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 | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 209 | 25 | 26 | 27 | 25 | 22 | 27 | 22 | 22 |
N.S. |
1 | 10.45 | 1.25 | 1.30 | 1.35 | 1.25 | 1.10 | 1.35 | 1.10 | 1.10 |
time (sec) |
N/A | 2.422 | 0.081 | 4.307 | 0.171 | 0.080 | 0.160 | 0.135 | 0.250 | 3.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 99 | 48 | 154 | 154 | 94 | 525 | 192 | 0 |
N.S. |
1 | 0.00 | 2.68 | 1.30 | 4.16 | 4.16 | 2.54 | 14.19 | 5.19 | 0.00 |
time (sec) |
N/A | 0.000 | 10.151 | 201.679 | 0.351 | 0.105 | 0.275 | 0.503 | 0.260 | 0.000 |
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 | 29 | 23 | 48 | 24 | 70 | 26 | 24 | 26 | 19 | 18 |
N.S. |
1 | 0.79 | 1.66 | 0.83 | 2.41 | 0.90 | 0.83 | 0.90 | 0.66 | 0.62 |
time (sec) |
N/A | 0.369 | 0.040 | 1.991 | 0.279 | 0.083 | 0.093 | 0.124 | 0.237 | 0.418 |
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 | 30 | 0 | 30 | 29 | 34 | 28 | 24 | 28 | 238 | 26 |
N.S. |
1 | 0.00 | 1.00 | 0.97 | 1.13 | 0.93 | 0.80 | 0.93 | 7.93 | 0.87 |
time (sec) |
N/A | 0.000 | 0.213 | 0.382 | 0.067 | 0.082 | 0.154 | 0.143 | 0.291 | 3.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 11 | 11 | 9 | 43 | 8 | 8 | 8 | 9 | 8 |
N.S. |
1 | 0.85 | 0.85 | 0.69 | 3.31 | 0.62 | 0.62 | 0.62 | 0.69 | 0.62 |
time (sec) |
N/A | 0.174 | 0.005 | 0.168 | 0.062 | 0.068 | 0.049 | 0.113 | 0.252 | 3.623 |
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 | 23 | 24 | 17 | 17 | 17 | 17 | 17 | 17 | 31 | 17 |
N.S. |
1 | 1.04 | 0.74 | 0.74 | 0.74 | 0.74 | 0.74 | 0.74 | 1.35 | 0.74 |
time (sec) |
N/A | 0.167 | 0.004 | 0.168 | 0.032 | 0.070 | 0.087 | 0.114 | 0.242 | 3.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 38 | 34 | 33 | 55 | 31 | 33 | 37 | 43 |
N.S. |
1 | 0.96 | 1.46 | 1.31 | 1.27 | 2.12 | 1.19 | 1.27 | 1.42 | 1.65 |
time (sec) |
N/A | 0.720 | 0.148 | 0.566 | 0.156 | 0.075 | 0.215 | 0.118 | 0.252 | 4.025 |
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 | 27 | 26 | 26 | 26 | 25 | 25 | 20 | 25 | 22 | 25 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 0.93 | 0.93 | 0.74 | 0.93 | 0.81 | 0.93 |
time (sec) |
N/A | 0.202 | 0.007 | 0.174 | 0.027 | 0.079 | 0.043 | 0.115 | 0.282 | 3.688 |
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 | 27 | 27 | 16 | 19 | 20 | 12 | 13 | 22 | 19 |
N.S. |
1 | 1.12 | 1.12 | 0.67 | 0.79 | 0.83 | 0.50 | 0.54 | 0.92 | 0.79 |
time (sec) |
N/A | 0.283 | 0.140 | 0.184 | 0.044 | 0.085 | 0.052 | 0.108 | 0.260 | 0.068 |
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 | 14 | 11 | 11 | 10 | 11 | 11 | 8 | 11 | 14 | 11 |
N.S. |
1 | 0.79 | 0.79 | 0.71 | 0.79 | 0.79 | 0.57 | 0.79 | 1.00 | 0.79 |
time (sec) |
N/A | 0.150 | 0.002 | 0.036 | 0.032 | 0.062 | 0.034 | 0.109 | 0.244 | 3.627 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 5 | 10 | 29 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.50 | 1.00 | 2.90 | 1.00 |
time (sec) |
N/A | 0.296 | 0.010 | 0.148 | 0.073 | 0.080 | 0.053 | 0.116 | 0.187 | 3.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 27 | 60 | 60 | 65 | 100 | 118 | 92 |
N.S. |
1 | 0.00 | 0.93 | 1.00 | 2.22 | 2.22 | 2.41 | 3.70 | 4.37 | 3.41 |
time (sec) |
N/A | 0.000 | 0.372 | 2.155 | 0.117 | 0.077 | 0.162 | 0.193 | 0.236 | 3.995 |
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 | 12 | 15 | 16 | 13 | 14 | 14 | 14 | 14 | 12 | 14 |
N.S. |
1 | 1.25 | 1.33 | 1.08 | 1.17 | 1.17 | 1.17 | 1.17 | 1.00 | 1.17 |
