Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 213 | 37 | 40 | 480 | 73 | 42 | 83 | 44 |
N.S. | 1 | 8.52 | 1.48 | 1.60 | 19.20 | 2.92 | 1.68 | 3.32 | 1.76 |
time (sec) |
N/A | 1.143 | 2.175 | 3.727 | 0.319 | 0.456 | 0.627 | 0.430 | 2.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 366 | 26 | 26 | 27 | 26 | -1 |
N.S. | 1 | 0.00 | 1.00 | 14.08 | 1.00 | 1.00 | 1.04 | 1.00 | -0.04 |
time (sec) |
N/A | 6.454 | 0.133 | 0.905 | 0.506 | 0.355 | 0.107 | 0.539 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 17 | 20 | 16 | 13 | 13 | 14 | 13 | 13 |
N.S. | 1 | 0.77 | 0.91 | 0.73 | 0.59 | 0.59 | 0.64 | 0.59 | 0.59 |
time (sec) |
N/A | 0.008 | 0.000 | 0.172 | 0.255 | 0.392 | 0.004 | 0.406 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 64 | 34 | 29 | 29 | 29 | 24 | 29 | -1 |
N.S. | 1 | 2.00 | 1.06 | 0.91 | 0.91 | 0.91 | 0.75 | 0.91 | -0.03 |
time (sec) |
N/A | 1.179 | 0.296 | 0.134 | 0.313 | 0.427 | 0.495 | 0.414 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | C | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 158 | 20 | 19 | 0 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 7.52 | 0.95 | 0.90 | 0.00 | 0.90 | 0.90 |
time (sec) |
N/A | 0.247 | 0.045 | 0.449 | 0.316 | 0.400 | 0.000 | 0.435 | 2.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 7 |
N.S. | 1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.78 |
time (sec) |
N/A | 0.004 | 0.012 | 0.106 | 0.263 | 0.370 | 0.019 | 0.412 | 1.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 47 | 32 | 22 | 19 | 29 | 20 |
N.S. | 1 | 1.00 | 1.00 | 2.14 | 1.45 | 1.00 | 0.86 | 1.32 | 0.91 |
time (sec) |
N/A | 0.173 | 0.013 | 2.584 | 0.506 | 0.404 | 0.061 | 0.401 | 2.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 26 | 19 | 25 | 19 | 30 | 19 |
N.S. | 1 | 1.00 | 1.00 | 1.04 | 0.76 | 1.00 | 0.76 | 1.20 | 0.76 |
time (sec) |
N/A | 0.217 | 0.126 | 0.627 | 0.337 | 0.578 | 0.072 | 0.405 | 1.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 29 | 17 | 25 | 54 | 19 | 22 | 19 | 16 |
N.S. | 1 | 1.45 | 0.85 | 1.25 | 2.70 | 0.95 | 1.10 | 0.95 | 0.80 |
time (sec) |
N/A | 0.118 | 0.025 | 0.177 | 0.258 | 0.630 | 0.039 | 0.416 | 1.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 29 | 23 | 18 | 17 | 17 | 19 | 17 | 31 |
N.S. | 1 | 1.53 | 1.21 | 0.95 | 0.89 | 0.89 | 1.00 | 0.89 | 1.63 |
time (sec) |
N/A | 0.043 | 0.051 | 0.235 | 0.260 | 0.419 | 0.045 | 0.411 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 55 | 23 | 28 | 25 | 27 | 17 | 0 | 19 |
N.S. | 1 | 2.12 | 0.88 | 1.08 | 0.96 | 1.04 | 0.65 | 0.00 | 0.73 |
time (sec) |
N/A | 0.132 | 0.030 | 0.987 | 0.298 | 0.639 | 0.071 | 0.000 | 1.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 16 | 16 | 14 | 13 | 13 | 12 | 17 | 13 |
N.S. | 1 | 0.64 | 0.64 | 0.56 | 0.52 | 0.52 | 0.48 | 0.68 | 0.52 |
time (sec) |
N/A | 0.026 | 0.012 | 0.028 | 0.253 | 0.422 | 0.030 | 0.406 | 1.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 14 | 14 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. | 1 | 0.61 | 0.61 | 0.61 | 0.57 | 0.57 | 0.52 | 0.57 | 0.57 |
time (sec) |
