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 | Reduce | Mupad | |
grade |
N/A | C | C | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 263 | 200 | 41 | 173 | 41 | 58 | 58 | 56 | 40 |
N.S. |
1 | 9.07 | 6.90 | 1.41 | 5.97 | 1.41 | 2.00 | 2.00 | 1.93 | 1.38 |
time (sec) |
N/A | 1.213 | 0.280 | 0.575 | 0.163 | 0.105 | 0.302 | 0.117 | 0.224 | 2.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 30 | 30 | 31 | 29 | 32 | 29 | 34 | 31 | 30 |
N.S. |
1 | 1.36 | 1.36 | 1.41 | 1.32 | 1.45 | 1.32 | 1.55 | 1.41 | 1.36 |
time (sec) |
N/A | 0.971 | 0.020 | 0.090 | 0.026 | 0.085 | 0.934 | 0.115 | 0.220 | 2.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 22 | 22 | 23 | 22 | 28 | 24 | 27 | 27 | 23 |
N.S. |
1 | 0.85 | 0.85 | 0.88 | 0.85 | 1.08 | 0.92 | 1.04 | 1.04 | 0.88 |
time (sec) |
N/A | 0.419 | 0.017 | 0.138 | 0.038 | 0.087 | 0.093 | 0.113 | 0.240 | 2.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 15 | 21 | 15 | 16 | 20 | 14 | 20 | 21 | 17 |
N.S. |
1 | 0.94 | 1.31 | 0.94 | 1.00 | 1.25 | 0.88 | 1.25 | 1.31 | 1.06 |
time (sec) |
N/A | 0.283 | 1.140 | 0.145 | 0.064 | 0.083 | 0.068 | 0.114 | 0.237 | 2.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 33 | 38 | 249 | 52 | 46 | 58 | 108 | 156 |
N.S. |
1 | 0.00 | 1.57 | 1.81 | 11.86 | 2.48 | 2.19 | 2.76 | 5.14 | 7.43 |
time (sec) |
N/A | 0.000 | 1.115 | 3.001 | 0.262 | 0.078 | 0.138 | 0.564 | 0.237 | 2.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 32 | 24 | 21 | 21 | 21 | 20 | 21 | 31 | 22 |
N.S. |
1 | 1.45 | 1.09 | 0.95 | 0.95 | 0.95 | 0.91 | 0.95 | 1.41 | 1.00 |
time (sec) |
N/A | 0.357 | 0.010 | 0.084 | 0.030 | 0.132 | 0.275 | 0.118 | 0.232 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | B | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 49 | 71 | 51 | 48 | 50 | 123 | 56 |
N.S. |
1 | 0.00 | 0.00 | 1.69 | 2.45 | 1.76 | 1.66 | 1.72 | 4.24 | 1.93 |
time (sec) |
N/A | 0.000 | 0.000 | 0.396 | 0.192 | 0.092 | 0.189 | 0.178 | 50.416 | 2.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 6 | 6 | 7 | 6 | 6 | 3 | 7 | 6 | 6 |
N.S. |
1 | 0.18 | 0.18 | 0.21 | 0.18 | 0.18 | 0.09 | 0.21 | 0.18 | 0.18 |
time (sec) |
N/A | 0.143 | 0.001 | 0.013 | 0.036 | 0.087 | 0.027 | 0.106 | 0.211 | 0.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 16 | 17 | 23 | 23 | 17 | 16 | 16 | 16 |
N.S. |
1 | 0.00 | 0.94 | 1.00 | 1.35 | 1.35 | 1.00 | 0.94 | 0.94 | 0.94 |
time (sec) |
N/A | 0.000 | 0.291 | 0.049 | 0.063 | 0.084 | 0.105 | 0.105 | 0.207 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 20 | 12 | 11 | 0 | 10 | 10 | 0 | 15 | 11 |
N.S. |
1 | 1.54 | 0.92 | 0.85 | 0.00 | 0.77 | 0.77 | 0.00 | 1.15 | 0.85 |
time (sec) |
N/A | 0.288 | 0.043 | 0.101 | 0.000 | 0.074 | 0.086 | 0.000 | 0.233 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 71 | 33 | 35 | 124 | 34 | 29 | 33 | 93 | 251 |
N.S. |
1 | 2.45 | 1.14 | 1.21 | 4.28 | 1.17 | 1.00 | 1.14 | 3.21 | 8.66 |
time (sec) |
N/A | 0.770 | 0.056 | 0.751 | 0.202 | 0.089 | 0.083 | 0.125 | 0.230 | 6.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 34 | 32 | 36 | 29 | 29 | 57 | 33 | 29 |
N.S. |
1 | 0.00 | 1.10 | 1.03 | 1.16 | 0.94 | 0.94 | 1.84 | 1.06 | 0.94 |
time (sec) |