time (sec) |
N/A | 0.135 | 0.001 | 0.039 | 0.024 | 0.061 | 0.018 | 0.110 | 0.202 | 0.040 |
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 | 14 | 14 | 14 | 13 | 12 | 14 | 12 | 12 | 15 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.00 | 0.86 | 0.86 | 1.07 | 0.86 |
time (sec) |
N/A | 0.179 | 0.008 | 0.208 | 0.084 | 0.081 | 0.102 | 0.110 | 0.182 | 3.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 110 | 165 | 100 | 39 | 466 | 369 | 0 |
N.S. |
1 | 0.00 | 0.96 | 4.23 | 6.35 | 3.85 | 1.50 | 17.92 | 14.19 | 0.00 |
time (sec) |
N/A | 0.000 | 0.079 | 7.694 | 0.139 | 0.091 | 0.176 | 1.639 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 31 | 51 | 50 | 47 | 69 | 75 | 100 | 78 | 55 |
N.S. |
1 | 1.03 | 1.70 | 1.67 | 1.57 | 2.30 | 2.50 | 3.33 | 2.60 | 1.83 |
time (sec) |
N/A | 0.483 | 0.143 | 0.555 | 0.070 | 0.086 | 0.077 | 0.130 | 0.207 | 3.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 63 | 27 | 200 | 24 | 26 | 67 | 57 | 0 |
N.S. |
1 | 0.00 | 2.25 | 0.96 | 7.14 | 0.86 | 0.93 | 2.39 | 2.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.232 | 21.276 | 0.264 | 0.084 | 0.286 | 0.326 | 0.193 | 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 | 16 | 13 | 13 | 12 | 11 | 16 | 10 | 11 | 19 | 12 |
N.S. |
1 | 0.81 | 0.81 | 0.75 | 0.69 | 1.00 | 0.62 | 0.69 | 1.19 | 0.75 |
time (sec) |
N/A | 0.256 | 0.011 | 0.051 | 0.034 | 0.073 | 0.073 | 0.111 | 0.173 | 0.074 |
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 | 15 | 15 | 14 | 13 | 13 | 12 | 13 | 19 | 13 |
N.S. |
1 | 0.68 | 0.68 | 0.64 | 0.59 | 0.59 | 0.55 | 0.59 | 0.86 | 0.59 |
time (sec) |
N/A | 0.223 | 0.037 | 0.088 | 0.031 | 0.084 | 0.071 | 0.110 | 0.181 | 3.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 24 | 60 | 48 | 65 | 60 | 40 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 2.61 | 2.09 | 2.83 | 2.61 | 1.74 | 0.00 |
time (sec) |
N/A | 0.000 | 0.392 | 0.301 | 0.161 | 0.069 | 0.090 | 0.135 | 0.192 | 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 | 19 | 15 | 12 | 14 | 13 | 13 | 12 | 13 | 14 | 14 |
N.S. |
1 | 0.79 | 0.63 | 0.74 | 0.68 | 0.68 | 0.63 | 0.68 | 0.74 | 0.74 |
time (sec) |
N/A | 0.147 | 0.002 | 0.056 | 0.032 | 0.072 | 0.035 | 0.121 | 0.174 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 32 | 27 | 27 | 32 | 29 | 29 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.23 | 1.04 | 1.04 | 1.23 | 1.12 | 1.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.685 | 0.168 | 0.086 | 0.133 | 0.152 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 55 | 28 | 33 | 55 | 46 | 36 | 53 | 63 | 32 |
N.S. |
1 | 1.90 | 0.97 | 1.14 | 1.90 | 1.59 | 1.24 | 1.83 | 2.17 | 1.10 |
time (sec) |
N/A | 0.995 | 0.477 | 0.612 | 0.059 | 0.085 | 0.078 | 0.130 | 0.182 | 3.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | F(-1) | F(-1) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 110 | 312 | 292 | 154 | 0 | 0 | 849 | 308 |
N.S. |
1 | 0.00 | 3.55 | 10.06 | 9.42 | 4.97 | 0.00 | 0.00 | 27.39 | 9.94 |
time (sec) |
N/A | 0.000 | 0.643 | 2.255 | 3.939 | 0.131 | 0.000 | 0.000 | 200.036 | 4.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 30 | 17 | 33 | 37 | 23 | 26 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.50 | 0.85 | 1.65 | 1.85 | 1.15 | 1.30 | 0.00 |
time (sec) |
N/A | 0.000 | 0.332 | 0.562 | 0.124 | 0.087 | 0.184 | 0.113 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 32 | 30 | 34 | 40 | 31 | 2593 | 642 | 0 |
