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 | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 54 | 66 | 62 | 65 | 61 | 68 | 0 |
N.S. |
1 | 0.00 | 1.80 | 2.20 | 2.07 | 2.17 | 2.03 | 2.27 | 0.00 |
time (sec) |
N/A | 0.000 | 1.228 | 0.701 | 0.527 | 0.264 | 0.437 | 0.880 | 0.000 |
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 | 39 | 28 | 37 | 49 | 32 | 37 | 31 |
N.S. |
1 | 0.00 | 1.44 | 1.04 | 1.37 | 1.81 | 1.19 | 1.37 | 1.15 |
time (sec) |
N/A | 0.000 | 0.089 | 0.592 | 0.360 | 0.268 | 0.082 | 0.350 | 14.165 |
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 | 10 | 12 | 10 | 11 | 13 | 13 | 8 | 16 | 15 |
N.S. |
1 | 1.20 | 1.00 | 1.10 | 1.30 | 1.30 | 0.80 | 1.60 | 1.50 |
time (sec) |
N/A | 0.159 | 0.008 | 0.024 | 0.187 | 0.251 | 0.045 | 0.275 | 11.999 |
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 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 4 |
N.S. |
1 | 0.36 | 0.36 | 0.36 | 0.29 | 0.29 | 0.21 | 0.29 | 0.29 |
time (sec) |
N/A | 0.131 | 0.001 | 0.059 | 0.190 | 0.237 | 0.028 | 0.257 | 0.014 |
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 | 29 | 0 | 27 | 33 | 37 | 31 | 31 | 41 | 33 |
N.S. |
1 | 0.00 | 0.93 | 1.14 | 1.28 | 1.07 | 1.07 | 1.41 | 1.14 |
time (sec) |
N/A | 0.000 | 0.579 | 10.110 | 0.289 | 0.253 | 0.508 | 0.367 | 12.566 |
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 | 19 | 0 | 18 | 23 | 22 | 22 | 24 | 0 | 22 |
N.S. |
1 | 0.00 | 0.95 | 1.21 | 1.16 | 1.16 | 1.26 | 0.00 | 1.16 |
time (sec) |
N/A | 0.000 | 0.138 | 0.203 | 0.240 | 0.254 | 0.451 | 0.000 | 12.326 |
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 | 14 | 0 | 14 | 15 | 12 | 14 | 12 | 14 | 14 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 0.86 | 1.00 | 0.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.100 | 1.018 | 0.229 | 0.251 | 0.059 | 0.263 | 12.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 204 | 89 | 627 | 285 | 1028 | 0 | 520 |
N.S. |
1 | 0.00 | 6.00 | 2.62 | 18.44 | 8.38 | 30.24 | 0.00 | 15.29 |
time (sec) |
N/A | 0.000 | 0.140 | 19.553 | 0.323 | 0.260 | 1.348 | 0.000 | 13.041 |
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 | 29 | 0 | 45 | 51 | 44 | 44 | 44 | 381 | 0 |
N.S. |
1 | 0.00 | 1.55 | 1.76 | 1.52 | 1.52 | 1.52 | 13.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.171 | 0.907 | 0.366 | 0.263 | 0.248 | 0.378 | 0.000 |
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 | 31 | 0 | 26 | 24 | 23 | 23 | 24 | 44 | 21 |
N.S. |
1 | 0.00 | 0.84 | 0.77 | 0.74 | 0.74 | 0.77 | 1.42 | 0.68 |
time (sec) |
N/A | 0.000 | 0.976 | 0.633 | 0.363 | 0.242 | 0.110 | 0.406 | 11.597 |
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 | 33 | 0 | 30 | 29 | 38 | 40 | 53 | 45 | 28 |
N.S. |
1 | 0.00 | 0.91 | 0.88 | 1.15 | 1.21 | 1.61 | 1.36 | 0.85 |
time (sec) |
N/A | 0.000 | 5.083 | 1.122 | 0.247 | 0.260 | 0.202 | 0.337 | 12.296 |
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 | 38 | 38 | 32 | 33 | 37 | 26 | 39 | 29 |
N.S. |
1 | 1.65 | 1.65 | 1.39 | 1.43 | 1.61 | 1.13 | 1.70 | 1.26 |
time (sec) |
N/A | 0.300 | 0.016 | 0.096 | 0.190 | 0.243 | 0.115 | 0.265 | 11.146 |
