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 | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 33 | 35 | 30 | 28 | 28 | 32 | 28 | 27 | 23 |
N.S. |
1 | 1.27 | 1.35 | 1.15 | 1.08 | 1.08 | 1.23 | 1.08 | 1.04 | 0.88 |
time (sec) |
N/A | 0.177 | 0.011 | 0.269 | 0.032 | 0.070 | 0.058 | 0.109 | 0.186 | 1.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 39 | 44 | 45 | 45 | 49 | 0 | 814 | 46 |
N.S. |
1 | 0.00 | 1.30 | 1.47 | 1.50 | 1.50 | 1.63 | 0.00 | 27.13 | 1.53 |
time (sec) |
N/A | 0.000 | 0.163 | 134.589 | 0.542 | 0.074 | 23.649 | 0.000 | 0.540 | 1.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 49 | 68 | 35 | 65 | 34 | 34 | 36 | 58 | 20 |
N.S. |
1 | 2.33 | 3.24 | 1.67 | 3.10 | 1.62 | 1.62 | 1.71 | 2.76 | 0.95 |
time (sec) |
N/A | 0.589 | 0.070 | 0.972 | 0.077 | 0.065 | 0.084 | 0.160 | 0.189 | 1.578 |
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 | 17 | 18 | 17 | 17 | 17 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.259 | 0.011 | 1.442 | 0.032 | 0.065 | 0.111 | 0.115 | 0.178 | 0.138 |
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 | 20 | 20 | 21 | 20 | 20 | 20 | 21 | 20 | 20 |
N.S. |
1 | 0.77 | 0.77 | 0.81 | 0.77 | 0.77 | 0.77 | 0.81 | 0.77 | 0.77 |
time (sec) |
N/A | 0.174 | 0.005 | 0.125 | 0.026 | 0.060 | 0.179 | 0.119 | 0.192 | 0.077 |
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 | 8 | 7 | 7 | 8 | 7 | 7 | 7 | 8 | 7 | 7 |
N.S. |
1 | 0.88 | 0.88 | 1.00 | 0.88 | 0.88 | 0.88 | 1.00 | 0.88 | 0.88 |
time (sec) |
N/A | 0.151 | 0.001 | 0.038 | 0.030 | 0.056 | 0.028 | 0.115 | 0.196 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F(-2) | A | F(-1) | A | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 46 | 205 | 0 | 45 | 0 | 48 | 34 | 0 |
N.S. |
1 | 0.00 | 1.53 | 6.83 | 0.00 | 1.50 | 0.00 | 1.60 | 1.13 | 0.00 |
time (sec) |
N/A | 0.000 | 0.188 | 0.198 | 0.000 | 0.082 | 0.000 | 0.778 | 0.216 | 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 | 30 | 23 | 23 | 24 | 24 | 23 | 24 | 26 | 23 | 23 |
N.S. |
1 | 0.77 | 0.77 | 0.80 | 0.80 | 0.77 | 0.80 | 0.87 | 0.77 | 0.77 |
time (sec) |
N/A | 0.495 | 0.142 | 3.678 | 0.068 | 0.077 | 0.102 | 0.141 | 0.206 | 1.553 |
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 | 15 | 15 | 15 | 16 | 15 | 15 | 14 | 15 | 15 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 0.93 | 1.00 | 1.00 | 1.53 |
time (sec) |
N/A | 0.470 | 0.013 | 0.381 | 0.068 | 0.063 | 0.060 | 0.118 | 0.200 | 1.531 |
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 | 28 | 0 | 30 | 30 | 32 | 32 | 26 | 30 | 31 | 29 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 1.14 | 1.14 | 0.93 | 1.07 | 1.11 | 1.04 |
time (sec) |
N/A | 0.000 | 3.175 | 0.213 | 0.079 | 0.066 | 0.121 | 0.119 | 0.208 | 1.439 |
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 | 32 | 31 | 31 | 28 | 27 | 42 | 24 | 27 | 28 | 26 |
N.S. |
1 | 0.97 | 0.97 | 0.88 | 0.84 | 1.31 | 0.75 | 0.84 | 0.88 | 0.81 |
time (sec) |