N/A | 0.000 | 0.075 | 1.129 | 0.068 | 0.090 | 0.171 | 0.319 | 0.215 | 2.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 30 | 23 | 32 | 22 | 24 | 45 | 29 | 0 |
N.S. |
1 | 0.00 | 1.30 | 1.00 | 1.39 | 0.96 | 1.04 | 1.96 | 1.26 | 0.00 |
time (sec) |
N/A | 0.000 | 0.913 | 0.349 | 0.223 | 0.080 | 0.111 | 0.165 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 15 | 15 | 12 | 15 | 34 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.71 | 0.88 | 2.00 | 1.06 |
time (sec) |
N/A | 0.422 | 0.181 | 0.167 | 0.103 | 0.113 | 0.105 | 0.120 | 52.492 | 2.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 15 | 16 | 97 | 330 | 87 | 109 | 107 | 123 | 99 |
N.S. |
1 | 0.68 | 0.73 | 4.41 | 15.00 | 3.95 | 4.95 | 4.86 | 5.59 | 4.50 |
time (sec) |
N/A | 0.564 | 0.015 | 0.099 | 0.054 | 0.089 | 0.357 | 0.120 | 0.196 | 2.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 27 | 26 | 26 | 22 | 26 | 513 | 26 |
N.S. |
1 | 0.00 | 0.87 | 0.87 | 0.84 | 0.84 | 0.71 | 0.84 | 16.55 | 0.84 |
time (sec) |
N/A | 0.000 | 1.824 | 0.206 | 0.074 | 0.090 | 0.071 | 0.118 | 0.210 | 2.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 51 | 19 | 17 | 27 | 22 | 20 | 27 | 23 | 24 |
N.S. |
1 | 2.22 | 0.83 | 0.74 | 1.17 | 0.96 | 0.87 | 1.17 | 1.00 | 1.04 |
time (sec) |
N/A | 1.307 | 0.114 | 0.159 | 0.084 | 0.082 | 0.062 | 0.115 | 0.196 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 40 | 22 | 38 | 34 | 34 | 51 | 34 | 33 | 19 |
N.S. |
1 | 1.48 | 0.81 | 1.41 | 1.26 | 1.26 | 1.89 | 1.26 | 1.22 | 0.70 |
time (sec) |
N/A | 0.392 | 0.123 | 0.452 | 0.028 | 0.093 | 0.075 | 0.112 | 0.176 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 30 | 27 | 24 | 24 | 37 | 27 | 24 | 47 | 26 |
N.S. |
1 | 1.25 | 1.12 | 1.00 | 1.00 | 1.54 | 1.12 | 1.00 | 1.96 | 1.08 |
time (sec) |
N/A | 0.444 | 0.249 | 0.199 | 0.029 | 0.095 | 0.074 | 0.115 | 0.193 | 0.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 9 | 15 | 10 | 11 | 11 | 10 | 11 | 13 | 11 |
N.S. |
1 | 0.60 | 1.00 | 0.67 | 0.73 | 0.73 | 0.67 | 0.73 | 0.87 | 0.73 |
time (sec) |
N/A | 0.165 | 0.004 | 0.072 | 0.033 | 0.084 | 0.058 | 0.110 | 0.196 | 2.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 51 | 18 | 32 | 0 | 42 | 32 | 54 | 34 | 17 |
N.S. |
1 | 2.83 | 1.00 | 1.78 | 0.00 | 2.33 | 1.78 | 3.00 | 1.89 | 0.94 |
time (sec) |
N/A | 0.607 | 0.300 | 0.425 | 0.000 | 0.090 | 0.172 | 0.111 | 0.200 | 2.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 11 | 11 | 12 | 20 | 11 | 10 | 11 | 11 | 11 |
N.S. |
1 | 0.58 | 0.58 | 0.63 | 1.05 | 0.58 | 0.53 | 0.58 | 0.58 | 0.58 |
time (sec) |
N/A | 0.160 | 0.003 | 0.072 | 0.024 | 0.097 | 0.059 | 0.116 | 0.194 | 2.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 64 | 24 | 59 | 57 | 0 | 30 | 30 | 186 |
N.S. |
1 | 0.00 | 1.83 | 0.69 | 1.69 | 1.63 | 0.00 | 0.86 | 0.86 | 5.31 |
time (sec) |
N/A | 0.000 | 0.264 | 0.693 | 0.159 | 0.093 | 0.000 | 0.122 | 0.216 | 26.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 25 | 29 | 72 | 22 | 0 | 28 | 22 |
N.S. |
1 | 0.00 | 0.91 | 1.09 | 1.26 | 3.13 | 0.96 | 0.00 | 1.22 | 0.96 |
time (sec) |
N/A | 0.000 | 0.078 | 0.170 | 0.120 | 0.089 | 0.100 | 0.000 | 0.205 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 48 | 39 | 48 | 50 | 51 | 53 | 55 | 48 |
N.S. |
1 | 0.00 | 1.33 | 1.08 | 1.33 | 1.39 | 1.42 | 1.47 | 1.53 | 1.33 |
time (sec) |