N/A | 0.004 | 0.003 | 0.180 | 0.264 | 0.425 | 0.024 | 0.409 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | F | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 34 | 28 | 53 | 30 | 36 | 0 | -1 |
N.S. | 1 | 0.00 | 1.17 | 0.97 | 1.83 | 1.03 | 1.24 | 0.00 | -0.03 |
time (sec) |
N/A | 11.337 | 0.238 | 0.298 | 0.312 | 0.422 | 0.187 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 18 | 18 | 21 | 21 | 19 | 23 | 16 |
N.S. | 1 | 0.00 | 1.06 | 1.06 | 1.24 | 1.24 | 1.12 | 1.35 | 0.94 |
time (sec) |
N/A | 0.751 | 0.035 | 11.380 | 0.286 | 0.418 | 0.053 | 0.403 | 1.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 22 | 22 | 17 | 17 | 17 | 17 | 22 |
N.S. | 1 | 0.96 | 0.85 | 0.85 | 0.65 | 0.65 | 0.65 | 0.65 | 0.85 |
time (sec) |
N/A | 0.096 | 0.006 | 0.191 | 0.261 | 0.452 | 0.079 | 0.410 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 34 | 49 | 31 | 35 | 31 | 22 | 0 | 164 |
N.S. | 1 | 1.03 | 1.48 | 0.94 | 1.06 | 0.94 | 0.67 | 0.00 | 4.97 |
time (sec) |
N/A | 3.828 | 0.074 | 6.819 | 0.568 | 0.479 | 0.092 | 0.000 | 2.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | F | F | A | A | C | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 0 | 0 | 29 | 26 | 1581 | -1 |
N.S. | 1 | 0.00 | 0.88 | 0.00 | 0.00 | 1.21 | 1.08 | 65.88 | -0.04 |
time (sec) |
N/A | 3.567 | 0.079 | 15.079 | 0.000 | 0.424 | 0.207 | 0.737 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 27 | 28 | 33 | 33 | 32 | 47 | 27 |
N.S. | 1 | 1.17 | 1.17 | 1.22 | 1.43 | 1.43 | 1.39 | 2.04 | 1.17 |
time (sec) |
N/A | 0.085 | 0.062 | 0.681 | 0.289 | 0.389 | 0.129 | 0.437 | 2.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 51 | 38 | 45 | 34 | 42 | 37 | -1 |
N.S. | 1 | 0.00 | 1.42 | 1.06 | 1.25 | 0.94 | 1.17 | 1.03 | -0.03 |
time (sec) |
N/A | 2.989 | 0.151 | 0.360 | 0.497 | 0.373 | 0.157 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | B | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 160 | 163 | 63 | 27 | 64 | 483 |
N.S. | 1 | 0.00 | 0.97 | 5.52 | 5.62 | 2.17 | 0.93 | 2.21 | 16.66 |
time (sec) |
N/A | 3.146 | 0.082 | 0.864 | 0.557 | 0.451 | 0.139 | 1.047 | 2.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 22 | 57 | 38 | 17 | 38 | 21 |
N.S. | 1 | 0.00 | 0.79 | 0.79 | 2.04 | 1.36 | 0.61 | 1.36 | 0.75 |
time (sec) |
N/A | 34.764 | 0.050 | 2.739 | 0.512 | 0.468 | 0.063 | 0.467 | 2.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 11 | 11 | 13 | 14 | 14 | 14 | 14 | 10 |
N.S. | 1 | 0.69 | 0.69 | 0.81 | 0.88 | 0.88 | 0.88 | 0.88 | 0.62 |
time (sec) |
N/A | 0.116 | 0.010 | 1.267 | 0.292 | 0.492 | 0.037 | 0.407 | 2.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 41 | 39 | 68 | 711 | 116 | 148 | 167 | 724 |
N.S. | 1 | 1.41 | 1.34 | 2.34 | 24.52 | 4.00 | 5.10 | 5.76 | 24.97 |
time (sec) |
N/A | 4.391 | 0.097 | 60.227 | 3.894 | 0.385 | 1.841 | 3.701 | 3.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 34 | 0 | 32 | 51 | 61 | 32 |
N.S. | 1 | 0.00 | 0.90 | 1.13 | 0.00 | 1.07 | 1.70 | 2.03 | 1.07 |
time (sec) |
N/A | 1.359 | 0.788 | 0.716 | 0.000 | 0.427 | 0.081 | 0.399 | 2.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 50 | 35 | 36 | 41 | 32 | 36 | 35 |
