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 | 6 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 0.33 | 0.33 | 0.50 | 0.33 | 0.33 | 0.33 | 0.50 | 0.33 |
time (sec) |
N/A | 0.116 | 0.000 | 0.011 | 0.210 | 0.230 | 0.051 | 0.267 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 59 | 64 | 82 | 79 | 61 | 0 | 103 |
N.S. |
1 | 0.00 | 2.27 | 2.46 | 3.15 | 3.04 | 2.35 | 0.00 | 3.96 |
time (sec) |
N/A | 0.000 | 0.306 | 5.618 | 0.359 | 0.251 | 0.412 | 0.000 | 15.159 |
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 | 19 | 19 | 22 | 27 | 26 | 26 | 26 | 20 |
N.S. |
1 | 0.79 | 0.79 | 0.92 | 1.12 | 1.08 | 1.08 | 1.08 | 0.83 |
time (sec) |
N/A | 0.286 | 0.021 | 0.083 | 0.200 | 0.238 | 0.228 | 0.268 | 0.117 |
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 | 43 | 44 | 43 | 42 | 44 | 58 | 0 |
N.S. |
1 | 0.00 | 1.30 | 1.33 | 1.30 | 1.27 | 1.33 | 1.76 | 0.00 |
time (sec) |
N/A | 0.000 | 0.151 | 3.844 | 0.353 | 0.250 | 0.551 | 0.323 | 0.000 |
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 | 24 | 109 | 88 | 29 | 94 | 92 | 102 | 99 | 138 |
N.S. |
1 | 4.54 | 3.67 | 1.21 | 3.92 | 3.83 | 4.25 | 4.12 | 5.75 |
time (sec) |
N/A | 0.357 | 0.046 | 0.486 | 0.219 | 0.249 | 0.423 | 0.272 | 15.446 |
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 | 31 | 25 | 25 | 23 | 24 | 22 | 17 | 24 | 22 |
N.S. |
1 | 0.81 | 0.81 | 0.74 | 0.77 | 0.71 | 0.55 | 0.77 | 0.71 |
time (sec) |
N/A | 0.511 | 0.058 | 0.266 | 0.336 | 0.248 | 0.122 | 0.291 | 16.506 |
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 | 30 | 0 | 39 | 40 | 58 | 39 | 36 | 45 | 270 |
N.S. |
1 | 0.00 | 1.30 | 1.33 | 1.93 | 1.30 | 1.20 | 1.50 | 9.00 |
time (sec) |
N/A | 0.000 | 0.125 | 13.569 | 0.314 | 0.266 | 0.254 | 5.894 | 15.907 |
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 | 16 | 14 | 14 | 17 | 16 | 16 | 14 | 72 | 13 |
N.S. |
1 | 0.88 | 0.88 | 1.06 | 1.00 | 1.00 | 0.88 | 4.50 | 0.81 |
time (sec) |
N/A | 0.422 | 0.132 | 1.973 | 0.249 | 0.238 | 0.122 | 0.286 | 16.440 |
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 | 29 | 30 | 28 | 28 | 27 | 34 | 27 |
N.S. |
1 | 0.00 | 1.07 | 1.11 | 1.04 | 1.04 | 1.00 | 1.26 | 1.00 |
time (sec) |
N/A | 0.000 | 0.280 | 31.996 | 0.338 | 0.252 | 0.096 | 0.279 | 15.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 18 | 47 | 43 | 21 | 46 | 46 | 22 |
N.S. |
1 | 0.00 | 1.06 | 2.76 | 2.53 | 1.24 | 2.71 | 2.71 | 1.29 |
time (sec) |
N/A | 0.000 | 0.122 | 1.969 | 0.321 | 0.252 | 0.367 | 0.373 | 15.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 158 | 60 | 26 | 512 | 26 | 22 | 149 | 26 |
N.S. |
1 | 7.18 | 2.73 | 1.18 | 23.27 | 1.18 | 1.00 | 6.77 | 1.18 |
time (sec) |
N/A | 0.671 | 0.049 | 2.077 | 0.372 | 0.247 | 0.136 | 0.367 | 1.332 |
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 | 49 | 31 | 32 | 28 | 32 | 32 | 27 |
N.S. |
1 | 0.00 | 1.81 | 1.15 | 1.19 | 1.04 | 1.19 | 1.19 | 1.00 |
time (sec) |
N/A | 0.000 | 0.682 | 0.171 | 0.345 | 0.262 | 0.093 | 0.275 | 15.965 |
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 | 13 | 13 | 13 | 12 | 12 | 14 | 12 | 12 |
N.S. |
1 | 0.54 | 0.54 | 0.54 | 0.50 | 0.50 | 0.58 | 0.50 | 0.50 |
time (sec) |