N/A | 0.000 | 0.058 | 1.151 | 0.196 | 0.087 | 0.217 | 0.203 | 0.941 | 2.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 35 | 21 | 21 | 47 | 33 | 48 | 37 | 36 | 23 |
N.S. |
1 | 1.40 | 0.84 | 0.84 | 1.88 | 1.32 | 1.92 | 1.48 | 1.44 | 0.92 |
time (sec) |
N/A | 0.226 | 0.006 | 0.156 | 0.039 | 0.076 | 0.171 | 0.109 | 0.203 | 2.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 14 | 14 | 15 | 15 | 15 | 17 | 14 | 13 |
N.S. |
1 | 1.47 | 0.82 | 0.82 | 0.88 | 0.88 | 0.88 | 1.00 | 0.82 | 0.76 |
time (sec) |
N/A | 0.177 | 0.005 | 0.120 | 0.036 | 0.090 | 0.295 | 0.109 | 0.199 | 2.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 18 | 20 | 23 | 21 | 24 | 23 | 18 | 16 |
N.S. |
1 | 1.29 | 0.86 | 0.95 | 1.10 | 1.00 | 1.14 | 1.10 | 0.86 | 0.76 |
time (sec) |
N/A | 0.194 | 0.024 | 0.092 | 0.031 | 0.086 | 0.074 | 0.113 | 0.214 | 2.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 15 | 15 | 16 | 15 | 15 | 15 | 15 | 17 | 15 |
N.S. |
1 | 0.79 | 0.79 | 0.84 | 0.79 | 0.79 | 0.79 | 0.79 | 0.89 | 0.79 |
time (sec) |
N/A | 0.347 | 0.053 | 0.115 | 0.057 | 0.098 | 0.117 | 0.117 | 0.198 | 2.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 19 | 16 | 15 | 14 | 20 | 14 | 14 | 25 | 14 |
N.S. |
1 | 1.12 | 0.94 | 0.88 | 0.82 | 1.18 | 0.82 | 0.82 | 1.47 | 0.82 |
time (sec) |
N/A | 0.210 | 0.008 | 0.098 | 0.027 | 0.100 | 0.063 | 0.107 | 0.194 | 2.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 38 | 47 | 38 | 68 | 63 | 73 | 34 | 82 | 33 |
N.S. |
1 | 1.52 | 1.88 | 1.52 | 2.72 | 2.52 | 2.92 | 1.36 | 3.28 | 1.32 |
time (sec) |
N/A | 0.476 | 0.038 | 0.261 | 0.048 | 0.099 | 1.596 | 0.124 | 0.186 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 22 | 23 | 23 | 20 | 22 | 22 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.00 | 1.00 | 0.87 | 0.96 | 0.96 | 0.91 |
time (sec) |
N/A | 0.000 | 0.095 | 0.087 | 0.071 | 0.079 | 0.111 | 0.114 | 0.198 | 2.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 61 | 18 | 51 | 49 | 49 | 49 | 49 | 59 | 19 |
N.S. |
1 | 2.90 | 0.86 | 2.43 | 2.33 | 2.33 | 2.33 | 2.33 | 2.81 | 0.90 |
time (sec) |
N/A | 0.584 | 1.809 | 0.634 | 0.038 | 0.084 | 0.070 | 0.113 | 0.211 | 2.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 36 | 30 | 0 | 36 | 32 | 0 | 53 | 77 |
N.S. |
1 | 0.00 | 1.24 | 1.03 | 0.00 | 1.24 | 1.10 | 0.00 | 1.83 | 2.66 |
time (sec) |
N/A | 0.000 | 0.069 | 3.674 | 0.000 | 0.094 | 0.305 | 0.000 | 0.207 | 2.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 45 | 41 | 40 | 76 | 72 | 80 | 103 | 45 | 0 |
N.S. |
1 | 1.41 | 1.28 | 1.25 | 2.38 | 2.25 | 2.50 | 3.22 | 1.41 | 0.00 |
time (sec) |
N/A | 0.885 | 0.065 | 14.006 | 0.184 | 0.088 | 0.571 | 0.132 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 19 | 23 | 114 | 33 | 14 | 35 | 45 | 22 |
N.S. |
1 | 0.00 | 0.59 | 0.72 | 3.56 | 1.03 | 0.44 | 1.09 | 1.41 | 0.69 |
time (sec) |
N/A | 0.000 | 0.098 | 0.203 | 0.113 | 0.089 | 0.072 | 0.123 | 0.192 | 2.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 73 | 67 | 27 | 295 | 26 | 27 | 32 | 68 | 23 |
N.S. |
1 | 3.48 | 3.19 | 1.29 | 14.05 | 1.24 | 1.29 | 1.52 | 3.24 | 1.10 |
time (sec) |
N/A | 0.497 | 0.048 | 0.366 | 0.039 | 0.091 | 0.114 | 0.124 | 0.187 | 3.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 49 | 29 | 25 | 24 | 29 | 24 | 24 | 23 | 22 |
N.S. |