N.S. | 1 | 1.20 | 1.67 | 1.17 | 1.20 | 1.37 | 1.07 | 1.20 | 1.17 |
time (sec) |
N/A | 0.020 | 0.000 | 0.189 | 0.263 | 0.386 | 0.005 | 0.400 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 194 | 38 | 49 | 67 | 61 | 73 | 435 | 69 |
N.S. | 1 | 5.11 | 1.00 | 1.29 | 1.76 | 1.61 | 1.92 | 11.45 | 1.82 |
time (sec) |
N/A | 0.881 | 0.210 | 2.672 | 1.424 | 0.403 | 6.489 | 0.435 | 2.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 25 | 23 | 80 | 80 | 34 | 301 | 181 |
N.S. | 1 | 0.00 | 1.14 | 1.05 | 3.64 | 3.64 | 1.55 | 13.68 | 8.23 |
time (sec) |
N/A | 2.148 | 0.086 | 11.826 | 0.311 | 0.449 | 0.191 | 0.484 | 2.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 27 | 25 | 41 | 47 | 20 | 37 | 25 |
N.S. | 1 | 0.00 | 1.08 | 1.00 | 1.64 | 1.88 | 0.80 | 1.48 | 1.00 |
time (sec) |
N/A | 4.608 | 0.406 | 0.063 | 0.321 | 0.377 | 0.086 | 0.435 | 2.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 36 | 36 | 37 | 36 | 31 | 29 | 33 | 34 |
N.S. | 1 | 1.44 | 1.44 | 1.48 | 1.44 | 1.24 | 1.16 | 1.32 | 1.36 |
time (sec) |
N/A | 0.116 | 0.015 | 0.190 | 0.266 | 0.440 | 0.072 | 0.404 | 1.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 6 | 6 | 7 | 6 | 6 | 3 | 6 | 6 |
N.S. | 1 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 | 0.23 | 0.46 | 0.46 |
time (sec) |
N/A | 0.001 | 0.000 | 0.101 | 0.263 | 0.389 | 0.004 | 0.390 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 44 | 173 | 149 | 48 | 48 | 46 | 25 | 2500 |
N.S. | 1 | 1.63 | 6.41 | 5.52 | 1.78 | 1.78 | 1.70 | 0.93 | 92.59 |
time (sec) |
N/A | 0.415 | 0.092 | 0.937 | 0.255 | 0.387 | 0.919 | 0.411 | 7.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | A | A | A | A | A | F |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 27 | 27 | 27 | 26 | 27 | -1 |
N.S. | 1 | 0.00 | 0.00 | 1.35 | 1.35 | 1.35 | 1.30 | 1.35 | -0.05 |
time (sec) |
N/A | 3.041 | 0.473 | 0.708 | 0.503 | 0.399 | 0.117 | 0.421 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 37 | 41 | 18 | 14 | 18 | 17 |
N.S. | 1 | 0.00 | 1.00 | 1.68 | 1.86 | 0.82 | 0.64 | 0.82 | 0.77 |
time (sec) |
N/A | 1.007 | 0.078 | 1.602 | 0.516 | 0.351 | 0.044 | 0.409 | 2.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 227 | 47 | 173 | 85 | 90 | 82 | 92 | 47 |
N.S. | 1 | 7.83 | 1.62 | 5.97 | 2.93 | 3.10 | 2.83 | 3.17 | 1.62 |
time (sec) |
N/A | 0.427 | 0.182 | 0.331 | 0.266 | 0.384 | 0.098 | 0.401 | 2.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 29 | 29 | 40 | 48 | 48 | 46 | 43 | 58 |
N.S. | 1 | 1.61 | 1.61 | 2.22 | 2.67 | 2.67 | 2.56 | 2.39 | 3.22 |
time (sec) |
N/A | 0.057 | 0.027 | 0.412 | 0.264 | 0.388 | 0.154 | 0.404 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 84 | 27 | 58 | 79 | 23 | 24 | 29 | 22 |
N.S. | 1 | 4.20 | 1.35 | 2.90 | 3.95 | 1.15 | 1.20 | 1.45 | 1.10 |
time (sec) |
N/A | 0.377 | 0.070 | 1.488 | 0.504 | 0.405 | 0.158 | 0.429 | 1.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 24 | 24 | 23 | 23 | 20 | 23 | 23 |
N.S. | 1 | 0.96 | 0.96 | 0.96 | 0.92 | 0.92 | 0.80 | 0.92 | 0.92 |