N/A | 0.163 | 0.006 | 0.154 | 0.204 | 0.252 | 0.070 | 0.274 | 0.053 |
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 | 9 | 9 | 9 | 8 | 17 | 7 | 8 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.89 | 0.78 | 0.89 | 0.78 | 0.78 |
time (sec) |
N/A | 0.149 | 0.004 | 0.068 | 0.209 | 0.248 | 0.065 | 0.271 | 15.651 |
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 | 31 | 0 | 37 | 25 | 44 | 33 | 27 | 0 | 26 |
N.S. |
1 | 0.00 | 1.19 | 0.81 | 1.42 | 1.06 | 0.87 | 0.00 | 0.84 |
time (sec) |
N/A | 0.000 | 0.839 | 2.313 | 0.335 | 0.235 | 0.312 | 0.000 | 15.751 |
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 | 18 | 42 | 42 | 42 | 41 | 41 | 41 | 41 | 41 |
N.S. |
1 | 2.33 | 2.33 | 2.33 | 2.28 | 2.28 | 2.28 | 2.28 | 2.28 |
time (sec) |
N/A | 0.164 | 0.014 | 0.066 | 0.206 | 0.242 | 0.046 | 0.264 | 15.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 23 | 30 | 24 | 95 | 27 | 24 | 0 | 0 |
N.S. |
1 | 0.82 | 1.07 | 0.86 | 3.39 | 0.96 | 0.86 | 0.00 | 0.00 |
time (sec) |
N/A | 2.292 | 0.543 | 4.549 | 0.358 | 0.255 | 2.596 | 0.000 | 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 | 26 | 0 | 21 | 17 | 16 | 16 | 20 | 16 | 22 |
N.S. |
1 | 0.00 | 0.81 | 0.65 | 0.62 | 0.62 | 0.77 | 0.62 | 0.85 |
time (sec) |
N/A | 0.000 | 0.298 | 1.220 | 0.261 | 0.252 | 0.095 | 0.273 | 16.678 |
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 | 21 | 28 | 21 | 27 | 35 | 22 | 31 | 27 | 24 |
N.S. |
1 | 1.33 | 1.00 | 1.29 | 1.67 | 1.05 | 1.48 | 1.29 | 1.14 |
time (sec) |
N/A | 0.236 | 0.147 | 0.513 | 0.247 | 0.256 | 0.086 | 0.268 | 0.086 |
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 | 20 | 21 | 19 | 20 | 18 | 14 | 37 | 29 |
N.S. |
1 | 0.74 | 0.78 | 0.70 | 0.74 | 0.67 | 0.52 | 1.37 | 1.07 |
time (sec) |
N/A | 0.191 | 0.025 | 0.870 | 0.210 | 0.243 | 0.092 | 0.261 | 16.260 |
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 | 34 | 36 | 32 | 28 | 22 | 27 | 31 | 27 | 27 |
N.S. |
1 | 1.06 | 0.94 | 0.82 | 0.65 | 0.79 | 0.91 | 0.79 | 0.79 |
time (sec) |
N/A | 0.226 | 0.009 | 0.793 | 0.208 | 0.239 | 0.078 | 0.275 | 0.714 |
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 | 28 | 24 | 18 | 23 | 20 | 19 | 21 | 17 |
N.S. |
1 | 1.00 | 0.86 | 0.64 | 0.82 | 0.71 | 0.68 | 0.75 | 0.61 |
time (sec) |
N/A | 0.679 | 0.156 | 0.882 | 0.248 | 0.253 | 0.141 | 0.268 | 16.504 |
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 | 19 | 19 | 19 | 18 | 18 | 102 | 18 | 18 |
N.S. |
1 | 0.70 | 0.70 | 0.70 | 0.67 | 0.67 | 3.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.676 | 0.117 | 0.887 | 0.237 | 0.262 | 0.214 | 0.265 | 16.883 |
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 | 7 | 7 | 8 | 7 | 9 | 5 | 7 | 7 |
N.S. |
1 | 0.54 | 0.54 | 0.62 | 0.54 | 0.69 | 0.38 | 0.54 | 0.54 |
time (sec) |
N/A | 0.133 | 0.001 | 0.060 | 0.209 | 0.264 | 0.036 | 0.267 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 69 | 25 | 49 | 62 | 46 | 34 | 33 | 0 |
N.S. |
1 | 2.56 | 0.93 | 1.81 | 2.30 | 1.70 | 1.26 | 1.22 | 0.00 |
time (sec) |
N/A | 2.572 | 0.396 | 0.220 | 0.269 | 0.264 | 0.190 | 0.287 | 0.000 |
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 | 24 | 0 | 32 | 35 | 0 | 32 | 34 | 34 | 35 |