N.S. |
1 | 0.00 | 1.14 | 1.07 | 1.21 | 1.43 | 1.11 | 92.61 | 22.93 | 0.00 |
time (sec) |
N/A | 0.000 | 1.111 | 0.422 | 0.083 | 0.072 | 0.141 | 0.219 | 0.694 | 0.000 |
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 | 32 | 0 | 38 | 49 | 33 | 34 | 31 | 34 | 36 | 0 |
N.S. |
1 | 0.00 | 1.19 | 1.53 | 1.03 | 1.06 | 0.97 | 1.06 | 1.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.276 | 60.836 | 0.094 | 0.089 | 0.342 | 0.185 | 0.198 | 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 | 19 | 15 | 15 | 16 | 15 | 17 | 14 | 15 | 15 | 15 |
N.S. |
1 | 0.79 | 0.79 | 0.84 | 0.79 | 0.89 | 0.74 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.273 | 0.003 | 0.089 | 0.031 | 0.075 | 0.066 | 0.113 | 0.191 | 3.638 |
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 | 6 | 6 | 6 | 5 | 5 | 7 | 5 | 6 | 5 |
N.S. |
1 | 0.38 | 0.38 | 0.38 | 0.31 | 0.31 | 0.44 | 0.31 | 0.38 | 0.31 |
time (sec) |
N/A | 0.121 | 0.000 | 0.023 | 0.026 | 0.053 | 0.017 | 0.112 | 0.194 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 24 | 33 | 36 | 37 | 51 | 302 | 54 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 1.50 | 1.64 | 1.68 | 2.32 | 13.73 | 2.45 |
time (sec) |
N/A | 0.000 | 2.414 | 0.460 | 0.145 | 0.076 | 11.118 | 0.137 | 0.301 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 26 | 22 | 21 | 29 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.13 | 0.96 | 0.91 | 1.26 | 0.87 | 0.87 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.206 | 0.041 | 0.152 | 0.060 | 0.085 | 0.065 | 0.111 | 0.202 | 3.667 |
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 | 32 | 0 | 29 | 44 | 41 | 30 | 24 | 44 | 0 | 33 |
N.S. |
1 | 0.00 | 0.91 | 1.38 | 1.28 | 0.94 | 0.75 | 1.38 | 0.00 | 1.03 |
time (sec) |
N/A | 0.000 | 0.038 | 2.779 | 0.176 | 0.091 | 0.214 | 0.251 | 0.828 | 4.123 |
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 | 26 | 0 | 27 | 29 | 29 | 28 | 24 | 28 | 30 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.12 | 1.12 | 1.08 | 0.92 | 1.08 | 1.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.041 | 127.744 | 0.126 | 0.090 | 0.256 | 0.177 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 1146 | 23 | 23 | 76 | 21 | 24 | 21 | 25 | 22 |
N.S. |
1 | 49.83 | 1.00 | 1.00 | 3.30 | 0.91 | 1.04 | 0.91 | 1.09 | 0.96 |
time (sec) |
N/A | 5.550 | 1.146 | 0.405 | 0.168 | 0.077 | 0.082 | 0.122 | 0.190 | 0.130 |
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 | 20 | 20 | 22 | 21 | 21 | 19 | 21 | 20 | 21 |
N.S. |
1 | 0.91 | 0.91 | 1.00 | 0.95 | 0.95 | 0.86 | 0.95 | 0.91 | 0.95 |
time (sec) |
N/A | 0.217 | 0.006 | 0.121 | 0.033 | 0.074 | 0.070 | 0.115 | 0.210 | 3.867 |
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 | 22 | 26 | 22 | 21 | 21 | 34 | 23 | 22 | 21 |
N.S. |
1 | 0.76 | 0.90 | 0.76 | 0.72 | 0.72 | 1.17 | 0.79 | 0.76 | 0.72 |
time (sec) |
N/A | 0.215 | 0.008 | 0.097 | 0.029 | 0.079 | 0.258 | 0.110 | 0.239 | 3.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 36 | 42 | 38 | 41 | 46 | 26 | 41 | 45 | 21 |
N.S. |
1 | 1.44 | 1.68 | 1.52 | 1.64 | 1.84 | 1.04 | 1.64 | 1.80 | 0.84 |
time (sec) |
N/A | 0.182 | 0.003 | 0.125 | 0.026 | 0.073 | 0.029 | 0.110 | 0.196 | 0.085 |
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 | 33 | 39 | 39 | 39 | 39 | 40 | 36 | 39 | 39 | 38 |
N.S. |
1 | 1.18 | 1.18 | 1.18 | 1.18 | 1.21 | 1.09 | 1.18 | 1.18 | 1.15 |