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 | 15 | 14 | 14 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 1.00 | 0.93 | 0.93 |
time (sec) |
N/A | 0.153 | 0.015 | 0.162 | 0.182 | 0.263 | 0.039 | 0.272 | 0.026 |
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 | 35 | 28 | 24 | 19 | 18 | 21 | 17 | 19 | 18 |
N.S. |
1 | 0.80 | 0.69 | 0.54 | 0.51 | 0.60 | 0.49 | 0.54 | 0.51 |
time (sec) |
N/A | 0.233 | 0.010 | 0.048 | 0.177 | 0.246 | 0.051 | 0.268 | 0.067 |
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 | 22 | 0 | 22 | 21 | 27 | 20 | 15 | 20 | 20 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 1.23 | 0.91 | 0.68 | 0.91 | 0.91 |
time (sec) |
N/A | 0.000 | 0.427 | 0.757 | 0.305 | 0.240 | 0.072 | 0.372 | 0.695 |
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 | 21 | 43 | 29 | 35 | 76 | 30 | 37 | 30 | 22 |
N.S. |
1 | 2.05 | 1.38 | 1.67 | 3.62 | 1.43 | 1.76 | 1.43 | 1.05 |
time (sec) |
N/A | 0.605 | 0.068 | 0.668 | 0.226 | 0.252 | 0.241 | 0.272 | 11.825 |
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 | 14 | 40 | 36 | 37 | 36 | 36 | 37 | 36 | 0 |
N.S. |
1 | 2.86 | 2.57 | 2.64 | 2.57 | 2.57 | 2.64 | 2.57 | 0.00 |
time (sec) |
N/A | 0.771 | 0.037 | 0.953 | 0.244 | 0.244 | 0.099 | 0.311 | 0.000 |
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 | 29 | 24 | 17 | 20 | 27 | 16 | 19 | 16 | 16 |
N.S. |
1 | 0.83 | 0.59 | 0.69 | 0.93 | 0.55 | 0.66 | 0.55 | 0.55 |
time (sec) |
N/A | 0.204 | 0.025 | 0.055 | 0.212 | 0.252 | 0.085 | 0.269 | 12.144 |
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 | 19 | 22 | 19 | 20 | 16 | 19 | 19 | 16 | 19 |
N.S. |
1 | 1.16 | 1.00 | 1.05 | 0.84 | 1.00 | 1.00 | 0.84 | 1.00 |
time (sec) |
N/A | 0.313 | 0.054 | 0.079 | 0.324 | 0.236 | 0.067 | 0.286 | 12.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 0 | 145 | 54 | 77 | 79 | 44 | 53 | 0 |
N.S. |
1 | 0.00 | 3.62 | 1.35 | 1.92 | 1.98 | 1.10 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.115 | 0.904 | 0.245 | 0.284 | 0.249 | 0.359 | 0.000 |
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 | 22 | 0 | 28 | 26 | 17 | 26 | 22 | 26 | 46 |
N.S. |
1 | 0.00 | 1.27 | 1.18 | 0.77 | 1.18 | 1.00 | 1.18 | 2.09 |
time (sec) |
N/A | 0.000 | 0.558 | 0.298 | 0.367 | 0.247 | 0.089 | 0.316 | 12.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 45 | 31 | 37 | 205 | 41 | 39 | 0 | 110 |
N.S. |
1 | 1.45 | 1.00 | 1.19 | 6.61 | 1.32 | 1.26 | 0.00 | 3.55 |
time (sec) |
N/A | 0.439 | 3.518 | 0.221 | 0.342 | 0.253 | 0.295 | 0.000 | 12.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 33 | 21 | 21 | 0 | 23 | 19 | 32 | 22 |
N.S. |
1 | 1.74 | 1.11 | 1.11 | 0.00 | 1.21 | 1.00 | 1.68 | 1.16 |
time (sec) |
N/A | 0.421 | 0.497 | 0.358 | 0.000 | 0.237 | 0.057 | 0.286 | 0.126 |
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 | 18 | 14 | 14 | 13 | 14 | 14 | 12 | 16 | 12 |
N.S. |
1 | 0.78 | 0.78 | 0.72 | 0.78 | 0.78 | 0.67 | 0.89 | 0.67 |
time (sec) |
N/A | 0.201 | 0.008 | 0.407 | 0.182 | 0.267 | 0.042 | 0.264 | 11.729 |
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 | 19 | 12 | 12 | 12 | 42 | 14 | 12 | 14 | 11 |
N.S. |
1 | 0.63 | 0.63 | 0.63 | 2.21 | 0.74 | 0.63 | 0.74 | 0.58 |