N.S. |
1 | 0.00 | 1.33 | 1.46 | 0.00 | 1.33 | 1.42 | 1.42 | 1.46 |
time (sec) |
N/A | 0.000 | 0.113 | 5.980 | 0.000 | 0.241 | 0.662 | 0.841 | 16.134 |
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 | 23 | 21 | 18 | 19 | 17 | 17 | 22 | 17 |
N.S. |
1 | 0.85 | 0.78 | 0.67 | 0.70 | 0.63 | 0.63 | 0.81 | 0.63 |
time (sec) |
N/A | 0.212 | 0.010 | 1.531 | 0.211 | 0.231 | 0.054 | 0.264 | 14.720 |
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 | 23 | 51 | 44 | 25 | 108 | 46 | 29 | 46 | 33 |
N.S. |
1 | 2.22 | 1.91 | 1.09 | 4.70 | 2.00 | 1.26 | 2.00 | 1.43 |
time (sec) |
N/A | 0.854 | 0.357 | 0.096 | 0.264 | 0.262 | 0.096 | 0.269 | 0.208 |
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 | 52 | 23 | 23 | 22 | 22 | 24 | 22 | 23 |
N.S. |
1 | 2.17 | 0.96 | 0.96 | 0.92 | 0.92 | 1.00 | 0.92 | 0.96 |
time (sec) |
N/A | 0.232 | 1.256 | 0.505 | 0.280 | 0.249 | 0.084 | 0.276 | 0.152 |
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 | 19 | 19 | 17 | 19 | 19 | 17 | 19 | 19 |
N.S. |
1 | 1.12 | 1.12 | 1.00 | 1.12 | 1.12 | 1.00 | 1.12 | 1.12 |
time (sec) |
N/A | 0.141 | 0.000 | 0.087 | 0.219 | 0.244 | 0.036 | 0.262 | 0.033 |
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 | 15 | 15 | 16 | 15 | 21 | 12 | 17 | 15 |
N.S. |
1 | 0.52 | 0.52 | 0.55 | 0.52 | 0.72 | 0.41 | 0.59 | 0.52 |
time (sec) |
N/A | 0.193 | 0.008 | 1.186 | 0.219 | 0.240 | 0.050 | 0.274 | 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 | 23 | 0 | 21 | 22 | 13 | 13 | 17 | 21 | 21 |
N.S. |
1 | 0.00 | 0.91 | 0.96 | 0.57 | 0.57 | 0.74 | 0.91 | 0.91 |
time (sec) |
N/A | 0.000 | 0.123 | 2.074 | 0.232 | 0.257 | 0.194 | 0.269 | 15.288 |
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 | 18 | 25 | 18 | 32 | 103 | 26 | 24 | 79 | 26 |
N.S. |
1 | 1.39 | 1.00 | 1.78 | 5.72 | 1.44 | 1.33 | 4.39 | 1.44 |
time (sec) |
N/A | 0.461 | 0.046 | 0.510 | 0.326 | 0.243 | 0.197 | 0.302 | 14.410 |
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 | 13 | 15 | 13 | 13 | 13 | 12 | 13 | 12 |
N.S. |
1 | 0.57 | 0.65 | 0.57 | 0.57 | 0.57 | 0.52 | 0.57 | 0.52 |
time (sec) |
N/A | 0.128 | 0.001 | 0.143 | 0.207 | 0.249 | 0.021 | 0.266 | 13.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 35 | 27 | 34 | 0 | 44 | 73 | 44 | 27 |
N.S. |
1 | 1.46 | 1.12 | 1.42 | 0.00 | 1.83 | 3.04 | 1.83 | 1.12 |
time (sec) |
N/A | 0.846 | 0.311 | 0.230 | 0.000 | 0.248 | 0.126 | 0.276 | 0.499 |
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 | 15 | 15 | 19 | 24 | 18 | 15 | 18 | 18 |
N.S. |
1 | 0.75 | 0.75 | 0.95 | 1.20 | 0.90 | 0.75 | 0.90 | 0.90 |
time (sec) |
N/A | 0.306 | 0.051 | 4.688 | 0.541 | 0.240 | 0.084 | 0.280 | 13.351 |
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 | 24 | 25 | 27 | 25 | 24 | 31 | 25 | 23 |
N.S. |
1 | 1.04 | 1.09 | 1.17 | 1.09 | 1.04 | 1.35 | 1.09 | 1.00 |
time (sec) |
N/A | 0.179 | 0.012 | 0.392 | 0.206 | 0.237 | 1.026 | 0.271 | 0.248 |
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 | 31 | 0 | 31 | 33 | 28 | 100 | 29 | 0 | 60 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 0.90 | 3.23 | 0.94 | 0.00 | 1.94 |
time (sec) |