time (sec) |
N/A | 0.042 | 0.025 | 0.128 | 0.257 | 0.405 | 0.075 | 0.427 | 1.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 62 | 47 | 51 | 63 | 44 | 51 | 44 | 27 |
N.S. | 1 | 2.00 | 1.52 | 1.65 | 2.03 | 1.42 | 1.65 | 1.42 | 0.87 |
time (sec) |
N/A | 0.489 | 0.048 | 0.774 | 0.302 | 0.431 | 0.102 | 0.412 | 2.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 29 | 21 | 23 | 22 | 16 | 20 | 16 | 15 |
N.S. | 1 | 1.53 | 1.11 | 1.21 | 1.16 | 0.84 | 1.05 | 0.84 | 0.79 |
time (sec) |
N/A | 0.018 | 0.029 | 0.138 | 0.261 | 0.407 | 0.046 | 0.406 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 31 | 30 | 29 | 29 | 32 | 29 | 30 |
N.S. | 1 | 1.19 | 1.19 | 1.15 | 1.12 | 1.12 | 1.23 | 1.12 | 1.15 |
time (sec) |
N/A | 0.008 | 0.000 | 0.217 | 0.258 | 0.365 | 0.014 | 0.417 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 20 | 21 | 17 | 16 | 22 | 12 | 16 | 16 |
N.S. | 1 | 0.80 | 0.84 | 0.68 | 0.64 | 0.88 | 0.48 | 0.64 | 0.64 |
time (sec) |
N/A | 0.027 | 0.007 | 1.297 | 0.282 | 0.395 | 0.020 | 0.405 | 1.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 29 | 27 | 44 | 35 | 31 | 35 | 32 |
N.S. | 1 | 1.12 | 1.12 | 1.04 | 1.69 | 1.35 | 1.19 | 1.35 | 1.23 |
time (sec) |
N/A | 0.109 | 0.034 | 0.651 | 0.289 | 0.374 | 0.068 | 0.407 | 1.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 15 | 14 | 14 | 12 | 14 | 14 |
N.S. | 1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.75 | 0.88 | 0.88 |
time (sec) |
N/A | 0.018 | 0.003 | 0.264 | 0.258 | 0.399 | 0.026 | 0.400 | 1.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 27 | 27 | 23 | 22 | 23 | 25 |
N.S. | 1 | 0.00 | 0.95 | 1.23 | 1.23 | 1.05 | 1.00 | 1.05 | 1.14 |
time (sec) |
N/A | 1.229 | 0.066 | 0.510 | 0.326 | 0.376 | 0.066 | 0.419 | 1.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 14 | 14 | 13 | 12 | 12 | 12 | 12 | 13 |
N.S. | 1 | 0.61 | 0.61 | 0.57 | 0.52 | 0.52 | 0.52 | 0.52 | 0.57 |
time (sec) |
N/A | 0.004 | 0.001 | 0.178 | 0.269 | 0.423 | 0.010 | 0.392 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 46 | 30 | 80 | 0 | 28 | 44 | 30 | 23 |
N.S. | 1 | 1.77 | 1.15 | 3.08 | 0.00 | 1.08 | 1.69 | 1.15 | 0.88 |
time (sec) |
N/A | 0.299 | 0.111 | 1.373 | 0.000 | 0.392 | 0.139 | 0.403 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | B | C | F(-1) | A | F(-1) | B | B |
verified |
N/A | N/A | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 98 | 359 | 0 | 37 | 0 | 70 | 79 |
N.S. |
1 | 0.00 | 3.06 | 11.22 | 0.00 | 1.16 | 0.00 | 2.19 | 2.47 |
time (sec) |
N/A | 21.470 | 0.285 | 1.349 | 0.000 | 0.383 | 0.000 | 0.992 | 2.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 32 | 556 | 92 | 24 | 0 | 34 | 24 |
N.S. |
1 | 0.00 | 1.19 | 20.59 | 3.41 | 0.89 | 0.00 | 1.26 | 0.89 |
time (sec) |
N/A | 0.884 | 0.137 | 0.772 | 0.529 | 0.388 | 0.000 | 0.416 | 2.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 23 | 25 | 103 | 0 | 40 | 20 | 42 | 24 |
N.S. | 1 | 1.05 | 1.14 | 4.68 | 0.00 | 1.82 | 0.91 | 1.91 | 1.09 |
time (sec) |