time (sec) |
N/A | 0.251 | 0.092 | 0.044 | 0.178 | 0.286 | 0.120 | 0.274 | 0.051 |
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 | 20 | 88 | 23 | 78 | 61 | 61 | 95 | 61 | 93 |
N.S. |
1 | 4.40 | 1.15 | 3.90 | 3.05 | 3.05 | 4.75 | 3.05 | 4.65 |
time (sec) |
N/A | 0.214 | 0.013 | 0.156 | 0.195 | 0.249 | 0.031 | 0.269 | 0.084 |
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 | 32 | 82 | 61 | 47 | 93 | 35 | 49 | 58 | 44 |
N.S. |
1 | 2.56 | 1.91 | 1.47 | 2.91 | 1.09 | 1.53 | 1.81 | 1.38 |
time (sec) |
N/A | 0.290 | 0.041 | 0.095 | 0.192 | 0.283 | 0.083 | 0.277 | 12.083 |
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 | 8 | 8 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 0.33 | 0.33 | 0.33 | 0.29 | 0.29 | 0.29 | 0.29 | 0.29 |
time (sec) |
N/A | 0.120 | 0.001 | 0.029 | 0.183 | 0.239 | 0.020 | 0.263 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 48 | 22 | 39 | 74 | 34 | 41 | 40 | 21 |
N.S. |
1 | 2.29 | 1.05 | 1.86 | 3.52 | 1.62 | 1.95 | 1.90 | 1.00 |
time (sec) |
N/A | 0.343 | 1.403 | 0.063 | 0.217 | 0.242 | 0.060 | 0.263 | 11.315 |
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 | 31 | 32 | 28 | 29 | 51 | 26 | 32 | 36 | 27 |
N.S. |
1 | 1.03 | 0.90 | 0.94 | 1.65 | 0.84 | 1.03 | 1.16 | 0.87 |
time (sec) |
N/A | 0.232 | 0.725 | 0.073 | 0.224 | 0.239 | 0.074 | 0.268 | 10.902 |
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 | 18 | 15 | 13 | 13 | 15 | 13 | 14 |
N.S. |
1 | 1.24 | 1.06 | 0.88 | 0.76 | 0.76 | 0.88 | 0.76 | 0.82 |
time (sec) |
N/A | 0.132 | 0.004 | 0.074 | 0.191 | 0.254 | 0.042 | 0.261 | 10.666 |
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 | 25 | 25 | 24 | 42 | 26 | 24 | 22 | 0 | 24 |
N.S. |
1 | 1.00 | 0.96 | 1.68 | 1.04 | 0.96 | 0.88 | 0.00 | 0.96 |
time (sec) |
N/A | 0.556 | 0.069 | 0.895 | 0.256 | 0.268 | 0.230 | 0.000 | 11.986 |
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 | 31 | 22 | 28 | 21 | 20 | 21 | 21 |
N.S. |
1 | 0.00 | 1.15 | 0.81 | 1.04 | 0.78 | 0.74 | 0.78 | 0.78 |
time (sec) |
N/A | 0.000 | 5.116 | 0.971 | 0.220 | 0.255 | 6.523 | 0.283 | 11.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 25 | 88 | 48 | 87 | 82 | 56 | 59 |
N.S. |
1 | 0.89 | 0.89 | 3.14 | 1.71 | 3.11 | 2.93 | 2.00 | 2.11 |
time (sec) |
N/A | 7.668 | 0.358 | 5.328 | 0.597 | 0.258 | 5.188 | 16.977 | 11.268 |
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 | 36 | 36 | 34 | 31 | 34 | 32 | 36 | 33 |
N.S. |
1 | 1.44 | 1.44 | 1.36 | 1.24 | 1.36 | 1.28 | 1.44 | 1.32 |
time (sec) |
N/A | 4.310 | 0.099 | 1.186 | 0.262 | 0.247 | 0.242 | 0.285 | 11.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 28 | 21 | 81 | 18 | 24 | 50 | 18 |
N.S. |
1 | 1.21 | 1.17 | 0.88 | 3.38 | 0.75 | 1.00 | 2.08 | 0.75 |
time (sec) |
N/A | 0.608 | 0.111 | 0.344 | 0.338 | 0.261 | 0.125 | 0.281 | 11.340 |
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 | 36 | 35 | 24 | 33 | 32 | 66 | 33 | 64 |
N.S. |
1 | 1.33 | 1.30 | 0.89 | 1.22 | 1.19 | 2.44 | 1.22 | 2.37 |
time (sec) |
N/A | 0.165 | 0.004 | 0.132 | 0.185 | 0.253 | 0.025 | 0.268 | 10.720 |