N/A | 0.000 | 0.683 | 9.720 | 0.377 | 0.273 | 15.362 | 0.000 | 14.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 111 | 19 | 15 | 97 | 15 | 15 | 49 | 14 |
N.S. |
1 | 5.29 | 0.90 | 0.71 | 4.62 | 0.71 | 0.71 | 2.33 | 0.67 |
time (sec) |
N/A | 0.311 | 0.099 | 0.338 | 0.308 | 0.255 | 0.065 | 0.260 | 13.707 |
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 | 17 | 17 | 17 | 22 | 17 | 18 |
N.S. |
1 | 0.89 | 0.89 | 0.94 | 0.94 | 0.94 | 1.22 | 0.94 | 1.00 |
time (sec) |
N/A | 0.299 | 0.067 | 1.107 | 0.228 | 0.243 | 0.061 | 0.273 | 13.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 56 | 147 | 370 | 157 | 158 | 0 | 549 |
N.S. |
1 | 0.00 | 1.87 | 4.90 | 12.33 | 5.23 | 5.27 | 0.00 | 18.30 |
time (sec) |
N/A | 0.000 | 0.787 | 5.444 | 0.855 | 0.249 | 0.663 | 0.000 | 14.181 |
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 | 23 | 21 | 21 | 30 | 25 | 31 | 28 | 20 |
N.S. |
1 | 0.92 | 0.84 | 0.84 | 1.20 | 1.00 | 1.24 | 1.12 | 0.80 |
time (sec) |
N/A | 0.271 | 0.010 | 0.253 | 0.213 | 0.241 | 0.255 | 0.273 | 0.146 |
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 | 36 | 24 | 21 | 44 | 27 | 17 | 32 | 26 |
N.S. |
1 | 1.64 | 1.09 | 0.95 | 2.00 | 1.23 | 0.77 | 1.45 | 1.18 |
time (sec) |
N/A | 0.345 | 0.108 | 0.218 | 0.249 | 0.251 | 0.042 | 0.281 | 13.385 |
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 | 30 | 30 | 28 | 27 | 30 | 18 |
N.S. |
1 | 1.36 | 1.36 | 1.36 | 1.36 | 1.27 | 1.23 | 1.36 | 0.82 |
time (sec) |
N/A | 0.367 | 0.087 | 1.074 | 0.241 | 0.238 | 0.144 | 0.267 | 13.841 |
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 | 8 | 6 | 6 | 7 | 6 | 6 | 8 | 7 | 6 |
N.S. |
1 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 | 1.00 | 0.88 | 0.75 |
time (sec) |
N/A | 0.155 | 0.007 | 0.386 | 0.202 | 0.246 | 0.051 | 0.260 | 13.475 |
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 | 36 | 20 | 17 | 20 | 21 | 22 | 21 | 21 |
N.S. |
1 | 1.33 | 0.74 | 0.63 | 0.74 | 0.78 | 0.81 | 0.78 | 0.78 |
time (sec) |
N/A | 0.161 | 0.007 | 0.125 | 0.205 | 0.247 | 0.143 | 0.268 | 13.468 |
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 | 19 | 22 | 24 | 25 | 24 | 23 | 22 | 0 | 27 |
N.S. |
1 | 1.16 | 1.26 | 1.32 | 1.26 | 1.21 | 1.16 | 0.00 | 1.42 |
time (sec) |
N/A | 0.402 | 0.361 | 0.463 | 0.380 | 0.257 | 0.135 | 0.000 | 13.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 68 | 264 | 233 | 124 | 100 | 0 | 0 |
N.S. |
1 | 0.00 | 2.19 | 8.52 | 7.52 | 4.00 | 3.23 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.178 | 10.016 | 0.368 | 0.269 | 0.385 | 0.000 | 0.000 |
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 | 26 | 0 | 30 | 35 | 31 | 39 | 36 | 0 | 41 |
N.S. |
1 | 0.00 | 1.15 | 1.35 | 1.19 | 1.50 | 1.38 | 0.00 | 1.58 |
time (sec) |
N/A | 0.000 | 5.119 | 1.478 | 0.401 | 0.254 | 0.218 | 0.000 | 13.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 24 | 23 | 27 | 0 | 32 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 0.88 | 1.04 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.000 | 0.698 | 17.173 | 0.371 | 0.255 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 26 | 26 | 83 | 83 | 63 | 73 | 83 | 67 |
N.S. |
1 | 0.87 | 0.87 | 2.77 | 2.77 | 2.10 | 2.43 | 2.77 | 2.23 |