N/A | 0.540 | 0.020 | 0.342 | 0.148 | 0.076 | 0.162 | 0.125 | 0.250 | 1.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 503 | 36 | 53 | 52 | 52 | 51 | 89 | 63 | 33 |
N.S. |
1 | 18.63 | 1.33 | 1.96 | 1.93 | 1.93 | 1.89 | 3.30 | 2.33 | 1.22 |
time (sec) |
N/A | 3.355 | 0.293 | 1.092 | 0.100 | 0.058 | 0.107 | 0.136 | 0.199 | 1.609 |
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 | 23 | 0 | 21 | 47 | 25 | 25 | 24 | 63 | 24 | 19 |
N.S. |
1 | 0.00 | 0.91 | 2.04 | 1.09 | 1.09 | 1.04 | 2.74 | 1.04 | 0.83 |
time (sec) |
N/A | 0.000 | 0.045 | 0.198 | 0.046 | 0.068 | 0.130 | 0.119 | 0.200 | 1.637 |
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 | 22 | 20 | 21 | 23 | 22 | 20 | 23 | 20 | 20 |
N.S. |
1 | 0.92 | 0.83 | 0.88 | 0.96 | 0.92 | 0.83 | 0.96 | 0.83 | 0.83 |
time (sec) |
N/A | 0.317 | 0.091 | 0.795 | 0.158 | 0.085 | 0.232 | 0.127 | 0.202 | 17.320 |
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 | 31 | 0 | 29 | 29 | 58 | 32 | 26 | 32 | 61 | 28 |
N.S. |
1 | 0.00 | 0.94 | 0.94 | 1.87 | 1.03 | 0.84 | 1.03 | 1.97 | 0.90 |
time (sec) |
N/A | 0.000 | 0.190 | 0.817 | 0.104 | 0.073 | 4.712 | 0.141 | 0.230 | 1.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 23 | 0 | 16 | 26 | 0 | 21 | 16 |
N.S. |
1 | 0.00 | 0.90 | 1.10 | 0.00 | 0.76 | 1.24 | 0.00 | 1.00 | 0.76 |
time (sec) |
N/A | 0.000 | 0.013 | 1.306 | 0.000 | 0.065 | 0.102 | 0.000 | 0.217 | 0.135 |
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 | 22 | 41 | 21 | 20 | 40 | 40 | 46 | 40 | 38 | 37 |
N.S. |
1 | 1.86 | 0.95 | 0.91 | 1.82 | 1.82 | 2.09 | 1.82 | 1.73 | 1.68 |
time (sec) |
N/A | 0.184 | 0.007 | 0.204 | 0.033 | 0.053 | 0.021 | 0.113 | 0.200 | 1.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 90 | 24 | 21 | 46 | 30 | 26 | 0 | 54 | 49 |
N.S. |
1 | 3.21 | 0.86 | 0.75 | 1.64 | 1.07 | 0.93 | 0.00 | 1.93 | 1.75 |
time (sec) |
N/A | 1.642 | 0.039 | 9.852 | 0.190 | 0.075 | 0.154 | 0.000 | 0.195 | 1.576 |
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 | 24 | 26 | 23 | 24 | 26 | 35 | 22 | 27 | 47 | 26 |
N.S. |
1 | 1.08 | 0.96 | 1.00 | 1.08 | 1.46 | 0.92 | 1.12 | 1.96 | 1.08 |
time (sec) |
N/A | 0.676 | 0.011 | 0.203 | 0.033 | 0.066 | 0.453 | 0.115 | 0.212 | 0.093 |
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 | 17 | 46 | 16 | 18 | 38 | 23 | 12 | 25 | 21 | 17 |
N.S. |
1 | 2.71 | 0.94 | 1.06 | 2.24 | 1.35 | 0.71 | 1.47 | 1.24 | 1.00 |
time (sec) |
N/A | 0.849 | 0.092 | 0.270 | 0.088 | 0.065 | 0.039 | 0.120 | 0.207 | 0.142 |
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 | 12 | 17 | 19 | 15 | 22 | 18 | 19 | 19 |
N.S. |
1 | 1.25 | 1.00 | 1.42 | 1.58 | 1.25 | 1.83 | 1.50 | 1.58 | 1.58 |
time (sec) |
N/A | 0.288 | 0.007 | 1.756 | 0.031 | 0.061 | 0.069 | 0.110 | 0.198 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F(-1) | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 34 | 34 | 35 | 33 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.03 | 0.97 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.444 | 0.095 | 0.434 | 0.078 | 0.000 | 0.000 | 0.215 | 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 | 28 | 15 | 15 | 14 | 11 | 14 | 14 | 11 | 14 | 14 |