1 | 1.69 | 1.00 | 0.86 | 0.83 | 1.00 | 0.83 | 0.83 | 0.79 | 0.76 |
time (sec) |
N/A | 0.212 | 0.023 | 0.868 | 0.029 | 0.087 | 0.144 | 0.117 | 0.196 | 2.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 56 | 50 | 48 | 49 | 69 | 51 | 45 | 64 | 50 |
N.S. |
1 | 2.00 | 1.79 | 1.71 | 1.75 | 2.46 | 1.82 | 1.61 | 2.29 | 1.79 |
time (sec) |
N/A | 0.423 | 0.024 | 0.158 | 0.039 | 0.076 | 0.330 | 0.107 | 0.207 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 8 | 8 | 9 | 8 | 8 | 8 | 9 | 8 | 8 |
N.S. |
1 | 0.73 | 0.73 | 0.82 | 0.73 | 0.73 | 0.73 | 0.82 | 0.73 | 0.73 |
time (sec) |
N/A | 0.150 | 0.001 | 0.020 | 0.029 | 0.085 | 0.035 | 0.109 | 0.203 | 0.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 24 | 22 | 26 | 20 | 24 | 25 | 27 | 20 |
N.S. |
1 | 0.00 | 1.04 | 0.96 | 1.13 | 0.87 | 1.04 | 1.09 | 1.17 | 0.87 |
time (sec) |
N/A | 0.000 | 4.209 | 0.829 | 0.175 | 0.088 | 0.338 | 0.208 | 0.193 | 2.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 30 | 30 | 0 | 44 | 27 | 0 | 102 | 25 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 0.00 | 1.57 | 0.96 | 0.00 | 3.64 | 0.89 |
time (sec) |
N/A | 0.000 | 0.090 | 0.668 | 0.000 | 0.088 | 0.218 | 0.000 | 42.266 | 2.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 53 | 94 | 111 | 62 | 46 | 172 | 97 | 53 |
N.S. |
1 | 0.00 | 1.39 | 2.47 | 2.92 | 1.63 | 1.21 | 4.53 | 2.55 | 1.39 |
time (sec) |
N/A | 0.000 | 0.154 | 41.904 | 0.173 | 0.100 | 5.920 | 0.173 | 0.208 | 2.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 59 | 59 | 60 | 59 | 65 | 58 | 61 | 67 | 59 |
N.S. |
1 | 2.36 | 2.36 | 2.40 | 2.36 | 2.60 | 2.32 | 2.44 | 2.68 | 2.36 |
time (sec) |
N/A | 2.419 | 0.033 | 0.068 | 0.029 | 0.115 | 0.117 | 0.131 | 0.206 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 68 | 284 | 35 | 29 | 31 | 104 | 29 |
N.S. |
1 | 0.00 | 1.17 | 2.83 | 11.83 | 1.46 | 1.21 | 1.29 | 4.33 | 1.21 |
time (sec) |
N/A | 0.000 | 0.048 | 1.059 | 0.211 | 0.094 | 0.216 | 1.770 | 0.206 | 2.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 29 | 24 | 24 | 34 | 28 | 31 | 28 |
N.S. |
1 | 0.00 | 1.13 | 1.26 | 1.04 | 1.04 | 1.48 | 1.22 | 1.35 | 1.22 |
time (sec) |
N/A | 0.000 | 0.333 | 0.125 | 0.093 | 0.090 | 0.128 | 0.152 | 0.216 | 2.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 246 | 24 | 25 | 43 | 51 | 29 | 59 | 64 | 50 |
N.S. |
1 | 9.11 | 0.89 | 0.93 | 1.59 | 1.89 | 1.07 | 2.19 | 2.37 | 1.85 |
time (sec) |
N/A | 1.509 | 1.578 | 0.196 | 0.096 | 0.087 | 0.100 | 0.120 | 0.210 | 2.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 56 | 60 | 52 | 53 | 53 | 54 | 58 | 60 | 49 |
N.S. |
1 | 1.75 | 1.88 | 1.62 | 1.66 | 1.66 | 1.69 | 1.81 | 1.88 | 1.53 |
time (sec) |
N/A | 0.616 | 0.056 | 0.339 | 0.034 | 0.110 | 4.195 | 0.129 | 0.208 | 2.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 34 | 61 | 94 | 60 | 68 | 132 | 72 | 32 |
N.S. |
1 | 0.00 | 1.17 | 2.10 | 3.24 | 2.07 | 2.34 | 4.55 | 2.48 | 1.10 |
time (sec) |
N/A | 0.000 | 5.040 | 5.113 | 0.188 | 0.095 | 1.186 | 0.124 | 0.212 | 2.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 50 | 0 | 46 | 39 | 0 | 41 | 37 |
N.S. |
1 | 0.00 | 1.00 | 1.61 | 0.00 | 1.48 | 1.26 | 0.00 | 1.32 | 1.19 |
time (sec) |
N/A | 0.000 | 0.159 | 0.105 | 0.000 | 0.088 | 19.339 | 0.000 | 0.220 | 3.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 35 | 32 | 34 | 33 | 31 | 32 | 35 | 32 | 33 |