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 | 15 | 13 | 16 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.87 | 1.07 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.294 | 0.180 | 0.057 | 0.266 | 0.248 | 0.077 | 0.265 | 10.372 |
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 | 22 | 28 | 27 | 26 | 32 | 31 | 29 | 26 | 28 |
N.S. |
1 | 1.27 | 1.23 | 1.18 | 1.45 | 1.41 | 1.32 | 1.18 | 1.27 |
time (sec) |
N/A | 0.277 | 0.276 | 0.141 | 0.216 | 0.277 | 0.057 | 0.270 | 10.641 |
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 | 20 | 22 | 20 | 17 | 17 | 22 | 17 | 14 |
N.S. |
1 | 0.87 | 0.96 | 0.87 | 0.74 | 0.74 | 0.96 | 0.74 | 0.61 |
time (sec) |
N/A | 0.129 | 0.002 | 0.080 | 0.178 | 0.241 | 0.019 | 0.271 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 24 | 54 | 26 | 148 | 127 | 21 |
N.S. |
1 | 0.00 | 0.91 | 1.04 | 2.35 | 1.13 | 6.43 | 5.52 | 0.91 |
time (sec) |
N/A | 0.000 | 0.322 | 1.382 | 0.321 | 0.268 | 0.152 | 0.291 | 10.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 80 | 47 | 28 | 111 | 59 | 31 | 60 | 58 |
N.S. |
1 | 2.86 | 1.68 | 1.00 | 3.96 | 2.11 | 1.11 | 2.14 | 2.07 |
time (sec) |
N/A | 2.214 | 8.169 | 0.214 | 0.253 | 0.247 | 0.077 | 0.282 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 17 | 16 | 0 | 18 | 14 | 22 | 15 |
N.S. |
1 | 0.00 | 1.21 | 1.14 | 0.00 | 1.29 | 1.00 | 1.57 | 1.07 |
time (sec) |
N/A | 0.000 | 0.084 | 0.502 | 0.000 | 0.256 | 0.131 | 0.302 | 10.748 |
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 | 13 | 13 | 12 | 11 | 16 | 22 | 12 | 11 |
N.S. |
1 | 0.81 | 0.81 | 0.75 | 0.69 | 1.00 | 1.38 | 0.75 | 0.69 |
time (sec) |
N/A | 0.148 | 0.004 | 0.044 | 0.179 | 0.248 | 0.046 | 0.258 | 10.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 55 | 70 | 58 | 53 | 54 | 58 | 0 | 63 |
N.S. |
1 | 2.04 | 2.59 | 2.15 | 1.96 | 2.00 | 2.15 | 0.00 | 2.33 |
time (sec) |
N/A | 1.020 | 0.055 | 0.110 | 0.176 | 0.259 | 3.337 | 0.000 | 10.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 34 | 84 | 59 | 147 | 116 | 898950 | 0 |
N.S. |
1 | 0.00 | 1.48 | 3.65 | 2.57 | 6.39 | 5.04 | 39084.78 | 0.00 |
time (sec) |
N/A | 0.000 | 0.085 | 50.975 | 0.269 | 0.276 | 0.206 | 6.975 | 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 | 29 | 12 | 12 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 0.41 | 0.41 | 0.41 | 0.38 | 0.38 | 0.28 | 0.38 | 0.38 |
time (sec) |
N/A | 0.147 | 0.006 | 0.059 | 0.184 | 0.259 | 0.059 | 0.263 | 10.771 |
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 | 18 | 18 | 18 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 0.69 | 0.69 | 0.69 | 0.65 | 0.65 | 0.58 | 0.65 | 0.65 |
time (sec) |
N/A | 0.198 | 0.047 | 0.037 | 0.185 | 0.261 | 0.051 | 0.273 | 11.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 71 | 95 | 474 | 81 | 0 | 0 | 295 |
N.S. |
1 | 0.00 | 2.45 | 3.28 | 16.34 | 2.79 | 0.00 | 0.00 | 10.17 |
time (sec) |
N/A | 0.000 | 1.231 | 1.564 | 0.358 | 0.282 | 0.000 | 0.000 | 11.741 |
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 | 27 | 0 | 23 | 30 | 39 | 30 | 29 | 40 | 0 |
N.S. |
1 | 0.00 | 0.85 | 1.11 | 1.44 | 1.11 | 1.07 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.272 | 2.326 | 0.328 | 0.251 | 0.163 | 0.294 | 0.000 |