N/A | 0.218 | 0.064 | 1.422 | 0.000 | 0.433 | 0.100 | 0.403 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | A | A | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 36 | 31 | 732 | 0 | 27 | 27 | 1588 | -1 |
N.S. | 1 | 1.16 | 1.00 | 23.61 | 0.00 | 0.87 | 0.87 | 51.23 | -0.03 |
time (sec) |
N/A | 1.684 | 0.115 | 35.911 | 0.000 | 0.453 | 1.053 | 150.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 55 | 36 | 39 | 31 | 41 | 36 | 41 | 18 |
N.S. | 1 | 2.04 | 1.33 | 1.44 | 1.15 | 1.52 | 1.33 | 1.52 | 0.67 |
time (sec) |
N/A | 0.447 | 0.055 | 2.728 | 0.316 | 0.402 | 0.064 | 0.409 | 2.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 12 | 13 | 12 | 12 | 17 | 67 | 12 |
N.S. | 1 | 0.00 | 0.86 | 0.93 | 0.86 | 0.86 | 1.21 | 4.79 | 0.86 |
time (sec) |
N/A | 2.311 | 0.111 | 0.162 | 0.292 | 0.402 | 0.254 | 0.948 | 2.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. | 1 | 0.17 | 0.17 | 0.25 | 0.17 | 0.17 | 0.17 | 0.25 | 0.17 |
time (sec) |
N/A | 0.000 | 0.000 | 0.004 | 0.258 | 0.393 | 0.007 | 0.405 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 104 | 32 | 127 | 54 | 51 | 66 | 59 | 205 |
N.S. | 1 | 2.97 | 0.91 | 3.63 | 1.54 | 1.46 | 1.89 | 1.69 | 5.86 |
time (sec) |
N/A | 0.383 | 0.081 | 0.581 | 0.271 | 0.411 | 34.988 | 0.415 | 6.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 26 | 26 | 25 | 39 | 39 | 17 | 39 | 24 |
N.S. | 1 | 0.76 | 0.76 | 0.74 | 1.15 | 1.15 | 0.50 | 1.15 | 0.71 |
time (sec) |
N/A | 0.523 | 0.038 | 0.328 | 0.516 | 0.445 | 0.108 | 0.730 | 2.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | B | B | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 41 | 43 | 103 | 92 | 61 | 57 | -1 |
N.S. | 1 | 0.00 | 1.32 | 1.39 | 3.32 | 2.97 | 1.97 | 1.84 | -0.03 |
time (sec) |
N/A | 3.421 | 0.064 | 0.987 | 0.519 | 0.390 | 0.126 | 0.468 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 20 | 167 | 45 | 36 | 24 | 25 | 55 |
N.S. | 1 | 0.00 | 0.95 | 7.95 | 2.14 | 1.71 | 1.14 | 1.19 | 2.62 |
time (sec) |
N/A | 1.758 | 0.184 | 3.583 | 0.304 | 0.411 | 0.085 | 0.475 | 2.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 18 | 16 | 15 | 14 | 14 | 12 | 14 | 13 |
N.S. | 1 | 0.75 | 0.67 | 0.62 | 0.58 | 0.58 | 0.50 | 0.58 | 0.54 |
time (sec) |
N/A | 0.006 | 0.000 | 0.097 | 0.263 | 0.406 | 0.009 | 0.413 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 23 | 23 | 28 | 25 | 14 | 18 | 17 |
N.S. | 1 | 1.18 | 1.05 | 1.05 | 1.27 | 1.14 | 0.64 | 0.82 | 0.77 |
time (sec) |
N/A | 0.351 | 0.048 | 1.490 | 0.283 | 0.457 | 0.035 | 0.418 | 1.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 41 | 33 | 29 | 72 | 29 | 52 | 46 |
N.S. | 1 | 0.00 | 1.28 | 1.03 | 0.91 | 2.25 | 0.91 | 1.62 | 1.44 |
time (sec) |
N/A | 9.549 | 3.133 | 0.134 | 0.334 | 0.433 | 0.112 | 0.433 | 2.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 0 | 10 | 9 | 8 | 8 | 14 | 8 | 9 |
N.S. | 1 | 0.00 | 1.00 | 0.90 | 0.80 | 0.80 | 1.40 | 0.80 | 0.90 |
time (sec) |
N/A | 0.142 | 0.028 | 0.315 | 0.300 | 0.410 | 0.071 | 0.402 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 18 | 17 | 19 | 16 | 12 | 19 | 16 |
N.S. | 1 | 0.00 | 1.12 | 1.06 | 1.19 | 1.00 | 0.75 | 1.19 | 1.00 |
time (sec) |