N.S. |
1 | 1.59 | 1.45 | 1.55 | 1.50 | 1.41 | 1.45 | 1.59 | 1.45 | 1.50 |
time (sec) |
N/A | 0.535 | 0.015 | 0.097 | 0.035 | 0.089 | 0.463 | 0.119 | 0.198 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 23 | 23 | 20 | 21 | 20 | 24 | 0 | 22 | 20 |
N.S. |
1 | 0.92 | 0.92 | 0.80 | 0.84 | 0.80 | 0.96 | 0.00 | 0.88 | 0.80 |
time (sec) |
N/A | 0.359 | 0.023 | 0.157 | 0.116 | 0.089 | 73.394 | 0.000 | 0.216 | 2.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 38 | 37 | 38 | 36 | 29 | 41 | 44 | 36 |
N.S. |
1 | 0.00 | 1.41 | 1.37 | 1.41 | 1.33 | 1.07 | 1.52 | 1.63 | 1.33 |
time (sec) |
N/A | 0.000 | 0.074 | 9.869 | 1.502 | 0.093 | 0.308 | 0.454 | 0.225 | 2.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 24 | 30 | 22 | 22 | 38 | 19 | 19 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 1.25 | 0.92 | 0.92 | 1.58 | 0.79 | 0.79 |
time (sec) |
N/A | 0.000 | 0.101 | 0.978 | 0.155 | 0.085 | 0.174 | 0.124 | 0.215 | 2.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F | A | A | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 32 | 0 | 50 | 26 | 170 | 81 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.07 | 0.00 | 1.67 | 0.87 | 5.67 | 2.70 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.032 | 0.000 | 0.107 | 0.301 | 0.326 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 19 | 19 | 17 | 19 | 19 | 15 | 19 | 17 | 19 |
N.S. |
1 | 1.27 | 1.27 | 1.13 | 1.27 | 1.27 | 1.00 | 1.27 | 1.13 | 1.27 |
time (sec) |
N/A | 0.165 | 0.000 | 0.016 | 0.032 | 0.087 | 0.018 | 0.116 | 0.203 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 22 | 19 | 13 | 0 | 18 | 14 | 22 | 31 | 22 |
N.S. |
1 | 1.38 | 1.19 | 0.81 | 0.00 | 1.12 | 0.88 | 1.38 | 1.94 | 1.38 |
time (sec) |
N/A | 0.379 | 0.084 | 0.086 | 0.000 | 0.086 | 0.094 | 0.117 | 0.213 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 25 | 22 | 28 | 20 | 24 | 36 | 41 | 39 |
N.S. |
1 | 0.00 | 0.86 | 0.76 | 0.97 | 0.69 | 0.83 | 1.24 | 1.41 | 1.34 |
time (sec) |
N/A | 0.000 | 4.481 | 2.886 | 0.234 | 0.093 | 0.387 | 0.141 | 0.227 | 2.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 24 | 24 | 25 | 22 | 23 | 19 | 22 | 23 | 24 |
N.S. |
1 | 1.20 | 1.20 | 1.25 | 1.10 | 1.15 | 0.95 | 1.10 | 1.15 | 1.20 |
time (sec) |
N/A | 0.320 | 0.004 | 0.049 | 0.027 | 0.079 | 0.034 | 0.112 | 0.221 | 2.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 90 | 63 | 74 | 135 | 75 | 73 | 84 | 89 | 78 |
N.S. |
1 | 3.46 | 2.42 | 2.85 | 5.19 | 2.88 | 2.81 | 3.23 | 3.42 | 3.00 |
time (sec) |
N/A | 1.008 | 0.065 | 58.977 | 0.074 | 0.092 | 0.207 | 0.123 | 0.211 | 2.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 50 | 56 | 52 | 52 | 51 | 55 | 56 | 55 |
N.S. |
1 | 0.00 | 2.00 | 2.24 | 2.08 | 2.08 | 2.04 | 2.20 | 2.24 | 2.20 |
time (sec) |
N/A | 0.000 | 0.243 | 34.359 | 0.104 | 0.120 | 0.732 | 0.480 | 0.271 | 2.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 35 | 55 | 60 | 52 | 53 | 63 | 45 | 69 |
N.S. |
1 | 0.00 | 1.21 | 1.90 | 2.07 | 1.79 | 1.83 | 2.17 | 1.55 | 2.38 |
time (sec) |
N/A | 0.000 | 0.120 | 2.161 | 0.203 | 0.089 | 0.710 | 0.445 | 0.411 | 2.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 43 | 27 | 29 | 0 | 30 | 38 | 26 |
N.S. |