N.S. |
1 | 0.54 | 0.54 | 0.50 | 0.39 | 0.50 | 0.50 | 0.39 | 0.50 | 0.50 |
time (sec) |
N/A | 0.260 | 0.002 | 0.069 | 0.028 | 0.054 | 0.039 | 0.106 | 0.223 | 0.037 |
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 | 22 | 34 | 21 | 20 | 62 | 19 | 17 | 21 | 35 | 25 |
N.S. |
1 | 1.55 | 0.95 | 0.91 | 2.82 | 0.86 | 0.77 | 0.95 | 1.59 | 1.14 |
time (sec) |
N/A | 0.440 | 0.027 | 0.280 | 0.036 | 0.068 | 0.050 | 0.113 | 0.190 | 0.073 |
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 | 29 | 22 | 27 | 19 | 26 | 26 | 19 | 28 | 21 |
N.S. |
1 | 1.21 | 0.92 | 1.12 | 0.79 | 1.08 | 1.08 | 0.79 | 1.17 | 0.88 |
time (sec) |
N/A | 0.939 | 0.530 | 0.704 | 0.156 | 0.072 | 0.232 | 0.127 | 0.204 | 1.487 |
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 | 21 | 22 | 20 | 20 | 19 | 21 | 16 | 10 |
N.S. |
1 | 1.40 | 1.05 | 1.10 | 1.00 | 1.00 | 0.95 | 1.05 | 0.80 | 0.50 |
time (sec) |
N/A | 0.281 | 0.005 | 0.114 | 0.033 | 0.064 | 0.047 | 0.104 | 0.195 | 1.401 |
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 | 18 | 18 | 17 | 16 | 16 | 15 | 16 | 18 | 16 |
N.S. |
1 | 0.90 | 0.90 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.90 | 0.80 |
time (sec) |
N/A | 0.264 | 0.014 | 0.126 | 0.039 | 0.061 | 0.041 | 0.114 | 0.200 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 150 | 35 | 66 | 49 | 36 | 63 | 0 | 293 |
N.S. |
1 | 0.00 | 4.55 | 1.06 | 2.00 | 1.48 | 1.09 | 1.91 | 0.00 | 8.88 |
time (sec) |
N/A | 0.000 | 0.212 | 0.779 | 0.582 | 0.070 | 0.156 | 0.390 | 0.348 | 0.596 |
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 | 19 | 19 | 17 | 16 | 16 | 17 | 16 | 17 | 16 |
N.S. |
1 | 0.70 | 0.70 | 0.63 | 0.59 | 0.59 | 0.63 | 0.59 | 0.63 | 0.59 |
time (sec) |
N/A | 0.634 | 0.109 | 0.151 | 0.062 | 0.076 | 0.103 | 0.124 | 0.187 | 1.475 |
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 | 25 | 44 | 44 | 44 | 42 | 42 | 97 | 42 | 41 | 76 |
N.S. |
1 | 1.76 | 1.76 | 1.76 | 1.68 | 1.68 | 3.88 | 1.68 | 1.64 | 3.04 |
time (sec) |
N/A | 0.235 | 0.004 | 0.207 | 0.041 | 0.058 | 0.032 | 0.109 | 0.196 | 1.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 30 | 29 | 54 | 59 | 26 | 0 | 65 | 23 |
N.S. |
1 | 0.00 | 1.15 | 1.12 | 2.08 | 2.27 | 1.00 | 0.00 | 2.50 | 0.88 |
time (sec) |
N/A | 0.000 | 0.107 | 5.972 | 0.098 | 0.072 | 0.126 | 0.000 | 2.282 | 1.560 |
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 | 33 | 0 | 45 | 42 | 45 | 39 | 36 | 93 | 75 | 98 |
N.S. |
1 | 0.00 | 1.36 | 1.27 | 1.36 | 1.18 | 1.09 | 2.82 | 2.27 | 2.97 |
time (sec) |
N/A | 0.000 | 0.098 | 0.934 | 0.359 | 0.066 | 0.279 | 0.288 | 0.234 | 1.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 47 | 20 | 18 | 323 | 19 | 22 | 19 | 25 | 21 |
N.S. |
1 | 2.76 | 1.18 | 1.06 | 19.00 | 1.12 | 1.29 | 1.12 | 1.47 | 1.24 |
time (sec) |