N/A | 0.970 | 0.186 | 0.604 | 0.301 | 0.455 | 0.044 | 0.390 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 19 | 19 | 19 | 18 | 22 | 15 | 17 | 17 |
N.S. | 1 | 0.70 | 0.70 | 0.70 | 0.67 | 0.81 | 0.56 | 0.63 | 0.63 |
time (sec) |
N/A | 0.176 | 0.015 | 0.073 | 0.541 | 0.411 | 0.099 | 0.413 | 2.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 20 | 21 | 19 | 21 | 19 | 22 | 19 |
N.S. | 1 | 0.83 | 0.83 | 0.88 | 0.79 | 0.88 | 0.79 | 0.92 | 0.79 |
time (sec) |
N/A | 0.078 | 0.017 | 0.263 | 0.270 | 0.454 | 0.427 | 0.404 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 26 | 16 | 39 | 24 | 13 | 15 | 13 | 15 |
N.S. | 1 | 1.44 | 0.89 | 2.17 | 1.33 | 0.72 | 0.83 | 0.72 | 0.83 |
time (sec) |
N/A | 0.019 | 0.012 | 0.525 | 0.273 | 0.410 | 0.037 | 0.402 | 1.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. | 1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.77 | 0.92 | 0.92 |
time (sec) |
N/A | 0.019 | 0.042 | 0.066 | 0.258 | 0.411 | 0.027 | 0.399 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 12 | 12 | 12 | 0 | 11 | 10 | 11 | 11 |
N.S. | 1 | 0.86 | 0.86 | 0.86 | 0.00 | 0.79 | 0.71 | 0.79 | 0.79 |
time (sec) |
N/A | 0.155 | 0.022 | 0.698 | 0.000 | 0.447 | 0.055 | 0.395 | 1.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 15 | 14 | 15 | 15 | 12 | 15 | 15 |
N.S. | 1 | 0.00 | 1.00 | 0.93 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 |
time (sec) |
N/A | 0.358 | 0.024 | 1.097 | 0.283 | 0.421 | 0.041 | 0.399 | 2.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 21 | 24 | 22 | 22 | 24 | 22 | 24 |
N.S. | 1 | 0.84 | 1.11 | 1.26 | 1.16 | 1.16 | 1.26 | 1.16 | 1.26 |
time (sec) |
N/A | 0.008 | 0.003 | 0.255 | 0.256 | 0.450 | 0.009 | 0.407 | 0.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 16 | 15 | 27 | 17 | 0 | 15 |
N.S. | 1 | 0.00 | 1.00 | 0.89 | 0.83 | 1.50 | 0.94 | 0.00 | 0.83 |
time (sec) |
N/A | 2.054 | 0.368 | 0.170 | 0.309 | 0.415 | 1.988 | 0.000 | 2.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 26 | 25 | 25 | 20 | 25 | -1 |
N.S. | 1 | 1.00 | 1.00 | 0.96 | 0.93 | 0.93 | 0.74 | 0.93 | -0.04 |
time (sec) |
N/A | 2.874 | 0.137 | 0.099 | 0.512 | 0.491 | 1.749 | 0.651 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 56 | 56 | 43 | 44 | 47 | 46 | 44 | 43 |
N.S. | 1 | 1.87 | 1.87 | 1.43 | 1.47 | 1.57 | 1.53 | 1.47 | 1.43 |
time (sec) |
N/A | 0.028 | 0.004 | 0.119 | 0.261 | 0.425 | 0.040 | 0.413 | 1.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | B | A | B | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 78 | 97 | 84 | 71 | 59 | 75 | 81 | -1 |
N.S. | 1 | 2.36 | 2.94 | 2.55 | 2.15 | 1.79 | 2.27 | 2.45 | -0.03 |
time (sec) |
N/A | 0.741 | 0.084 | 4.394 | 0.359 | 0.423 | 0.323 | 0.878 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 35 | 32 | 32 | 26 | 34 | 24 |
N.S. | 1 | 0.00 | 1.00 | 1.35 | 1.23 | 1.23 | 1.00 | 1.31 | 0.92 |
time (sec) |
N/A | 15.718 | 0.106 | 0.289 | 0.526 | 0.374 | 0.123 | 0.430 | 2.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 37 | 23 | 31 | 0 | 27 | 15 | 28 | 27 |
N.S. | 1 | 1.54 | 0.96 | 1.29 | 0.00 | 1.12 | 0.62 | 1.17 | 1.12 |