1 | 0.00 | 0.96 | 1.87 | 1.17 | 1.26 | 0.00 | 1.30 | 1.65 | 1.13 |
time (sec) |
N/A | 0.000 | 0.070 | 0.997 | 0.152 | 0.104 | 0.000 | 0.176 | 0.214 | 2.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 32 | 0 | 31 | 31 | 31 | 32 | 31 |
N.S. |
1 | 0.00 | 0.90 | 1.10 | 0.00 | 1.07 | 1.07 | 1.07 | 1.10 | 1.07 |
time (sec) |
N/A | 0.000 | 0.054 | 1.858 | 0.000 | 0.095 | 0.180 | 2.173 | 0.213 | 2.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 68 | 77 | 66 | 94 | 53 | 61 | 65 | 59 | 59 |
N.S. |
1 | 2.83 | 3.21 | 2.75 | 3.92 | 2.21 | 2.54 | 2.71 | 2.46 | 2.46 |
time (sec) |
N/A | 0.296 | 0.018 | 0.872 | 0.033 | 0.127 | 0.094 | 0.118 | 0.214 | 2.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 15 | 12 | 15 | 11 | 14 | 12 | 11 | 17 | 13 |
N.S. |
1 | 0.71 | 0.57 | 0.71 | 0.52 | 0.67 | 0.57 | 0.52 | 0.81 | 0.62 |
time (sec) |
N/A | 0.298 | 0.045 | 0.030 | 0.086 | 0.076 | 0.061 | 0.110 | 0.931 | 2.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 26 | 25 | 29 | 28 | 27 | 35 | 26 | 28 |
N.S. |
1 | 0.00 | 0.76 | 0.74 | 0.85 | 0.82 | 0.79 | 1.03 | 0.76 | 0.82 |
time (sec) |
N/A | 0.000 | 0.286 | 0.363 | 0.074 | 0.095 | 0.195 | 0.127 | 0.222 | 2.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 21 | 21 | 22 | 20 | 0 | 0 | 23 | 20 |
N.S. |
1 | 1.09 | 0.91 | 0.91 | 0.96 | 0.87 | 0.00 | 0.00 | 1.00 | 0.87 |
time (sec) |
N/A | 2.379 | 0.099 | 175.708 | 0.360 | 0.086 | 0.000 | 0.000 | 0.234 | 4.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 17 | 17 | 18 | 17 | 19 | 19 | 19 | 65 | 17 |
N.S. |
1 | 0.85 | 0.85 | 0.90 | 0.85 | 0.95 | 0.95 | 0.95 | 3.25 | 0.85 |
time (sec) |
N/A | 0.421 | 0.053 | 0.090 | 0.063 | 0.088 | 0.082 | 0.108 | 0.199 | 2.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 82 | 35 | 56 | 56 | 48 | 37 | 34 | 57 |
N.S. |
1 | 0.00 | 3.57 | 1.52 | 2.43 | 2.43 | 2.09 | 1.61 | 1.48 | 2.48 |
time (sec) |
N/A | 0.000 | 0.046 | 1.550 | 0.178 | 0.114 | 0.799 | 0.156 | 0.198 | 5.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 2367 | 35 | 36 | 1260 | 36 | 32 | 295 | 107 | 36 |
N.S. |
1 | 76.35 | 1.13 | 1.16 | 40.65 | 1.16 | 1.03 | 9.52 | 3.45 | 1.16 |
time (sec) |
N/A | 5.518 | 0.088 | 2.042 | 0.289 | 0.089 | 0.188 | 0.590 | 0.202 | 3.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 19 | 21 | 25 | 20 | 20 | 25 | 21 | 21 |
N.S. |
1 | 0.90 | 0.90 | 1.00 | 1.19 | 0.95 | 0.95 | 1.19 | 1.00 | 1.00 |
time (sec) |
N/A | 0.981 | 0.127 | 0.360 | 0.153 | 0.117 | 0.134 | 0.137 | 0.200 | 2.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 39 | 55 | 52 | 81 | 56 | 0 | 1088 | 56 |
N.S. |
1 | 0.00 | 1.26 | 1.77 | 1.68 | 2.61 | 1.81 | 0.00 | 35.10 | 1.81 |
time (sec) |
N/A | 0.000 | 0.211 | 25.565 | 0.265 | 0.109 | 0.653 | 0.000 | 0.581 | 2.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 19 | 20 | 77 | 81 | 39 | 83 | 82 | 0 |
N.S. |
1 | 0.00 | 0.76 | 0.80 | 3.08 | 3.24 | 1.56 | 3.32 | 3.28 | 0.00 |
time (sec) |
N/A | 0.000 | 0.054 | 4.989 | 0.085 | 0.105 | 0.162 | 0.136 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 34 | 22 | 25 | 21 | 14 | 21 | 26 | 18 |
N.S. |
1 | 0.00 | 1.48 | 0.96 | 1.09 | 0.91 | 0.61 | 0.91 | 1.13 | 0.78 |
time (sec) |