N/A | 0.220 | 0.023 | 0.286 | 0.179 | 0.070 | 0.067 | 0.112 | 0.214 | 1.438 |
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 | 22 | 29 | 31 | 42 | 64 | 64 | 56 | 64 | 61 | 37 |
N.S. |
1 | 1.32 | 1.41 | 1.91 | 2.91 | 2.91 | 2.55 | 2.91 | 2.77 | 1.68 |
time (sec) |
N/A | 0.181 | 0.009 | 0.201 | 0.032 | 0.061 | 0.027 | 0.107 | 0.190 | 1.508 |
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 | 13 | 11 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 1.00 | 0.85 | 0.69 | 0.62 | 0.62 | 0.54 | 0.62 | 0.69 | 0.62 |
time (sec) |
N/A | 0.290 | 0.016 | 0.073 | 0.041 | 0.070 | 0.045 | 0.112 | 0.207 | 0.048 |
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 | 27 | 0 | 28 | 28 | 44 | 44 | 27 | 55 | 54 | 95 |
N.S. |
1 | 0.00 | 1.04 | 1.04 | 1.63 | 1.63 | 1.00 | 2.04 | 2.00 | 3.52 |
time (sec) |
N/A | 0.000 | 0.046 | 0.526 | 0.173 | 0.069 | 0.120 | 0.293 | 0.225 | 1.602 |
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 | 10 | 10 | 11 | 10 | 11 | 7 | 11 | 12 | 10 |
N.S. |
1 | 0.53 | 0.53 | 0.58 | 0.53 | 0.58 | 0.37 | 0.58 | 0.63 | 0.53 |
time (sec) |
N/A | 0.153 | 0.001 | 0.043 | 0.032 | 0.061 | 0.033 | 0.108 | 0.191 | 1.365 |
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 | 30 | 29 | 25 | 32 | 20 | 32 | 47 | 32 |
N.S. |
1 | 0.00 | 1.11 | 1.07 | 0.93 | 1.19 | 0.74 | 1.19 | 1.74 | 1.19 |
time (sec) |
N/A | 0.000 | 2.159 | 0.902 | 0.103 | 0.072 | 0.131 | 0.115 | 0.231 | 1.501 |
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 | 18 | 14 | 14 | 13 | 13 | 14 | 13 | 14 | 13 |
N.S. |
1 | 0.90 | 0.70 | 0.70 | 0.65 | 0.65 | 0.70 | 0.65 | 0.70 | 0.65 |
time (sec) |
N/A | 0.157 | 0.010 | 1.840 | 0.035 | 0.077 | 0.066 | 0.110 | 0.205 | 1.379 |
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 | 32 | 32 | 23 | 27 | 23 | 22 | 21 | 27 | 20 |
N.S. |
1 | 1.07 | 1.07 | 0.77 | 0.90 | 0.77 | 0.73 | 0.70 | 0.90 | 0.67 |
time (sec) |
N/A | 0.324 | 0.764 | 0.243 | 0.035 | 0.077 | 0.099 | 0.127 | 0.247 | 1.649 |
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 | 28 | 28 | 28 | 29 | 28 | 28 | 26 | 31 | 28 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.00 | 0.93 | 1.11 | 1.00 | 1.00 |
time (sec) |
N/A | 0.334 | 0.011 | 0.096 | 0.036 | 0.065 | 0.073 | 0.111 | 0.193 | 0.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 43 | 0 | 47 | 63 | 0 | 66 | 27 |
N.S. |
1 | 0.00 | 1.13 | 1.87 | 0.00 | 2.04 | 2.74 | 0.00 | 2.87 | 1.17 |
time (sec) |
N/A | 0.000 | 0.065 | 0.671 | 0.000 | 0.072 | 0.166 | 0.000 | 0.194 | 0.167 |
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 | 21 | 20 | 18 | 18 | 22 | 17 | 26 | 20 | 17 |
N.S. |
1 | 0.72 | 0.69 | 0.62 | 0.62 | 0.76 | 0.59 | 0.90 | 0.69 | 0.59 |
time (sec) |
N/A | 0.773 | 0.104 | 0.698 | 0.149 | 0.076 | 0.146 | 0.112 | 0.207 | 1.632 |
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 | 28 | 0 | 26 | 25 | 34 | 123 | 24 | 0 | 36 | 25 |
N.S. |
1 | 0.00 | 0.93 | 0.89 | 1.21 | 4.39 | 0.86 | 0.00 | 1.29 | 0.89 |
time (sec) |