time (sec) |
N/A | 0.218 | 0.003 | 0.055 | 0.026 | 0.069 | 0.034 | 0.108 | 0.195 | 3.605 |
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 | 16 | 18 | 17 | 17 | 15 | 17 | 18 | 17 |
N.S. |
1 | 0.00 | 0.70 | 0.78 | 0.74 | 0.74 | 0.65 | 0.74 | 0.78 | 0.74 |
time (sec) |
N/A | 0.000 | 0.131 | 0.050 | 0.059 | 0.078 | 0.064 | 0.112 | 0.178 | 3.856 |
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 | 23 | 34 | 18 | 22 | 26 | 15 | 17 | 26 | 17 |
N.S. |
1 | 0.88 | 1.31 | 0.69 | 0.85 | 1.00 | 0.58 | 0.65 | 1.00 | 0.65 |
time (sec) |
N/A | 0.369 | 0.107 | 0.568 | 0.147 | 0.080 | 0.049 | 0.116 | 0.222 | 4.101 |
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 | 31 | 27 | 22 | 27 | 28 | 22 | 28 | 34 | 21 |
N.S. |
1 | 1.29 | 1.12 | 0.92 | 1.12 | 1.17 | 0.92 | 1.17 | 1.42 | 0.88 |
time (sec) |
N/A | 0.189 | 0.032 | 0.269 | 0.098 | 0.079 | 0.127 | 0.133 | 0.197 | 3.984 |
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 | 16 | 15 | 14 | 13 | 13 | 14 | 13 | 25 | 15 |
N.S. |
1 | 0.84 | 0.79 | 0.74 | 0.68 | 0.68 | 0.74 | 0.68 | 1.32 | 0.79 |
time (sec) |
N/A | 0.158 | 0.002 | 0.134 | 0.026 | 0.069 | 0.082 | 0.104 | 0.196 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 32 | 34 | 31 | 27 | 0 | 85 | 37 |
N.S. |
1 | 0.00 | 0.87 | 1.03 | 1.10 | 1.00 | 0.87 | 0.00 | 2.74 | 1.19 |
time (sec) |
N/A | 0.000 | 1.205 | 0.299 | 0.155 | 0.079 | 0.151 | 0.000 | 0.224 | 4.127 |
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 | 27 | 0 | 27 | 28 | 32 | 26 | 19 | 1559 | 26 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.19 | 0.96 | 0.70 | 57.74 | 0.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.040 | 3.064 | 0.184 | 0.082 | 0.324 | 0.818 | 0.212 | 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 | 21 | 20 | 18 | 16 | 17 | 17 | 17 | 18 | 17 | 17 |
N.S. |
1 | 0.95 | 0.86 | 0.76 | 0.81 | 0.81 | 0.81 | 0.86 | 0.81 | 0.81 |
time (sec) |
N/A | 0.146 | 0.004 | 0.259 | 0.033 | 0.074 | 0.107 | 0.109 | 0.184 | 0.092 |
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 | 12 | 10 | 12 | 13 | 10 | 13 | 12 | 10 | 12 | 10 |
N.S. |
1 | 0.83 | 1.00 | 1.08 | 0.83 | 1.08 | 1.00 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.127 | 0.000 | 0.047 | 0.032 | 0.072 | 0.017 | 0.109 | 0.188 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 102 | 151 | 27 | 51 | 49 | 56 | 51 | 62 | 95 |
N.S. |
1 | 3.52 | 5.21 | 0.93 | 1.76 | 1.69 | 1.93 | 1.76 | 2.14 | 3.28 |
time (sec) |
N/A | 0.517 | 0.192 | 0.734 | 0.047 | 0.077 | 6.387 | 0.129 | 0.189 | 5.533 |
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 | 19 | 0 | 19 | 18 | 0 | 19 | 27 | 23 | 19 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.00 | 1.00 | 1.42 | 1.21 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.507 | 0.105 | 0.000 | 0.074 | 0.084 | 0.116 | 0.208 | 0.194 |
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 | 20 | 19 | 15 | 14 | 14 | 15 | 14 | 16 | 17 |
N.S. |
1 | 1.18 | 1.12 | 0.88 | 0.82 | 0.82 | 0.88 | 0.82 | 0.94 | 1.00 |
time (sec) |
N/A | 0.146 | 0.002 | 0.049 | 0.027 | 0.077 | 0.020 | 0.109 | 0.197 | 0.074 |
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 | 30 | 28 | 20 | 33 | 33 | 21 | 15 | 40 | 157 | 21 |
N.S. |
1 | 0.93 | 0.67 | 1.10 | 1.10 | 0.70 | 0.50 | 1.33 | 5.23 | 0.70 |
time (sec) |
N/A | 0.443 | 0.149 | 0.354 | 0.154 | 0.066 | 0.093 | 0.141 | 0.245 | 5.596 |