N/A | 0.000 | 0.736 | 0.724 | 0.148 | 0.088 | 0.067 | 0.144 | 0.201 | 2.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 20 | 37 | 19 | 19 | 37 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.85 | 0.95 | 0.95 | 1.85 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.353 | 8.719 | 0.225 | 0.110 | 0.447 | 0.382 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 82 | 87 | 74 | 74 | 76 | 0 | 98 | 0 |
N.S. |
1 | 0.00 | 3.73 | 3.95 | 3.36 | 3.36 | 3.45 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.216 | 1.130 | 0.722 | 0.105 | 0.516 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 31 | 20 | 25 | 28 | 24 | 27 | 28 | 19 | 28 |
N.S. |
1 | 1.55 | 1.00 | 1.25 | 1.40 | 1.20 | 1.35 | 1.40 | 0.95 | 1.40 |
time (sec) |
N/A | 2.099 | 0.086 | 0.339 | 0.086 | 0.104 | 0.244 | 0.124 | 0.213 | 0.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 41 | 165 | 29 | 24 | 331 | 0 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.52 | 6.11 | 1.07 | 0.89 | 12.26 | 0.00 | 1.07 |
time (sec) |
N/A | 0.000 | 0.049 | 12.888 | 0.146 | 0.089 | 0.149 | 0.755 | 0.284 | 2.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 29 | 82 | 28 | 0 | 85 | 34 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.45 | 4.10 | 1.40 | 0.00 | 4.25 | 1.70 | 0.75 |
time (sec) |
N/A | 12.618 | 0.962 | 1.029 | 0.257 | 0.098 | 0.000 | 0.131 | 0.219 | 2.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 23 | 17 | 38 | 16 | 19 | 38 | 18 | 15 |
N.S. |
1 | 1.00 | 1.15 | 0.85 | 1.90 | 0.80 | 0.95 | 1.90 | 0.90 | 0.75 |
time (sec) |
N/A | 0.163 | 0.004 | 0.055 | 0.032 | 0.092 | 0.056 | 0.113 | 0.197 | 2.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 50 | 241 | 1252 | 55 | 46 | 0 | 95 | 93 |
N.S. |
1 | 0.00 | 1.61 | 7.77 | 40.39 | 1.77 | 1.48 | 0.00 | 3.06 | 3.00 |
time (sec) |
N/A | 0.000 | 0.148 | 0.511 | 0.173 | 0.105 | 0.491 | 0.000 | 0.208 | 3.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 22 | 32 | 113 | 31 | 32 | 31 | 35 | 21 |
N.S. |
1 | 1.00 | 0.92 | 1.33 | 4.71 | 1.29 | 1.33 | 1.29 | 1.46 | 0.88 |
time (sec) |
N/A | 1.317 | 0.058 | 0.195 | 0.153 | 0.085 | 0.143 | 0.111 | 0.236 | 2.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 22 | 22 | 26 | 37 | 22 | 28 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.18 | 1.68 | 1.00 | 1.27 | 0.95 |
time (sec) |
N/A | 1.160 | 0.135 | 0.655 | 0.073 | 0.098 | 0.462 | 0.144 | 0.217 | 2.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 18 | 17 | 18 | 18 | 19 | 18 | 20 | 17 |
N.S. |
1 | 1.10 | 0.90 | 0.85 | 0.90 | 0.90 | 0.95 | 0.90 | 1.00 | 0.85 |
time (sec) |
N/A | 0.225 | 0.006 | 0.040 | 0.031 | 0.073 | 0.114 | 0.110 | 0.222 | 2.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 23 | 17 | 22 | 17 | 24 | 24 | 18 |
N.S. |
1 | 0.00 | 0.91 | 1.05 | 0.77 | 1.00 | 0.77 | 1.09 | 1.09 | 0.82 |
time (sec) |
N/A | 0.000 | 0.082 | 0.128 | 0.103 | 0.078 | 0.106 | 0.121 | 0.216 | 2.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 24 | 31 | 37 | 37 | 0 | 34 | 31 | 394 |
N.S. |
1 | 0.00 | 1.04 | 1.35 | 1.61 | 1.61 | 0.00 | 1.48 | 1.35 | 17.13 |
time (sec) |
N/A | 0.000 | 0.055 | 1.064 | 0.077 | 0.097 | 0.000 | 0.152 | 0.225 | 2.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 21 | 20 | 22 | 24 | 22 | 24 | 20 |
N.S. |
1 | 1.00 | 0.96 | 0.84 | 0.80 | 0.88 | 0.96 | 0.88 | 0.96 | 0.80 |
time (sec) |