N/A | 0.000 | 5.218 | 133.052 | 1.015 | 0.080 | 1.652 | 0.000 | 0.210 | 1.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 62 | 23 | 19 | 20 | 20 | 15 | 0 | 23 | 20 |
N.S. |
1 | 2.21 | 0.82 | 0.68 | 0.71 | 0.71 | 0.54 | 0.00 | 0.82 | 0.71 |
time (sec) |
N/A | 0.311 | 0.058 | 0.214 | 0.184 | 0.071 | 0.096 | 0.000 | 0.195 | 1.453 |
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 | 28 | 29 | 27 | 24 | 23 | 23 | 22 | 23 | 286 | 26 |
N.S. |
1 | 1.04 | 0.96 | 0.86 | 0.82 | 0.82 | 0.79 | 0.82 | 10.21 | 0.93 |
time (sec) |
N/A | 0.421 | 1.172 | 0.172 | 0.193 | 0.068 | 0.162 | 0.131 | 1.006 | 0.145 |
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 | 12 | 17 | 12 | 12 | 37 | 14 | 12 | 14 | 12 | 11 |
N.S. |
1 | 1.42 | 1.00 | 1.00 | 3.08 | 1.17 | 1.00 | 1.17 | 1.00 | 0.92 |
time (sec) |
N/A | 0.249 | 0.031 | 0.063 | 0.034 | 0.062 | 0.041 | 0.110 | 0.217 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 50 | 46 | 47 | 45 | 0 | 51 | 222 | 45 |
N.S. |
1 | 0.00 | 1.79 | 1.64 | 1.68 | 1.61 | 0.00 | 1.82 | 7.93 | 1.61 |
time (sec) |
N/A | 0.000 | 0.158 | 108.693 | 0.122 | 0.076 | 0.000 | 0.381 | 200.029 | 1.775 |
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 | 46 | 23 | 21 | 41 | 27 | 17 | 39 | 21 | 20 |
N.S. |
1 | 1.70 | 0.85 | 0.78 | 1.52 | 1.00 | 0.63 | 1.44 | 0.78 | 0.74 |
time (sec) |
N/A | 0.568 | 0.084 | 0.396 | 0.061 | 0.072 | 0.104 | 0.115 | 0.195 | 1.511 |
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 | 18 | 17 | 18 | 22 | 17 | 17 | 16 | 19 | 17 |
N.S. |
1 | 1.06 | 1.00 | 1.06 | 1.29 | 1.00 | 1.00 | 0.94 | 1.12 | 1.00 |
time (sec) |
N/A | 0.469 | 0.011 | 0.338 | 0.026 | 0.069 | 0.138 | 0.110 | 0.179 | 0.158 |
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 | 25 | 25 | 19 | 22 | 24 | 22 | 26 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.76 | 0.88 | 0.96 | 0.88 | 1.04 | 0.88 |
time (sec) |
N/A | 0.512 | 0.050 | 0.187 | 0.105 | 0.073 | 0.071 | 0.124 | 0.183 | 1.507 |
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 | 17 | 17 | 15 | 14 | 31 | 14 | 14 | 20 | 14 |
N.S. |
1 | 0.63 | 0.63 | 0.56 | 0.52 | 1.15 | 0.52 | 0.52 | 0.74 | 0.52 |
time (sec) |
N/A | 0.151 | 0.014 | 0.079 | 0.034 | 0.070 | 0.051 | 0.112 | 0.180 | 0.069 |
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 | 30 | 0 | 26 | 27 | 33 | 38 | 20 | 23 | 86 | 47 |
N.S. |
1 | 0.00 | 0.87 | 0.90 | 1.10 | 1.27 | 0.67 | 0.77 | 2.87 | 1.57 |
time (sec) |
N/A | 0.000 | 0.127 | 0.510 | 0.165 | 0.068 | 0.056 | 0.133 | 0.182 | 1.519 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 50 | 16 | 17 | 16 | 19 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 2.50 | 0.80 | 0.85 | 0.80 | 0.95 | 0.80 |
time (sec) |
N/A | 0.474 | 0.026 | 0.242 | 0.147 | 0.073 | 0.109 | 0.115 | 0.192 | 1.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 40 | 19 | 44 | 38 | 26 | 0 | 27 | 23 | 28 |
N.S. |
1 | 1.82 | 0.86 | 2.00 | 1.73 | 1.18 | 0.00 | 1.23 | 1.05 | 1.27 |
time (sec) |