time (sec) |
N/A | 0.593 | 0.028 | 2.615 | 0.000 | 0.353 | 0.044 | 0.405 | 1.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 235 | 26 | 34 | 27 | 31 | -1 |
N.S. | 1 | 0.00 | 0.97 | 7.34 | 0.81 | 1.06 | 0.84 | 0.97 | -0.03 |
time (sec) |
N/A | 1.202 | 0.445 | 2.615 | 0.305 | 0.423 | 0.122 | 0.605 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 27 | 192 | 0 | 25 | 1321 | 25 | 30 |
N.S. | 1 | 0.96 | 1.00 | 7.11 | 0.00 | 0.93 | 48.93 | 0.93 | 1.11 |
time (sec) |
N/A | 0.192 | 0.036 | 0.618 | 0.000 | 0.390 | 48.005 | 0.463 | 2.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 19 | 20 | 22 | 19 | 20 | 25 | 19 |
N.S. | 1 | 0.00 | 0.95 | 1.00 | 1.10 | 0.95 | 1.00 | 1.25 | 0.95 |
time (sec) |
N/A | 0.352 | 0.834 | 1.395 | 0.290 | 0.373 | 0.063 | 0.426 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | B | F | B | B | B | F(-1) | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 102 | 0 | 122 | 130 | 257 | 0 | -1 |
N.S. |
1 | 0.00 | 3.00 | 0.00 | 3.59 | 3.82 | 7.56 | 0.00 | -0.03 |
time (sec) |
N/A | 180.000 | 9.376 | 0.697 | 0.755 | 0.405 | 1.491 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 48 | 32 | 30 | 54 | 29 | 29 | 29 | 26 |
N.S. | 1 | 1.60 | 1.07 | 1.00 | 1.80 | 0.97 | 0.97 | 0.97 | 0.87 |
time (sec) |
N/A | 0.105 | 0.044 | 0.655 | 0.283 | 0.389 | 0.127 | 0.416 | 1.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 34 | 28 | 28 | 27 | 31 | 24 | 27 | 26 |
N.S. | 1 | 1.03 | 0.85 | 0.85 | 0.82 | 0.94 | 0.73 | 0.82 | 0.79 |
time (sec) |
N/A | 0.045 | 0.011 | 0.297 | 0.262 | 0.351 | 0.159 | 0.400 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 32 | 0 | 38 | 38 | 36 | 0 | 138 |
N.S. | 1 | 0.00 | 0.97 | 0.00 | 1.15 | 1.15 | 1.09 | 0.00 | 4.18 |
time (sec) |
N/A | 36.469 | 0.103 | 1.464 | 0.528 | 0.455 | 0.211 | 0.000 | 2.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 17 | 17 | 16 | 14 | 16 | -1 |
N.S. | 1 | 0.00 | 1.00 | 1.00 | 1.00 | 0.94 | 0.82 | 0.94 | -0.06 |
time (sec) |
N/A | 13.059 | 0.022 | 0.408 | 0.522 | 0.390 | 0.152 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 18 | 17 | 34 | 17 | 17 | 17 |
N.S. | 1 | 1.00 | 1.09 | 0.82 | 0.77 | 1.55 | 0.77 | 0.77 | 0.77 |
time (sec) |
N/A | 0.009 | 0.019 | 0.202 | 0.261 | 0.383 | 0.047 | 0.401 | 1.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | F | B | B | B | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 232 | 31 | 0 | 64 | 66 | 102 | 0 | 67 |
N.S. | 1 | 8.00 | 1.07 | 0.00 | 2.21 | 2.28 | 3.52 | 0.00 | 2.31 |
time (sec) |
N/A | 6.262 | 0.151 | 0.433 | 0.693 | 0.380 | 0.789 | 0.000 | 3.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | F | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 157 | 43 | 52 | 0 | 41 | 56 | 81 | 59 |
N.S. | 1 | 4.91 | 1.34 | 1.62 | 0.00 | 1.28 | 1.75 | 2.53 | 1.84 |
time (sec) |
N/A | 2.552 | 0.727 | 0.472 | 0.000 | 0.453 | 0.208 | 0.415 | 2.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 23 | 22 | 29 | 19 | 24 | 22 |
N.S. | 1 | 1.00 | 1.15 | 0.88 | 0.85 | 1.12 | 0.73 | 0.92 | 0.85 |
time (sec) |
