
N/A | 0.000 | 0.504 | 0.572 | 0.328 | 0.281 | 0.179 | 0.313 | 11.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 16 | 16 | 16 | 27 | 15 | 15 | 15 | 15 |
N.S. |
1 | 0.76 | 0.76 | 0.76 | 1.29 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.034 | 0.037 | 0.093 | 0.190 | 0.244 | 0.052 | 0.272 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 26 | 29 | 29 | 24 | 47 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 1.21 | 1.21 | 1.00 | 1.96 | 1.21 |
time (sec) |
N/A | 0.000 | 0.711 | 0.856 | 0.251 | 0.251 | 0.224 | 0.370 | 11.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 22 | 21 | 21 | 19 | 21 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.76 | 0.84 | 0.84 |
time (sec) |
N/A | 0.000 | 4.579 | 43.098 | 0.255 | 0.257 | 0.682 | 0.350 | 11.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 24 | 26 | 24 | 24 | 23 | 20 | 23 | 28 |
N.S. |
1 | 0.75 | 0.81 | 0.75 | 0.75 | 0.72 | 0.62 | 0.72 | 0.88 |
time (sec) |
N/A | 0.595 | 0.285 | 0.327 | 0.328 | 0.268 | 0.122 | 0.298 | 0.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 43 | 41 | 67 | 43 | 29 | 51 | 40 |
N.S. |
1 | 0.00 | 1.48 | 1.41 | 2.31 | 1.48 | 1.00 | 1.76 | 1.38 |
time (sec) |
N/A | 0.000 | 1.476 | 2.004 | 0.351 | 0.251 | 0.131 | 0.343 | 11.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 31 | 26 | 30 | 27 | 30 | 22 |
N.S. |
1 | 0.00 | 0.93 | 1.15 | 0.96 | 1.11 | 1.00 | 1.11 | 0.81 |
time (sec) |
N/A | 0.000 | 0.126 | 0.285 | 0.239 | 0.262 | 0.196 | 0.307 | 11.995 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 25 | 21 | 28 | 33 | 26 | 92 | 21 |
N.S. |
1 | 1.19 | 1.19 | 1.00 | 1.33 | 1.57 | 1.24 | 4.38 | 1.00 |
time (sec) |
N/A | 0.234 | 0.131 | 0.829 | 0.231 | 0.244 | 0.103 | 0.273 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 30 | 20 | 24 | 21 | 27 | 24 | 19 |
N.S. |
1 | 0.00 | 1.67 | 1.11 | 1.33 | 1.17 | 1.50 | 1.33 | 1.06 |
time (sec) |
N/A | 0.000 | 0.191 | 0.282 | 0.234 | 0.250 | 0.175 | 0.298 | 0.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 35 | 33 | 43 | 36 | 39 | 0 | 38 |
N.S. |
1 | 0.00 | 1.25 | 1.18 | 1.54 | 1.29 | 1.39 | 0.00 | 1.36 |
time (sec) |
N/A | 0.000 | 0.217 | 31.355 | 0.321 | 0.246 | 10.405 | 0.000 | 11.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 406 | 113 | 120 | 193 | 106 | 141 | 139 | 96 |
N.S. |
1 | 11.94 | 3.32 | 3.53 | 5.68 | 3.12 | 4.15 | 4.09 | 2.82 |
time (sec) |
N/A | 0.578 | 6.850 | 0.232 | 0.270 | 0.257 | 1.447 | 0.277 | 11.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 21 | 21 | 17 | 21 | 24 | 22 | 23 | 19 |
N.S. |
1 | 0.75 | 0.75 | 0.61 | 0.75 | 0.86 | 0.79 | 0.82 | 0.68 |
time (sec) |
N/A | 0.031 | 0.005 | 0.629 | 0.187 | 0.234 | 0.047 | 0.280 | 11.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 28 | 30 | 34 | 42 | 29 | 21 | 32 |
N.S. |
1 | 1.00 | 1.27 | 1.36 | 1.55 | 1.91 | 1.32 | 0.95 | 1.45 |
time (sec) |
N/A | 0.051 | 0.026 | 0.181 | 0.197 | 0.255 | 0.298 | 0.275 | 0.138 |
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 | 24 | 33 | 25 | 24 | 36 | 36 | 34 | 36 | 23 |
N.S. |
1 | 1.38 | 1.04 | 1.00 | 1.50 | 1.50 | 1.42 | 1.50 | 0.96 |
time (sec) |
N/A | 0.500 | 0.612 | 0.079 | 0.226 | 0.268 | 0.070 | 0.312 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 46 | 72 | 87 | 72 | 88 | 85 | 66 |
N.S. |
1 | 0.00 | 2.42 | 3.79 | 4.58 | 3.79 | 4.63 | 4.47 | 3.47 |
time (sec) |
N/A | 0.000 | 0.091 | 0.426 | 0.188 | 0.260 | 4.332 | 0.293 | 12.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 24 | 34 | 32 | 26 | 25 | 26 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 1.42 | 1.33 | 1.08 | 1.04 | 1.08 |
time (sec) |