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 | 37 | 0 | 31 | 29 | 25 | 114 | 31 | 0 | 26 |
N.S. |
1 | 0.00 | 0.84 | 0.78 | 0.68 | 3.08 | 0.84 | 0.00 | 0.70 |
time (sec) |
N/A | 0.000 | 3.267 | 0.428 | 0.397 | 0.262 | 0.470 | 0.000 | 11.658 |
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 | 31 | 0 | 0 | 26 | 42 | 44 | 0 | 0 | 44 |
N.S. |
1 | 0.00 | 0.00 | 0.84 | 1.35 | 1.42 | 0.00 | 0.00 | 1.42 |
time (sec) |
N/A | 0.000 | 0.000 | 28.289 | 0.338 | 0.255 | 0.000 | 0.000 | 11.619 |
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 | 24 | 21 | 20 | 20 | 15 | 20 | 27 |
N.S. |
1 | 0.96 | 0.96 | 0.84 | 0.80 | 0.80 | 0.60 | 0.80 | 1.08 |
time (sec) |
N/A | 0.251 | 0.313 | 0.121 | 0.185 | 0.238 | 0.091 | 0.273 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 34 | 32 | 17 | 0 | 25 | 19 | 30 | 18 |
N.S. |
1 | 1.48 | 1.39 | 0.74 | 0.00 | 1.09 | 0.83 | 1.30 | 0.78 |
time (sec) |
N/A | 0.402 | 0.173 | 0.335 | 0.000 | 0.250 | 0.082 | 0.270 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 77 | 82 | 213 | 246 | 78 | 0 | 232 |
N.S. |
1 | 0.00 | 2.33 | 2.48 | 6.45 | 7.45 | 2.36 | 0.00 | 7.03 |
time (sec) |
N/A | 0.000 | 1.812 | 21.870 | 1.876 | 0.255 | 0.529 | 0.000 | 16.703 |
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 | 19 | 19 | 15 | 18 | 17 | 17 | 20 | 17 | 15 |
N.S. |
1 | 1.00 | 0.79 | 0.95 | 0.89 | 0.89 | 1.05 | 0.89 | 0.79 |
time (sec) |
N/A | 0.143 | 0.002 | 0.021 | 0.178 | 0.248 | 0.042 | 0.291 | 10.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 18 | 16 | 33 | 17 | 0 | 17 | 15 |
N.S. |
1 | 0.00 | 0.86 | 0.76 | 1.57 | 0.81 | 0.00 | 0.81 | 0.71 |
time (sec) |
N/A | 0.000 | 0.746 | 2.437 | 0.450 | 0.249 | 0.000 | 0.331 | 10.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 20 | 0 | 19 | 33 | 18 | 17 | 18 | 18 |
N.S. |
1 | 0.80 | 0.00 | 0.76 | 1.32 | 0.72 | 0.68 | 0.72 | 0.72 |
time (sec) |
N/A | 0.378 | 0.000 | 0.498 | 0.372 | 0.243 | 0.102 | 0.300 | 11.411 |
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 | 19 | 0 | 19 | 20 | 47 | 19 | 15 | 19 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 2.47 | 1.00 | 0.79 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.107 | 0.122 | 0.219 | 0.254 | 0.047 | 0.281 | 11.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 63 | 72 | 60 | 139 | 133 | 0 | 68 | 0 |
N.S. |
1 | 2.17 | 2.48 | 2.07 | 4.79 | 4.59 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 2.599 | 2.978 | 0.736 | 0.312 | 0.275 | 0.000 | 0.481 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F(-1) | B | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 52 | 197 | 0 | 165 | 178 | 0 | 553 |
N.S. |
1 | 0.00 | 1.68 | 6.35 | 0.00 | 5.32 | 5.74 | 0.00 | 17.84 |
time (sec) |
N/A | 0.000 | 0.789 | 46.772 | 0.000 | 0.287 | 1.814 | 0.000 | 16.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 67 | 63 | 102 | 96 | 56 | 121 | 89 |
N.S. |
1 | 0.00 | 1.76 | 1.66 | 2.68 | 2.53 | 1.47 | 3.18 | 2.34 |
time (sec) |
N/A | 0.000 | 2.840 | 1.254 | 0.259 | 0.256 | 0.152 | 0.379 | 14.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 74 | 42 | 31 | 45 | 32 | 29 | 39 | 17 |
N.S. |