time (sec) |
N/A | 0.487 | 0.054 | 5.262 | 0.326 | 0.274 | 0.290 | 0.291 | 13.746 |
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 | 24 | 20 | 18 | 17 | 26 | 17 | 17 | 17 |
N.S. |
1 | 1.04 | 0.87 | 0.78 | 0.74 | 1.13 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 0.255 | 0.017 | 0.157 | 0.202 | 0.250 | 0.059 | 0.256 | 0.090 |
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 | 26 | 26 | 21 | 25 | 21 | 20 | 21 | 21 |
N.S. |
1 | 1.04 | 1.04 | 0.84 | 1.00 | 0.84 | 0.80 | 0.84 | 0.84 |
time (sec) |
N/A | 0.188 | 0.146 | 0.136 | 0.215 | 0.250 | 0.107 | 0.258 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | F(-1) | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 35 | 79 | 60 | 78 | 0 | 0 | 129 |
N.S. |
1 | 0.00 | 0.95 | 2.14 | 1.62 | 2.11 | 0.00 | 0.00 | 3.49 |
time (sec) |
N/A | 0.000 | 1.872 | 57.589 | 0.320 | 0.271 | 0.000 | 0.000 | 14.620 |
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 | 12 | 12 | 11 | 10 | 10 | 8 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.92 | 0.83 |
time (sec) |
N/A | 0.139 | 0.004 | 0.705 | 0.206 | 0.248 | 0.042 | 0.270 | 13.896 |
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 | 14 | 39 | 39 | 39 | 37 | 35 | 37 | 37 | 26 |
N.S. |
1 | 2.79 | 2.79 | 2.79 | 2.64 | 2.50 | 2.64 | 2.64 | 1.86 |
time (sec) |
N/A | 0.208 | 0.004 | 0.179 | 0.206 | 0.245 | 0.107 | 0.260 | 13.535 |
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 | 21 | 19 | 26 | 34 | 34 | 27 | 25 |
N.S. |
1 | 1.42 | 0.88 | 0.79 | 1.08 | 1.42 | 1.42 | 1.12 | 1.04 |
time (sec) |
N/A | 0.171 | 0.015 | 0.929 | 0.198 | 0.241 | 0.082 | 0.260 | 0.084 |
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 | 18 | 0 | 15 | 30 | 38 | 29 | 20 | 29 | 14 |
N.S. |
1 | 0.00 | 0.83 | 1.67 | 2.11 | 1.61 | 1.11 | 1.61 | 0.78 |
time (sec) |
N/A | 0.000 | 0.025 | 0.144 | 0.343 | 0.247 | 0.126 | 0.265 | 13.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 95 | 96 | 93 | 93 | 0 | 95 | 0 |
N.S. |
1 | 0.00 | 3.17 | 3.20 | 3.10 | 3.10 | 0.00 | 3.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.457 | 11.302 | 0.404 | 0.291 | 0.000 | 0.840 | 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 | 22 | 21 | 21 | 15 | 14 | 15 | 15 | 15 | 14 |
N.S. |
1 | 0.95 | 0.95 | 0.68 | 0.64 | 0.68 | 0.68 | 0.68 | 0.64 |
time (sec) |
N/A | 0.170 | 0.028 | 0.119 | 0.207 | 0.244 | 0.072 | 0.265 | 0.069 |
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 | 22 | 0 | 21 | 22 | 32 | 21 | 17 | 21 | 349 |
N.S. |
1 | 0.00 | 0.95 | 1.00 | 1.45 | 0.95 | 0.77 | 0.95 | 15.86 |
time (sec) |
N/A | 0.000 | 0.061 | 2.897 | 0.359 | 0.255 | 0.097 | 0.320 | 14.064 |
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 | 18 | 56 | 56 | 45 | 68 | 44 | 60 | 44 | 44 |
N.S. |
1 | 3.11 | 3.11 | 2.50 | 3.78 | 2.44 | 3.33 | 2.44 | 2.44 |
time (sec) |
N/A | 0.713 | 0.141 | 0.230 | 0.222 | 0.250 | 0.152 | 0.263 | 14.163 |
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 | 13 | 13 | 12 | 13 | 13 | 12 | 14 | 11 |
N.S. |
1 | 0.54 | 0.54 | 0.50 | 0.54 | 0.54 | 0.50 | 0.58 | 0.46 |
time (sec) |
N/A | 0.153 | 0.006 | 0.023 | 0.205 | 0.243 | 0.046 | 0.264 | 0.063 |