N/A | 0.253 | 0.289 | 0.085 | 0.034 | 0.089 | 0.099 | 0.118 | 0.213 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | F(-2) | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 76 | 104 | 79 | 0 | 114 | 80 | 39 |
N.S. |
1 | 0.00 | 0.00 | 2.53 | 3.47 | 2.63 | 0.00 | 3.80 | 2.67 | 1.30 |
time (sec) |
N/A | 0.000 | 0.000 | 60.441 | 0.113 | 0.099 | 0.000 | 16.815 | 0.235 | 3.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 109 | 168 | 208 | 208 | 318 | 291 | 315 | 0 |
N.S. |
1 | 0.00 | 4.04 | 6.22 | 7.70 | 7.70 | 11.78 | 10.78 | 11.67 | 0.00 |
time (sec) |
N/A | 0.000 | 10.139 | 1.073 | 0.256 | 0.113 | 0.539 | 0.217 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 61 | 59 | 61 | 61 | 60 | 61 | 61 | 61 |
N.S. |
1 | 0.00 | 2.35 | 2.27 | 2.35 | 2.35 | 2.31 | 2.35 | 2.35 | 2.35 |
time (sec) |
N/A | 0.000 | 0.023 | 0.148 | 0.030 | 0.082 | 1.798 | 0.144 | 0.228 | 2.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 34 | 37 | 43 | 45 | 37 | 0 | 72 | 0 |
N.S. |
1 | 0.00 | 1.55 | 1.68 | 1.95 | 2.05 | 1.68 | 0.00 | 3.27 | 0.00 |
time (sec) |
N/A | 0.000 | 0.073 | 5.285 | 0.416 | 0.099 | 0.165 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 22 | 23 | 22 | 22 | 20 | 39 | 24 | 0 |
N.S. |
1 | 0.92 | 0.92 | 0.96 | 0.92 | 0.92 | 0.83 | 1.62 | 1.00 | 0.00 |
time (sec) |
N/A | 1.407 | 0.060 | 60.146 | 0.175 | 0.098 | 0.333 | 0.215 | 0.692 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 71 | 68 | 137 | 65 | 56 | 0 | 139 | 37 |
N.S. |
1 | 0.00 | 2.54 | 2.43 | 4.89 | 2.32 | 2.00 | 0.00 | 4.96 | 1.32 |
time (sec) |
N/A | 0.000 | 0.040 | 4.505 | 0.125 | 0.090 | 0.125 | 0.000 | 0.218 | 2.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 50 | 14 | 28 | 62 | 27 | 48 | 27 | 31 | 11 |
N.S. |
1 | 3.33 | 0.93 | 1.87 | 4.13 | 1.80 | 3.20 | 1.80 | 2.07 | 0.73 |
time (sec) |
N/A | 0.334 | 0.132 | 0.420 | 0.095 | 0.087 | 0.099 | 0.149 | 0.236 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 32 | 34 | 30 | 26 | 0 | 39 | 31 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 1.13 | 1.00 | 0.87 | 0.00 | 1.30 | 1.03 |
time (sec) |
N/A | 0.000 | 5.065 | 2.428 | 0.127 | 0.105 | 0.200 | 0.000 | 5.295 | 2.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 20 | 19 | 18 | 18 | 14 | 18 | 28 | 20 |
N.S. |
1 | 0.83 | 0.83 | 0.79 | 0.75 | 0.75 | 0.58 | 0.75 | 1.17 | 0.83 |
time (sec) |
N/A | 0.181 | 0.056 | 0.045 | 0.027 | 0.090 | 0.068 | 0.122 | 0.198 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 28 | 28 | 25 | 24 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.40 | 1.40 | 1.25 | 1.20 | 1.20 | 1.20 | 1.30 | 1.20 | 1.20 |
time (sec) |
N/A | 0.415 | 0.008 | 0.031 | 0.034 | 0.080 | 0.057 | 0.137 | 0.211 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 27 | 0 | 27 | 20 | 63 | 620 | 0 |
N.S. |
1 | 0.00 | 0.90 | 0.93 | 0.00 | 0.93 | 0.69 | 2.17 | 21.38 | 0.00 |
time (sec) |
N/A | 0.000 | 1.766 | 0.382 | 0.000 | 0.085 | 1.164 | 0.145 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | A | B | B | F(-1) | F | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 193 | 0 | 40 | 51 | 62 | 0 | 0 | 120 | 48 |
N.S. |
1 | 6.66 | 0.00 | 1.38 | 1.76 | 2.14 | 0.00 | 0.00 | 4.14 | 1.66 |
time (sec) |
N/A | 3.922 | 0.000 | 1.834 | 0.294 | 0.118 | 0.000 | 0.000 | 200.021 | 2.348 |