1 | 3.70 | 2.10 | 1.55 | 2.25 | 1.60 | 1.45 | 1.95 | 0.85 |
time (sec) |
N/A | 1.260 | 0.212 | 0.649 | 0.307 | 0.253 | 0.301 | 0.286 | 14.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 174 | 279 | 262 | 260 | 242 | 0 |
N.S. |
1 | 0.00 | 0.00 | 5.80 | 9.30 | 8.73 | 8.67 | 8.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.092 | 0.380 | 0.276 | 1.105 | 0.367 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | B | A | A | B | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 0 | 47 | 48 | 45 | 20 | 61 | 0 |
N.S. |
1 | 1.16 | 0.00 | 1.88 | 1.92 | 1.80 | 0.80 | 2.44 | 0.00 |
time (sec) |
N/A | 1.452 | 0.000 | 0.336 | 0.314 | 0.251 | 0.114 | 0.286 | 0.000 |
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 | 23 | 43 | 26 | 25 | 56 | 34 | 22 | 37 | 24 |
N.S. |
1 | 1.87 | 1.13 | 1.09 | 2.43 | 1.48 | 0.96 | 1.61 | 1.04 |
time (sec) |
N/A | 0.444 | 0.085 | 0.589 | 0.211 | 0.242 | 0.120 | 0.269 | 14.238 |
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 | 22 | 0 | 22 | 29 | 35 | 29 | 31 | 454 | 112 |
N.S. |
1 | 0.00 | 1.00 | 1.32 | 1.59 | 1.32 | 1.41 | 20.64 | 5.09 |
time (sec) |
N/A | 0.000 | 0.528 | 1.071 | 0.312 | 0.244 | 0.099 | 0.356 | 14.750 |
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 | 18 | 16 | 16 | 14 | 20 | 20 | 22 | 20 | 13 |
N.S. |
1 | 0.89 | 0.89 | 0.78 | 1.11 | 1.11 | 1.22 | 1.11 | 0.72 |
time (sec) |
N/A | 0.577 | 0.359 | 0.061 | 0.231 | 0.238 | 0.057 | 0.278 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 38 | 27 | 42 | 57 | 29 | 25 | 26 |
N.S. |
1 | 0.00 | 1.41 | 1.00 | 1.56 | 2.11 | 1.07 | 0.93 | 0.96 |
time (sec) |
N/A | 0.000 | 5.152 | 1.327 | 0.223 | 0.247 | 0.199 | 0.273 | 13.950 |
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 | 31 | 0 | 32 | 28 | 30 | 30 | 24 | 30 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.90 | 0.97 | 0.97 | 0.77 | 0.97 | 0.00 |
time (sec) |
N/A | 0.000 | 0.120 | 0.157 | 0.236 | 0.247 | 0.102 | 0.302 | 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 | 9 | 9 | 9 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.161 | 0.009 | 0.040 | 0.183 | 0.265 | 0.065 | 0.264 | 0.049 |
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 | 32 | 0 | 58 | 63 | 61 | 62 | 26 | 61 | 33 |
N.S. |
1 | 0.00 | 1.81 | 1.97 | 1.91 | 1.94 | 0.81 | 1.91 | 1.03 |
time (sec) |
N/A | 0.000 | 0.160 | 8.785 | 0.328 | 0.240 | 0.165 | 0.671 | 14.148 |
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 | 24 | 24 | 23 | 22 | 22 | 20 | 22 | 23 |
N.S. |
1 | 0.89 | 0.89 | 0.85 | 0.81 | 0.81 | 0.74 | 0.81 | 0.85 |
time (sec) |
N/A | 0.488 | 0.046 | 0.530 | 0.273 | 0.241 | 0.069 | 0.262 | 0.099 |
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 | 27 | 41 | 23 | 28 | 38 | 27 | 27 | 33 | 36 |
N.S. |
1 | 1.52 | 0.85 | 1.04 | 1.41 | 1.00 | 1.00 | 1.22 | 1.33 |
time (sec) |
N/A | 0.336 | 0.049 | 0.158 | 0.223 | 0.247 | 0.065 | 0.255 | 14.006 |
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 | 20 | 32 | 18 | 19 | 35 | 18 | 14 | 18 | 21 |
N.S. |
1 | 1.60 | 0.90 | 0.95 | 1.75 | 0.90 | 0.70 | 0.90 | 1.05 |
time (sec) |
N/A | 0.766 | 0.343 | 0.069 | 0.231 | 0.251 | 0.058 | 0.258 | 14.057 |