N/A | 0.000 | 1.720 | 4.119 | 0.321 | 0.251 | 0.201 | 0.304 | 12.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 38 | 24 | 64 | 23 | 22 | 44 | 44 |
N.S. |
1 | 0.00 | 1.73 | 1.09 | 2.91 | 1.05 | 1.00 | 2.00 | 2.00 |
time (sec) |
N/A | 0.000 | 5.122 | 1.352 | 0.405 | 0.261 | 0.330 | 0.314 | 12.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 22 | 22 | 21 | 21 | 22 | 21 | 0 |
N.S. |
1 | 0.00 | 0.81 | 0.81 | 0.78 | 0.78 | 0.81 | 0.78 | 0.00 |
time (sec) |
N/A | 0.000 | 0.691 | 2.144 | 0.256 | 0.248 | 0.113 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 33 | 32 | 27 | 25 | 25 | 24 | 25 | 31 |
N.S. |
1 | 1.94 | 1.88 | 1.59 | 1.47 | 1.47 | 1.41 | 1.47 | 1.82 |
time (sec) |
N/A | 0.040 | 0.084 | 0.109 | 0.189 | 0.266 | 0.046 | 0.286 | 12.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 41 | 22 | 20 | 39 | 23 | 15 | 24 | 18 |
N.S. |
1 | 1.37 | 0.73 | 0.67 | 1.30 | 0.77 | 0.50 | 0.80 | 0.60 |
time (sec) |
N/A | 0.118 | 0.071 | 0.124 | 0.226 | 0.244 | 0.079 | 0.310 | 12.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 21 | 21 | 19 | 18 | 18 | 17 | 18 | 20 |
N.S. |
1 | 0.78 | 0.78 | 0.70 | 0.67 | 0.67 | 0.63 | 0.67 | 0.74 |
time (sec) |
N/A | 0.077 | 0.464 | 0.343 | 0.314 | 0.250 | 0.090 | 0.300 | 12.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 49 | 30 | 43 | 54 | 26 | 198 | 45 |
N.S. |
1 | 0.00 | 1.53 | 0.94 | 1.34 | 1.69 | 0.81 | 6.19 | 1.41 |
time (sec) |
N/A | 0.000 | 10.122 | 0.559 | 0.239 | 0.281 | 0.090 | 2.332 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 70 | 18 | 24 | 23 | 23 | 22 | 0 | 16 |
N.S. |
1 | 3.89 | 1.00 | 1.33 | 1.28 | 1.28 | 1.22 | 0.00 | 0.89 |
time (sec) |
N/A | 0.168 | 0.143 | 1.612 | 0.256 | 0.269 | 0.136 | 0.000 | 12.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 79 | 39 | 58 | 60 | 66 | 63 | 67 | 49 |
N.S. |
1 | 3.04 | 1.50 | 2.23 | 2.31 | 2.54 | 2.42 | 2.58 | 1.88 |
time (sec) |
N/A | 0.081 | 0.037 | 0.181 | 0.191 | 0.234 | 0.992 | 0.277 | 12.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 51 | 59 | 44 | 39 | 39 | 58 | 45 | 0 |
N.S. |
1 | 2.32 | 2.68 | 2.00 | 1.77 | 1.77 | 2.64 | 2.05 | 0.00 |
time (sec) |
N/A | 0.029 | 0.065 | 3.288 | 0.272 | 0.491 | 0.239 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 27 | 42 | 19 | 44 | 18 | 17 | 32 | 33 |
N.S. |
1 | 1.50 | 2.33 | 1.06 | 2.44 | 1.00 | 0.94 | 1.78 | 1.83 |
time (sec) |
N/A | 0.073 | 0.153 | 0.863 | 0.300 | 0.252 | 0.111 | 0.291 | 0.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 35 | 37 | 36 | 32 | 36 | 36 |
N.S. |
1 | 0.00 | 0.88 | 1.46 | 1.54 | 1.50 | 1.33 | 1.50 | 1.50 |
time (sec) |
N/A | 0.000 | 0.904 | 0.111 | 0.237 | 0.258 | 0.204 | 0.316 | 0.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 34 | 40 | 24 | 27 | 36 | 26 | 27 | 26 |
N.S. |
1 | 1.42 | 1.67 | 1.00 | 1.12 | 1.50 | 1.08 | 1.12 | 1.08 |
time (sec) |
N/A | 0.035 | 0.020 | 0.985 | 0.188 | 0.241 | 0.182 | 0.268 | 12.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 19 | 16 | 18 | 17 | 22 | 26 | 24 | 1027 |
N.S. |
1 | 0.86 | 0.73 | 0.82 | 0.77 | 1.00 | 1.18 | 1.09 | 46.68 |
time (sec) |
N/A | 0.007 | 0.020 | 1.232 | 0.191 | 0.251 | 0.174 | 0.268 | 14.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 22 | 23 | 20 | 24 | 17 | 15 | 19 | 19 |
N.S. |
1 | 0.79 | 0.82 | 0.71 | 0.86 | 0.61 | 0.54 | 0.68 | 0.68 |
time (sec) |
N/A | 0.163 | 0.192 | 1.307 | 0.222 | 0.248 | 0.128 | 0.276 | 13.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 138 | 138 | 99 | 111 | 111 | 112 | 135 | 0 |
N.S. |
1 | 8.62 | 8.62 | 6.19 | 6.94 | 6.94 | 7.00 | 8.44 | 0.00 |
time (sec) |
N/A | 1.501 | 0.243 | 1.159 | 0.251 | 0.258 | 0.767 | 0.992 | 0.000 |