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 | 37 | 64 | 74 | 86 | 53 | 205 | 123 | 35 |
N.S. |
1 | 0.00 | 1.28 | 2.21 | 2.55 | 2.97 | 1.83 | 7.07 | 4.24 | 1.21 |
time (sec) |
N/A | 0.000 | 0.110 | 0.786 | 0.164 | 0.089 | 0.948 | 0.228 | 0.203 | 5.014 |
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 | 19 | 19 | 28 | 41 | 124 | 33 | 31 | 96 | 42 | 38 |
N.S. |
1 | 1.00 | 1.47 | 2.16 | 6.53 | 1.74 | 1.63 | 5.05 | 2.21 | 2.00 |
time (sec) |
N/A | 0.638 | 0.823 | 0.924 | 0.166 | 0.073 | 0.120 | 0.162 | 0.214 | 4.703 |
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 | 5 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 5 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 0.80 | 0.60 | 0.80 | 1.00 | 0.80 |
time (sec) |
N/A | 0.134 | 0.001 | 0.036 | 0.034 | 0.075 | 0.035 | 0.111 | 0.206 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 17 | 16 | 31 | 14 | 0 | 18 | 16 |
N.S. |
1 | 0.00 | 0.96 | 0.74 | 0.70 | 1.35 | 0.61 | 0.00 | 0.78 | 0.70 |
time (sec) |
N/A | 0.000 | 0.065 | 0.105 | 0.093 | 0.083 | 0.125 | 0.000 | 0.203 | 4.221 |
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 | 27 | 22 | 20 | 26 | 87 | 22 | 20 | 60 | 22 | 22 |
N.S. |
1 | 0.81 | 0.74 | 0.96 | 3.22 | 0.81 | 0.74 | 2.22 | 0.81 | 0.81 |
time (sec) |
N/A | 0.789 | 0.016 | 0.234 | 0.146 | 0.077 | 0.128 | 0.143 | 0.205 | 5.063 |
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 | 31 | 0 | 39 | 35 | 64 | 55 | 53 | 68 | 116 | 38 |
N.S. |
1 | 0.00 | 1.26 | 1.13 | 2.06 | 1.77 | 1.71 | 2.19 | 3.74 | 1.23 |
time (sec) |
N/A | 0.000 | 0.295 | 0.737 | 0.166 | 0.080 | 0.234 | 0.132 | 0.213 | 4.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 34 | 35 | 38 | 35 | 34 | 66 | 39 | 22 |
N.S. |
1 | 0.00 | 1.17 | 1.21 | 1.31 | 1.21 | 1.17 | 2.28 | 1.34 | 0.76 |
time (sec) |
N/A | 0.000 | 1.481 | 0.408 | 0.174 | 0.083 | 0.112 | 0.125 | 0.210 | 4.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 45 | 47 | 48 | 60 | 53 | 46 | 59 | 65 | 40 |
N.S. |
1 | 1.36 | 1.42 | 1.45 | 1.82 | 1.61 | 1.39 | 1.79 | 1.97 | 1.21 |
time (sec) |
N/A | 0.336 | 0.049 | 0.442 | 0.065 | 0.094 | 0.102 | 0.104 | 0.208 | 4.077 |
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 | 25 | 0 | 23 | 25 | 25 | 22 | 20 | 30 | 28 | 23 |
N.S. |
1 | 0.00 | 0.92 | 1.00 | 1.00 | 0.88 | 0.80 | 1.20 | 1.12 | 0.92 |
time (sec) |
N/A | 0.000 | 0.456 | 0.319 | 0.137 | 0.088 | 0.156 | 0.131 | 0.197 | 4.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 65 | 33 | 33 | 51 | 42 | 27 | 63 | 74 | 38 |
N.S. |
1 | 1.97 | 1.00 | 1.00 | 1.55 | 1.27 | 0.82 | 1.91 | 2.24 | 1.15 |
time (sec) |
N/A | 0.542 | 0.082 | 0.583 | 0.072 | 0.079 | 0.085 | 0.118 | 0.241 | 3.944 |
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 | 18 | 0 | 18 | 17 | 16 | 24 | 15 | 16 | 26 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.89 | 1.33 | 0.83 | 0.89 | 1.44 | 1.06 |
time (sec) |
N/A | 0.000 | 0.190 | 0.988 | 0.078 | 0.087 | 0.065 | 0.115 | 0.196 | 4.175 |
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 | 24 | 0 | 44 | 59 | 49 | 50 | 53 | 58 | 176 | 51 |
N.S. |
1 | 0.00 | 1.83 | 2.46 | 2.04 | 2.08 | 2.21 | 2.42 | 7.33 | 2.12 |
time (sec) |
N/A | 0.000 | 0.048 | 0.907 | 0.041 | 0.086 | 3.635 | 0.125 | 0.207 | 4.457 |
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 | 20 | 16 | 17 | 16 | 16 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.25 | 1.00 | 1.06 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.399 | 0.014 | 0.073 | 0.027 | 0.081 | 0.048 | 0.111 | 0.217 | 3.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 33 | 33 | 598 | 188 | 31 | 22 | 178 | 30 | 26 |