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 | 24 | 0 | 33 | 28 | 41 | 27 | 22 | 0 | 27 |
N.S. |
1 | 0.00 | 1.38 | 1.17 | 1.71 | 1.12 | 0.92 | 0.00 | 1.12 |
time (sec) |
N/A | 0.000 | 0.392 | 0.163 | 0.254 | 0.238 | 2.079 | 0.000 | 14.225 |
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 | 19 | 15 | 10 | 9 | 9 | 10 | 9 | 9 |
N.S. |
1 | 1.46 | 1.15 | 0.77 | 0.69 | 0.69 | 0.77 | 0.69 | 0.69 |
time (sec) |
N/A | 0.181 | 0.026 | 0.060 | 0.185 | 0.257 | 0.035 | 0.263 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 24 | 21 | 44 | 57 | 43 | 41 | 405 | 25 |
N.S. |
1 | 0.92 | 0.81 | 1.69 | 2.19 | 1.65 | 1.58 | 15.58 | 0.96 |
time (sec) |
N/A | 0.315 | 0.023 | 0.517 | 0.283 | 0.266 | 0.072 | 1.544 | 17.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 31 | 28 | 49 | 62 | 27 | 0 | 28 |
N.S. |
1 | 0.00 | 1.11 | 1.00 | 1.75 | 2.21 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 1.100 | 3.151 | 0.205 | 0.249 | 0.609 | 0.000 | 14.751 |
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 | 12 | 12 | 13 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 0.80 | 0.80 | 0.87 | 0.80 | 0.80 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.328 | 0.094 | 0.457 | 0.219 | 0.255 | 0.059 | 0.266 | 14.444 |
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 | 42 | 33 | 22 | 32 | 20 | 19 | 32 | 34 |
N.S. |
1 | 1.83 | 1.43 | 0.96 | 1.39 | 0.87 | 0.83 | 1.39 | 1.48 |
time (sec) |
N/A | 0.248 | 0.274 | 0.031 | 0.266 | 0.246 | 0.051 | 0.274 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | A | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 93 | 77 | 42 | 77 | 116 | 163 | 0 |
N.S. |
1 | 0.00 | 2.58 | 2.14 | 1.17 | 2.14 | 3.22 | 4.53 | 0.00 |
time (sec) |
N/A | 0.000 | 0.184 | 1.640 | 0.328 | 0.269 | 0.461 | 0.469 | 0.000 |
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 | 12 | 12 | 12 | 13 | 20 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.67 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.216 | 0.063 | 12.622 | 0.286 | 0.261 | 0.108 | 0.279 | 15.429 |
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 | 18 | 18 | 16 | 18 | 14 | 12 | 18 | 16 |
N.S. |
1 | 0.82 | 0.82 | 0.73 | 0.82 | 0.64 | 0.55 | 0.82 | 0.73 |
time (sec) |
N/A | 0.170 | 0.005 | 0.047 | 0.191 | 0.266 | 0.051 | 0.268 | 14.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | A | F(-2) | F(-1) | F | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 31 | 0 | 24 | 0 | 0 | 0 | 22 |
N.S. |
1 | 0.00 | 1.24 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.206 | 0.000 | 0.251 | 0.000 | 0.000 | 0.000 | 16.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 198 | 0 | 23 | 0 | 0 | 23 |
N.S. |
1 | 0.00 | 1.00 | 7.33 | 0.00 | 0.85 | 0.00 | 0.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.245 | 1.239 | 0.000 | 0.260 | 0.000 | 0.000 | 14.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 0 | 0 | 23 | 68 | 33 | 24 | 0 | 38 |
N.S. |
1 | 0.00 | 0.00 | 0.53 | 1.58 | 0.77 | 0.56 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.000 | 3.765 | 0.397 | 0.249 | 0.388 | 0.000 | 14.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 39 | 37 | 40 | 0 | 43 | 32 | 46 | 37 |