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 | 33 | 0 | 29 | 39 | 42 | 43 | 39 | 0 | 69 |
N.S. |
1 | 0.00 | 0.88 | 1.18 | 1.27 | 1.30 | 1.18 | 0.00 | 2.09 |
time (sec) |
N/A | 0.000 | 0.289 | 5.497 | 0.353 | 0.267 | 0.154 | 0.000 | 14.130 |
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 | 19 | 38 | 20 | 21 | 72 | 25 | 24 | 34 | 22 |
N.S. |
1 | 2.00 | 1.05 | 1.11 | 3.79 | 1.32 | 1.26 | 1.79 | 1.16 |
time (sec) |
N/A | 0.271 | 0.216 | 0.147 | 0.223 | 0.256 | 0.071 | 0.262 | 0.076 |
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 | 34 | 0 | 33 | 30 | 40 | 62 | 49 | 52 | 100 |
N.S. |
1 | 0.00 | 0.97 | 0.88 | 1.18 | 1.82 | 1.44 | 1.53 | 2.94 |
time (sec) |
N/A | 0.000 | 0.095 | 2.298 | 0.385 | 0.277 | 0.177 | 0.301 | 14.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F(-2) | B | B | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 66 | 0 | 65 | 66 | 0 | 131 |
N.S. |
1 | 0.00 | 0.92 | 2.54 | 0.00 | 2.50 | 2.54 | 0.00 | 5.04 |
time (sec) |
N/A | 0.000 | 0.345 | 2.925 | 0.000 | 0.264 | 2.425 | 0.000 | 0.393 |
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 | 27 | 0 | 24 | 22 | 81 | 46 | 17 | 46 | 21 |
N.S. |
1 | 0.00 | 0.89 | 0.81 | 3.00 | 1.70 | 0.63 | 1.70 | 0.78 |
time (sec) |
N/A | 0.000 | 0.068 | 0.147 | 0.254 | 0.278 | 0.194 | 0.269 | 14.066 |
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 | 24 | 0 | 24 | 22 | 0 | 21 | 19 | 0 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.00 | 0.88 | 0.79 | 0.00 | 0.92 |
time (sec) |
N/A | 0.000 | 0.333 | 1.688 | 0.000 | 0.250 | 16.522 | 0.000 | 14.833 |
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 | 39 | 30 | 27 | 26 | 35 | 24 | 26 | 26 |
N.S. |
1 | 1.30 | 1.00 | 0.90 | 0.87 | 1.17 | 0.80 | 0.87 | 0.87 |
time (sec) |
N/A | 0.231 | 0.155 | 0.346 | 0.204 | 0.259 | 0.265 | 0.260 | 14.323 |
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 | 20 | 42 | 34 | 22 | 23 | 24 | 24 | 0 | 21 |
N.S. |
1 | 2.10 | 1.70 | 1.10 | 1.15 | 1.20 | 1.20 | 0.00 | 1.05 |
time (sec) |
N/A | 0.451 | 0.222 | 1.160 | 0.358 | 0.241 | 0.125 | 0.000 | 14.665 |
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 | 36 | 17 | 17 | 16 | 15 | 15 | 17 | 17 | 15 |
N.S. |
1 | 0.47 | 0.47 | 0.44 | 0.42 | 0.42 | 0.47 | 0.47 | 0.42 |
time (sec) |
N/A | 0.205 | 0.008 | 0.861 | 0.214 | 0.234 | 0.055 | 0.266 | 14.279 |
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 | 26 | 19 | 19 | 21 | 17 | 17 | 17 | 19 |
N.S. |
1 | 1.30 | 0.95 | 0.95 | 1.05 | 0.85 | 0.85 | 0.85 | 0.95 |
time (sec) |
N/A | 0.156 | 0.052 | 0.072 | 0.201 | 0.247 | 0.050 | 0.257 | 14.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 84 | 61 | 19 | 50 | 24 | 14 | 23 | 18 |
N.S. |
1 | 3.65 | 2.65 | 0.83 | 2.17 | 1.04 | 0.61 | 1.00 | 0.78 |
time (sec) |
N/A | 0.618 | 0.198 | 0.215 | 0.335 | 0.245 | 0.077 | 0.259 | 14.214 |
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 | 26 | 0 | 24 | 19 | 18 | 18 | 17 | 0 | 20 |
N.S. |
1 | 0.00 | 0.92 | 0.73 | 0.69 | 0.69 | 0.65 | 0.00 | 0.77 |
time (sec) |
N/A | 0.000 | 1.727 | 0.583 | 0.479 | 0.255 | 2.652 | 0.000 | 15.084 |
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 | 26 | 0 | 29 | 28 | 31 | 29 | 46 | 50 | 27 |