N.S. |
1 | 1.03 | 1.03 | 18.69 | 5.88 | 0.97 | 0.69 | 5.56 | 0.94 | 0.81 |
time (sec) |
N/A | 0.402 | 0.087 | 11.579 | 0.119 | 0.081 | 0.118 | 0.255 | 0.264 | 3.950 |
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 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 7 | 6 |
N.S. |
1 | 0.64 | 0.64 | 0.64 | 0.55 | 0.55 | 0.45 | 0.55 | 0.64 | 0.55 |
time (sec) |
N/A | 0.124 | 0.000 | 0.025 | 0.029 | 0.077 | 0.016 | 0.101 | 0.201 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | A | F(-2) | F(-1) | F | F | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 122 | 24 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 0.00 | 0.00 | 4.52 | 0.89 | 0.00 | 0.00 | 0.00 | 4.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 60.918 | 0.225 | 0.000 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 33 | 32 | 32 | 47 | 32 | 59 | 38 | 36 |
N.S. |
1 | 0.00 | 1.06 | 1.03 | 1.03 | 1.52 | 1.03 | 1.90 | 1.23 | 1.16 |
time (sec) |
N/A | 0.000 | 0.184 | 28.768 | 0.178 | 0.087 | 0.364 | 0.271 | 0.191 | 0.743 |
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 | 26 | 0 | 29 | 28 | 30 | 27 | 24 | 33 | 27 | 27 |
N.S. |
1 | 0.00 | 1.12 | 1.08 | 1.15 | 1.04 | 0.92 | 1.27 | 1.04 | 1.04 |
time (sec) |
N/A | 0.000 | 0.492 | 3.602 | 0.283 | 0.082 | 0.210 | 0.158 | 0.190 | 4.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 30 | 25 | 29 | 24 | 19 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 1.15 | 0.96 | 1.12 | 0.92 | 0.73 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.000 | 5.094 | 5.894 | 0.233 | 0.088 | 0.308 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | B | F(-2) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 77 | 81 | 0 | 79 | 80 | 0 | 258 | 232 |
N.S. |
1 | 0.00 | 2.14 | 2.25 | 0.00 | 2.19 | 2.22 | 0.00 | 7.17 | 6.44 |
time (sec) |
N/A | 0.000 | 0.424 | 0.067 | 0.000 | 0.102 | 1.398 | 0.000 | 200.021 | 4.561 |
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 | 27 | 52 | 27 | 28 | 36 | 35 | 34 | 37 | 42 | 25 |
N.S. |
1 | 1.93 | 1.00 | 1.04 | 1.33 | 1.30 | 1.26 | 1.37 | 1.56 | 0.93 |
time (sec) |
N/A | 1.842 | 1.295 | 0.481 | 0.075 | 0.078 | 0.088 | 0.118 | 0.172 | 0.229 |
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 | 17 | 15 | 14 | 14 | 14 | 14 | 14 | 15 | 14 |
N.S. |
1 | 1.00 | 0.88 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 | 0.88 | 0.82 |
time (sec) |
N/A | 0.145 | 0.003 | 0.061 | 0.033 | 0.087 | 0.046 | 0.106 | 0.170 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 33 | 27 | 0 | 26 | 24 | 26 | 120 | 36 |
N.S. |
1 | 0.00 | 1.06 | 0.87 | 0.00 | 0.84 | 0.77 | 0.84 | 3.87 | 1.16 |
time (sec) |
N/A | 0.000 | 0.089 | 13.693 | 0.000 | 0.074 | 0.460 | 0.254 | 200.022 | 4.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | C | A | A | F(-1) | B | F | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 216 | 483 | 47 | 46 | 0 | 108 | 965 | 0 |
N.S. |
1 | 0.00 | 7.20 | 16.10 | 1.57 | 1.53 | 0.00 | 3.60 | 32.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.141 | 2.967 | 0.198 | 0.098 | 0.000 | 0.250 | 0.233 | 0.000 |
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 | 19 | 57 | 56 | 51 | 47 | 48 | 46 | 47 | 50 | 42 |
N.S. |
1 | 3.00 | 2.95 | 2.68 | 2.47 | 2.53 | 2.42 | 2.47 | 2.63 | 2.21 |