N.S. |
1 | 1.50 | 1.42 | 1.54 | 0.00 | 1.65 | 1.23 | 1.77 | 1.42 |
time (sec) |
N/A | 0.277 | 0.220 | 0.109 | 0.000 | 0.260 | 0.123 | 0.263 | 14.343 |
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 | 31 | 0 | 32 | 27 | 31 | 26 | 29 | 26 | 26 |
N.S. |
1 | 0.00 | 1.03 | 0.87 | 1.00 | 0.84 | 0.94 | 0.84 | 0.84 |
time (sec) |
N/A | 0.000 | 0.103 | 0.921 | 0.359 | 0.255 | 0.242 | 0.407 | 14.531 |
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 | 30 | 30 | 27 | 30 | 30 | 29 | 30 | 30 |
N.S. |
1 | 1.36 | 1.36 | 1.23 | 1.36 | 1.36 | 1.32 | 1.36 | 1.36 |
time (sec) |
N/A | 0.171 | 0.000 | 0.038 | 0.178 | 0.235 | 0.022 | 0.277 | 0.043 |
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 | 9 | 11 | 12 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 0.75 | 0.92 | 1.00 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.131 | 0.000 | 0.031 | 0.182 | 0.239 | 0.015 | 0.273 | 0.003 |
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 | 25 | 23 | 20 | 24 | 19 | 17 | 21 | 21 |
N.S. |
1 | 1.09 | 1.00 | 0.87 | 1.04 | 0.83 | 0.74 | 0.91 | 0.91 |
time (sec) |
N/A | 0.480 | 0.281 | 0.573 | 0.306 | 0.275 | 0.074 | 0.266 | 14.715 |
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 | 26 | 0 | 26 | 25 | 39 | 35 | 34 | 45 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.50 | 1.35 | 1.31 | 1.73 | 1.04 |
time (sec) |
N/A | 0.000 | 0.512 | 1.733 | 0.264 | 0.274 | 0.188 | 0.330 | 14.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 21 | 79 | 76 | 90 | 74 | 58 |
N.S. |
1 | 0.00 | 1.00 | 1.11 | 4.16 | 4.00 | 4.74 | 3.89 | 3.05 |
time (sec) |
N/A | 0.000 | 0.794 | 0.292 | 0.346 | 0.256 | 0.158 | 0.267 | 14.014 |
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 | 24 | 34 | 19 | 18 | 18 | 18 | 15 | 51 | 29 |
N.S. |
1 | 1.42 | 0.79 | 0.75 | 0.75 | 0.75 | 0.62 | 2.12 | 1.21 |
time (sec) |
N/A | 0.187 | 0.078 | 0.076 | 0.250 | 0.254 | 1.880 | 0.271 | 14.007 |
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 | 13 | 11 | 10 | 9 | 12 | 7 | 9 | 9 |
N.S. |
1 | 0.81 | 0.69 | 0.62 | 0.56 | 0.75 | 0.44 | 0.56 | 0.56 |
time (sec) |
N/A | 0.140 | 0.001 | 0.021 | 0.185 | 0.234 | 0.028 | 0.265 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 93 | 48 | 46 | 2490 | 45 | 0 | 0 | 1132 |
N.S. |
1 | 3.21 | 1.66 | 1.59 | 85.86 | 1.55 | 0.00 | 0.00 | 39.03 |
time (sec) |
N/A | 10.629 | 0.474 | 58.472 | 0.466 | 0.256 | 0.000 | 0.000 | 14.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 16 | 17 | 48 | 48 | 48 | 101 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 3.00 | 3.00 | 3.00 | 6.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.160 | 0.640 | 0.241 | 0.240 | 0.090 | 0.285 | 0.000 |
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 | 15 | 16 | 26 | 26 | 14 | 15 | 33 |
N.S. |
1 | 0.00 | 0.71 | 0.76 | 1.24 | 1.24 | 0.67 | 0.71 | 1.57 |
time (sec) |
N/A | 0.000 | 0.162 | 0.510 | 0.224 | 0.250 | 0.066 | 0.274 | 13.388 |
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 | 13 | 0 | 13 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.62 | 0.85 | 0.85 |
time (sec) |
N/A | 0.000 | 0.155 | 0.070 | 0.227 | 0.266 | 0.087 | 0.286 | 13.124 |