N.S. |
1 | 0.00 | 1.12 | 1.08 | 1.19 | 1.12 | 1.77 | 1.92 | 1.04 |
time (sec) |
N/A | 0.000 | 1.340 | 6.043 | 0.336 | 0.265 | 13.174 | 0.344 | 14.712 |
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 | 37 | 24 | 20 | 679 | 20 | 20 | 22 | 18 |
N.S. |
1 | 1.95 | 1.26 | 1.05 | 35.74 | 1.05 | 1.05 | 1.16 | 0.95 |
time (sec) |
N/A | 0.352 | 0.104 | 0.807 | 0.227 | 0.250 | 0.085 | 0.276 | 0.302 |
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 | 24 | 27 | 27 | 24 | 116 | 20 | 22 | 20 | 35 |
N.S. |
1 | 1.12 | 1.12 | 1.00 | 4.83 | 0.83 | 0.92 | 0.83 | 1.46 |
time (sec) |
N/A | 0.231 | 0.098 | 0.127 | 0.327 | 0.257 | 0.170 | 0.296 | 16.349 |
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 | 36 | 25 | 42 | 43 | 24 | 43 | 24 |
N.S. |
1 | 0.00 | 1.38 | 0.96 | 1.62 | 1.65 | 0.92 | 1.65 | 0.92 |
time (sec) |
N/A | 0.000 | 1.158 | 0.412 | 0.332 | 0.242 | 0.086 | 0.267 | 0.724 |
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 | 20 | 0 | 20 | 21 | 26 | 26 | 20 | 55 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 1.30 | 1.30 | 1.00 | 2.75 | 1.00 |
time (sec) |
N/A | 0.000 | 0.359 | 1.384 | 0.258 | 0.258 | 0.069 | 0.266 | 15.500 |
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 | 37 | 0 | 59 | 55 | 83 | 202 | 51 | 83 | 343 |
N.S. |
1 | 0.00 | 1.59 | 1.49 | 2.24 | 5.46 | 1.38 | 2.24 | 9.27 |
time (sec) |
N/A | 0.000 | 0.220 | 188.224 | 0.337 | 0.256 | 0.421 | 0.690 | 16.878 |
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 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 |
N.S. |
1 | 0.40 | 0.40 | 0.50 | 0.40 | 0.40 | 0.30 | 0.50 | 0.40 |
time (sec) |
N/A | 0.129 | 0.000 | 0.050 | 0.198 | 0.233 | 0.026 | 0.253 | 0.002 |
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 | 28 | 0 | 24 | 24 | 0 | 26 | 19 | 0 | 21 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 0.00 | 0.93 | 0.68 | 0.00 | 0.75 |
time (sec) |
N/A | 0.000 | 0.337 | 0.391 | 0.000 | 0.286 | 0.127 | 0.000 | 15.972 |
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 | 27 | 0 | 25 | 25 | 0 | 24 | 20 | 25 | 41 |
N.S. |
1 | 0.00 | 0.93 | 0.93 | 0.00 | 0.89 | 0.74 | 0.93 | 1.52 |
time (sec) |
N/A | 0.000 | 0.493 | 1.234 | 0.000 | 0.245 | 0.171 | 0.305 | 13.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | A | F(-2) | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 35 | 28 | 0 | 57 | 19 | 0 | 0 |
N.S. |
1 | 0.00 | 1.21 | 0.97 | 0.00 | 1.97 | 0.66 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.313 | 13.464 | 0.000 | 0.252 | 0.935 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 33 | 28 | 69 | 27 | 0 | 29 | 30 |
N.S. |
1 | 0.00 | 1.32 | 1.12 | 2.76 | 1.08 | 0.00 | 1.16 | 1.20 |
time (sec) |
N/A | 0.000 | 0.066 | 1.516 | 0.491 | 0.257 | 0.000 | 0.359 | 15.290 |
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 | 20 | 17 | 16 | 16 | 17 | 20 | 110 |
N.S. |
1 | 0.00 | 1.11 | 0.94 | 0.89 | 0.89 | 0.94 | 1.11 | 6.11 |
time (sec) |
N/A | 0.000 | 0.146 | 4.344 | 0.322 | 0.275 | 0.078 | 0.271 | 14.214 |
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 | 20 | 18 | 16 | 17 | 17 | 15 | 17 | 18 |
N.S. |