time (sec) |
N/A | 0.215 | 0.006 | 0.102 | 0.036 | 0.075 | 0.031 | 0.113 | 0.171 | 3.761 |
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 | 34 | 22 | 20 | 22 | 30 | 20 | 44 | 66 | 22 |
N.S. |
1 | 1.17 | 0.76 | 0.69 | 0.76 | 1.03 | 0.69 | 1.52 | 2.28 | 0.76 |
time (sec) |
N/A | 1.150 | 0.080 | 0.390 | 0.113 | 0.081 | 0.108 | 0.118 | 0.178 | 3.858 |
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 | 23 | 23 | 19 | 18 | 18 | 17 | 18 | 24 | 18 |
N.S. |
1 | 1.05 | 1.05 | 0.86 | 0.82 | 0.82 | 0.77 | 0.82 | 1.09 | 0.82 |
time (sec) |
N/A | 0.203 | 0.044 | 0.105 | 0.040 | 0.071 | 0.045 | 0.105 | 0.178 | 0.060 |
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 | 35 | 664 | 181 | 253 | 855 | 205 | 291 | 349 | 333 | 229 |
N.S. |
1 | 18.97 | 5.17 | 7.23 | 24.43 | 5.86 | 8.31 | 9.97 | 9.51 | 6.54 |
time (sec) |
N/A | 12.817 | 0.201 | 20.348 | 0.165 | 0.114 | 0.265 | 0.124 | 0.179 | 4.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 28 | 57 | 18 | 17 | 17 | 15 | 17 | 34 | 17 |
N.S. |
1 | 0.80 | 1.63 | 0.51 | 0.49 | 0.49 | 0.43 | 0.49 | 0.97 | 0.49 |
time (sec) |
N/A | 0.194 | 0.040 | 0.078 | 0.034 | 0.088 | 0.082 | 0.111 | 0.187 | 0.081 |
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 | 32 | 0 | 42 | 27 | 36 | 26 | 24 | 26 | 55 | 28 |
N.S. |
1 | 0.00 | 1.31 | 0.84 | 1.12 | 0.81 | 0.75 | 0.81 | 1.72 | 0.88 |
time (sec) |
N/A | 0.000 | 0.075 | 0.256 | 0.127 | 0.076 | 0.105 | 0.190 | 124.073 | 3.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 62 | 64 | 72 | 65 | 70 | 84 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.48 | 2.56 | 2.88 | 2.60 | 2.80 | 3.36 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 4.546 | 0.177 | 0.086 | 0.142 | 0.127 | 0.368 | 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 | 24 | 0 | 25 | 33 | 29 | 32 | 31 | 32 | 28 | 29 |
N.S. |
1 | 0.00 | 1.04 | 1.38 | 1.21 | 1.33 | 1.29 | 1.33 | 1.17 | 1.21 |
time (sec) |
N/A | 0.000 | 0.205 | 0.534 | 0.160 | 0.097 | 0.178 | 0.133 | 0.334 | 4.355 |
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 | 25 | 36 | 24 | 22 | 73 | 38 | 17 | 39 | 36 | 21 |
N.S. |
1 | 1.44 | 0.96 | 0.88 | 2.92 | 1.52 | 0.68 | 1.56 | 1.44 | 0.84 |
time (sec) |
N/A | 0.491 | 0.959 | 1.681 | 0.082 | 0.085 | 0.108 | 0.123 | 0.270 | 0.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 24 | 23 | 34 | 53 | 26 | 0 | 36 | 25 |
N.S. |
1 | 0.00 | 0.89 | 0.85 | 1.26 | 1.96 | 0.96 | 0.00 | 1.33 | 0.93 |
time (sec) |
N/A | 0.000 | 2.476 | 0.215 | 0.078 | 0.109 | 0.106 | 0.000 | 0.280 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 63 | 63 | 97 | 108 | 122 | 117 | 0 | 0 |
N.S. |
1 | 0.00 | 2.33 | 2.33 | 3.59 | 4.00 | 4.52 | 4.33 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.060 | 136.815 | 4.962 | 0.094 | 0.163 | 0.357 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 23 | 58 | 0 | 37 | 37 | 39 | 25 | 0 |
N.S. |
1 | 1.04 | 0.88 | 2.23 | 0.00 | 1.42 | 1.42 | 1.50 | 0.96 | 0.00 |
time (sec) |
N/A | 0.849 | 0.246 | 3.184 | 0.000 | 0.085 | 0.421 | 0.728 | 0.293 | 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 | 13 | 7 | 7 | 6 | 5 | 5 | 8 | 5 | 5 | 5 |
N.S. |
1 | 0.54 | 0.54 | 0.46 | 0.38 | 0.38 | 0.62 | 0.38 | 0.38 | 0.38 |
time (sec) |
N/A | 0.122 | 0.000 | 0.025 | 0.027 | 0.081 | 0.014 | 0.105 | 0.264 | 0.002 |
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 | 20 | 15 | 19 | 16 | 16 | 22 | 17 | 21 | 12 |