N/A | 0.052 | 0.005 | 0.889 | 0.273 | 0.408 | 0.041 | 0.404 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 35 | 24 | 27 | 30 | 26 | 17 | 32 | 26 |
N.S. | 1 | 1.21 | 0.83 | 0.93 | 1.03 | 0.90 | 0.59 | 1.10 | 0.90 |
time (sec) |
N/A | 0.348 | 0.371 | 0.327 | 0.285 | 0.440 | 0.037 | 0.406 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | C | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 101 | 25 | 402 | 362 | 24 | 48 | 24 | 2500 |
N.S. | 1 | 4.04 | 1.00 | 16.08 | 14.48 | 0.96 | 1.92 | 0.96 | 100.00 |
time (sec) |
N/A | 1.646 | 0.149 | 0.653 | 0.519 | 0.453 | 0.229 | 0.401 | 7.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 26 | 19 | 21 | 26 | 11 | 12 | 11 | 13 |
N.S. | 1 | 1.86 | 1.36 | 1.50 | 1.86 | 0.79 | 0.86 | 0.79 | 0.93 |
time (sec) |
N/A | 0.015 | 0.010 | 0.444 | 0.280 | 0.376 | 0.033 | 0.413 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 23 | 18 | 22 | 38 | 30 | 26 | 30 | 21 |
N.S. | 1 | 1.21 | 0.95 | 1.16 | 2.00 | 1.58 | 1.37 | 1.58 | 1.11 |
time (sec) |
N/A | 0.376 | 0.048 | 1.351 | 0.499 | 0.402 | 0.047 | 0.398 | 2.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 |
N.S. | 1 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.56 | 0.78 | 0.67 |
time (sec) |
N/A | 0.002 | 0.001 | 0.140 | 0.284 | 0.369 | 0.015 | 0.402 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 55 | 22 | 21 | 20 | 23 | 15 | 23 | 20 |
N.S. | 1 | 2.50 | 1.00 | 0.95 | 0.91 | 1.05 | 0.68 | 1.05 | 0.91 |
time (sec) |
N/A | 0.187 | 0.080 | 0.272 | 0.355 | 0.430 | 0.063 | 0.417 | 1.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | A | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 28486 | 112 | 71 | 20 | 0 | 25 |
N.S. | 1 | 1.00 | 1.00 | 1095.62 | 4.31 | 2.73 | 0.77 | 0.00 | 0.96 |
time (sec) |
N/A | 2.364 | 0.082 | 6.104 | 0.534 | 0.426 | 3.181 | 0.000 | 3.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | B | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 54 | 47 | 70 | 72 | 61 | 95 | 155 |
N.S. | 1 | 0.00 | 2.08 | 1.81 | 2.69 | 2.77 | 2.35 | 3.65 | 5.96 |
time (sec) |
N/A | 9.267 | 0.065 | 0.149 | 0.338 | 0.444 | 0.093 | 0.580 | 2.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 |
N.S. | 1 | 0.17 | 0.17 | 0.22 | 0.17 | 0.17 | 0.13 | 0.22 | 0.17 |
time (sec) |
N/A | 0.001 | 0.000 | 0.004 | 0.255 | 0.352 | 0.006 | 0.409 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 47 | 23 | 62 | 39 | 36 | 48 | 36 | 21 |
N.S. | 1 | 1.96 | 0.96 | 2.58 | 1.62 | 1.50 | 2.00 | 1.50 | 0.88 |
time (sec) |
N/A | 0.123 | 0.063 | 0.377 | 0.288 | 0.390 | 0.058 | 0.408 | 2.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | B | B | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 69 | 64 | 64 | 90 | 78 | -1 |
N.S. | 1 | 0.00 | 0.91 | 3.14 | 2.91 | 2.91 | 4.09 | 3.55 | -0.05 |
time (sec) |
N/A | 2.779 | 0.154 | 66.435 | 0.534 | 0.362 | 0.199 | 0.459 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 33 | 13 | 11 | 10 | 10 | 10 | 10 | 13 |
N.S. | 1 | 2.54 | 1.00 | 0.85 | 0.77 | 0.77 | 0.77 | 0.77 | 1.00 |
time (sec) |
N/A | 0.045 | 0.010 | 0.196 | 0.257 | 0.409 | 0.044 | 0.417 | 1.990 |