1 | 1.33 | 1.20 | 1.07 | 1.13 | 1.13 | 1.00 | 1.13 | 1.20 |
time (sec) |
N/A | 0.152 | 0.000 | 0.167 | 0.199 | 0.262 | 0.023 | 0.277 | 0.032 |
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 | 34 | 40 | 39 | 57 | 54 | 49 | 110 | 54 | 45 |
N.S. |
1 | 1.18 | 1.15 | 1.68 | 1.59 | 1.44 | 3.24 | 1.59 | 1.32 |
time (sec) |
N/A | 4.227 | 0.191 | 5.582 | 0.332 | 0.284 | 0.599 | 0.375 | 14.154 |
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 | 30 | 0 | 21 | 22 | 58 | 58 | 41 | 66 | 38 |
N.S. |
1 | 0.00 | 0.70 | 0.73 | 1.93 | 1.93 | 1.37 | 2.20 | 1.27 |
time (sec) |
N/A | 0.000 | 0.174 | 1.257 | 0.215 | 0.283 | 0.095 | 0.283 | 13.588 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 34 | 0 | 42 | 31 | 58 | 60 |
N.S. |
1 | 0.00 | 0.93 | 1.26 | 0.00 | 1.56 | 1.15 | 2.15 | 2.22 |
time (sec) |
N/A | 0.000 | 1.301 | 1.546 | 0.000 | 0.282 | 0.157 | 0.408 | 13.567 |
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 | 20 | 0 | 20 | 16 | 16 | 16 | 19 | 0 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.95 | 0.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.611 | 2.441 | 0.424 | 0.285 | 3.351 | 0.000 | 14.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 172 | 36 | 58 | 46 | 40 | 36 | 52 | 43 |
N.S. |
1 | 5.06 | 1.06 | 1.71 | 1.35 | 1.18 | 1.06 | 1.53 | 1.26 |
time (sec) |
N/A | 0.819 | 0.534 | 2.937 | 0.317 | 0.269 | 0.366 | 0.282 | 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 | 26 | 20 | 20 | 17 | 16 | 17 | 12 | 16 | 17 |
N.S. |
1 | 0.77 | 0.77 | 0.65 | 0.62 | 0.65 | 0.46 | 0.62 | 0.65 |
time (sec) |
N/A | 0.151 | 0.004 | 0.108 | 0.195 | 0.266 | 0.031 | 0.257 | 0.046 |
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 | 32 | 55 | 49 | 46 | 45 | 45 | 44 | 45 | 49 |
N.S. |
1 | 1.72 | 1.53 | 1.44 | 1.41 | 1.41 | 1.38 | 1.41 | 1.53 |
time (sec) |
N/A | 0.629 | 2.701 | 1.118 | 0.365 | 0.293 | 0.146 | 0.268 | 14.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 774 | 46 | 35 | 34 | 37 | 32 | 55 | 24 |
N.S. |
1 | 25.80 | 1.53 | 1.17 | 1.13 | 1.23 | 1.07 | 1.83 | 0.80 |
time (sec) |
N/A | 2.197 | 2.728 | 1.112 | 0.314 | 0.265 | 0.079 | 0.263 | 15.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 35 | 0 | 51 | 31 | 0 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.75 | 0.00 | 2.55 | 1.55 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.614 | 26.421 | 0.000 | 0.270 | 0.372 | 0.000 | 16.074 |
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 | 15 | 1914 | 13 | 130 | 1620 | 240 | 357 | 448 | 448 |
N.S. |
1 | 127.60 | 0.87 | 8.67 | 108.00 | 16.00 | 23.80 | 29.87 | 29.87 |
time (sec) |
N/A | 2.530 | 0.068 | 0.473 | 0.239 | 0.271 | 0.586 | 0.347 | 20.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 13 | 77 | 54 | 411 | 65 | 58 | 65 | 61 |
N.S. |
1 | 0.81 | 4.81 | 3.38 | 25.69 | 4.06 | 3.62 | 4.06 | 3.81 |
time (sec) |
N/A | 0.400 | 2.286 | 2.350 | 0.220 | 0.259 | 0.108 | 0.275 | 16.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 3616 | 33 | 34 | 66 | 34 | 31 | 0 | 30 |
N.S. |
1 | 106.35 | 0.97 | 1.00 | 1.94 | 1.00 | 0.91 | 0.00 | 0.88 |
time (sec) |
N/A | 20.641 | 0.105 | 3.320 | 0.411 | 0.287 | 0.255 | 0.000 | 18.231 |