N.S. |
1 | 1.33 | 1.00 | 1.27 | 1.07 | 1.07 | 1.47 | 1.13 | 1.40 | 0.80 |
time (sec) |
N/A | 0.145 | 0.004 | 0.131 | 0.036 | 0.071 | 0.039 | 0.105 | 0.302 | 0.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 44 | 16 | 21 | 0 | 19 | 19 | 0 | 18 | 0 |
N.S. |
1 | 1.91 | 0.70 | 0.91 | 0.00 | 0.83 | 0.83 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.254 | 0.019 | 0.591 | 0.000 | 0.078 | 2.650 | 0.000 | 0.272 | 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 | 14 | 26 | 26 | 26 | 25 | 25 | 24 | 25 | 32 | 29 |
N.S. |
1 | 1.86 | 1.86 | 1.86 | 1.79 | 1.79 | 1.71 | 1.79 | 2.29 | 2.07 |
time (sec) |
N/A | 0.300 | 0.072 | 0.089 | 0.034 | 0.085 | 0.060 | 0.106 | 8.122 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 25 | 47 | 34 | 22 | 24 | 32 | 25 | 22 |
N.S. |
1 | 0.00 | 1.14 | 2.14 | 1.55 | 1.00 | 1.09 | 1.45 | 1.14 | 1.00 |
time (sec) |
N/A | 0.000 | 0.038 | 9.009 | 0.087 | 0.085 | 0.149 | 0.110 | 0.293 | 3.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 35 | 42 | 36 | 36 | 116 | 36 | 39 | 163 |
N.S. |
1 | 0.00 | 1.40 | 1.68 | 1.44 | 1.44 | 4.64 | 1.44 | 1.56 | 6.52 |
time (sec) |
N/A | 0.000 | 7.935 | 1.013 | 0.077 | 0.086 | 0.220 | 0.127 | 0.340 | 4.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 22 | 61 | 54 | 61 | 25 | 61 | 21 |
N.S. |
1 | 0.00 | 0.95 | 1.00 | 2.77 | 2.45 | 2.77 | 1.14 | 2.77 | 0.95 |
time (sec) |
N/A | 0.000 | 0.022 | 0.319 | 0.044 | 0.079 | 6.828 | 0.205 | 0.290 | 0.277 |
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 | 29 | 23 | 22 | 19 | 18 | 18 | 19 | 18 | 31 | 21 |
N.S. |
1 | 0.79 | 0.76 | 0.66 | 0.62 | 0.62 | 0.66 | 0.62 | 1.07 | 0.72 |
time (sec) |
N/A | 0.320 | 0.270 | 0.121 | 0.163 | 0.071 | 0.120 | 0.103 | 0.286 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 17 | 19 | 16 | 14 | 164 | 16 | 16 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 1.06 | 0.89 | 0.78 | 9.11 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 0.398 | 0.690 | 0.149 | 0.076 | 0.079 | 0.133 | 0.295 | 4.326 |
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 | 34 | 34 | 42 | 25 | 37 | 33 | 34 | 33 |
N.S. |
1 | 0.00 | 1.17 | 1.17 | 1.45 | 0.86 | 1.28 | 1.14 | 1.17 | 1.14 |
time (sec) |
N/A | 0.000 | 0.151 | 0.197 | 0.149 | 0.086 | 0.109 | 0.116 | 0.297 | 0.417 |
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 | 39 | 37 | 37 | 37 | 50 | 32 | 38 | 55 | 325 |
N.S. |
1 | 1.15 | 1.09 | 1.09 | 1.09 | 1.47 | 0.94 | 1.12 | 1.62 | 9.56 |
time (sec) |
N/A | 0.411 | 0.022 | 0.113 | 0.031 | 0.067 | 0.308 | 0.113 | 0.285 | 4.134 |
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 | 15 | 15 | 14 | 14 | 10 | 14 | 29 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.94 | 0.88 | 0.88 | 0.62 | 0.88 | 1.81 | 0.94 |
time (sec) |
N/A | 0.171 | 0.057 | 0.118 | 0.030 | 0.080 | 0.061 | 0.113 | 0.268 | 3.924 |
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 | 14 | 20 | 20 | 20 | 18 | 19 | 15 | 21 | 21 | 19 |
N.S. |
1 | 1.43 | 1.43 | 1.43 | 1.29 | 1.36 | 1.07 | 1.50 | 1.50 | 1.36 |
time (sec) |
N/A | 0.245 | 0.008 | 0.069 | 0.034 | 0.071 | 0.202 | 0.106 | 0.246 | 0.198 |
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 | 30 | 16 | 16 | 16 | 15 | 17 | 14 | 91 | 18 | 16 |
N.S. |
1 | 0.53 | 0.53 | 0.53 | 0.50 | 0.57 | 0.47 | 3.03 | 0.60 | 0.53 |
time (sec) |
N/A | 0.179 | 0.008 | 0.161 | 0.041 | 0.080 | 0.051 | 0.108 | 0.265 | 3.996 |