N/A | 4.098 | 0.074 | 2.566 | 0.160 | 0.080 | 0.000 | 0.223 | 0.175 | 2.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 51 | 0 | 52 | 49 | 81 | 77 | 55 |
N.S. |
1 | 0.00 | 1.09 | 1.59 | 0.00 | 1.62 | 1.53 | 2.53 | 2.41 | 1.72 |
time (sec) |
N/A | 0.000 | 0.192 | 123.751 | 0.000 | 0.079 | 3.756 | 0.535 | 0.192 | 3.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 52 | 34 | 45 | 45 | 29 | 48 | 40 | 35 |
N.S. |
1 | 0.00 | 2.36 | 1.55 | 2.05 | 2.05 | 1.32 | 2.18 | 1.82 | 1.59 |
time (sec) |
N/A | 0.000 | 3.558 | 0.113 | 0.087 | 0.071 | 0.250 | 0.114 | 0.175 | 1.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 23 | 12 | 23 | 20 | 20 | 22 | 22 | 29 | 27 |
N.S. |
1 | 1.92 | 1.00 | 1.92 | 1.67 | 1.67 | 1.83 | 1.83 | 2.42 | 2.25 |
time (sec) |
N/A | 0.273 | 0.020 | 0.234 | 0.027 | 0.070 | 0.052 | 0.122 | 0.193 | 0.140 |
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 | 40 | 29 | 27 | 52 | 33 | 24 | 33 | 39 | 26 |
N.S. |
1 | 1.67 | 1.21 | 1.12 | 2.17 | 1.38 | 1.00 | 1.38 | 1.62 | 1.08 |
time (sec) |
N/A | 0.526 | 0.038 | 0.521 | 0.037 | 0.073 | 0.087 | 0.113 | 0.178 | 1.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 55 | 27 | 61 | 51 | 0 | 299 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.83 | 0.90 | 2.03 | 1.70 | 0.00 | 9.97 | 0.97 |
time (sec) |
N/A | 0.000 | 1.463 | 0.849 | 0.443 | 0.072 | 0.296 | 0.000 | 0.345 | 1.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | F(-1) | B | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 48 | 67 | 88 | 167 | 80 | 80 | 0 | 352 | 191 |
N.S. |
1 | 1.41 | 1.97 | 2.59 | 4.91 | 2.35 | 2.35 | 0.00 | 10.35 | 5.62 |
time (sec) |
N/A | 34.859 | 0.445 | 10.112 | 1.158 | 0.097 | 0.793 | 0.000 | 0.199 | 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 | 29 | 22 | 22 | 27 | 20 | 26 | 22 | 20 | 33 | 22 |
N.S. |
1 | 0.76 | 0.76 | 0.93 | 0.69 | 0.90 | 0.76 | 0.69 | 1.14 | 0.76 |
time (sec) |
N/A | 0.595 | 1.110 | 0.697 | 0.109 | 0.068 | 1.090 | 0.137 | 0.192 | 1.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 19 | 19 | 18 | 11 | 20 | 14 | 12 | 17 | 16 |
N.S. |
1 | 1.73 | 1.73 | 1.64 | 1.00 | 1.82 | 1.27 | 1.09 | 1.55 | 1.45 |
time (sec) |
N/A | 0.176 | 0.005 | 0.153 | 0.036 | 0.067 | 0.048 | 0.116 | 0.185 | 1.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 32 | 31 | 31 | 0 | 0 | 27 | 31 |
N.S. |
1 | 0.00 | 0.90 | 1.07 | 1.03 | 1.03 | 0.00 | 0.00 | 0.90 | 1.03 |
time (sec) |
N/A | 0.000 | 0.382 | 72.963 | 0.088 | 0.079 | 0.000 | 0.000 | 0.187 | 1.657 |
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 | 17 | 20 | 6 | 11 | 5 | 6 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 0.35 | 0.65 | 0.29 | 0.35 | 0.88 | 0.82 |
time (sec) |
N/A | 0.544 | 0.050 | 0.292 | 0.105 | 0.072 | 0.061 | 0.117 | 0.182 | 1.622 |
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 | 28 | 27 | 20 | 21 | 21 | 26 | 21 | 21 | 21 |
N.S. |
1 | 1.12 | 1.08 | 0.80 | 0.84 | 0.84 | 1.04 | 0.84 | 0.84 | 0.84 |
time (sec) |
N/A | 0.150 | 0.003 | 0.115 | 0.036 | 0.062 | 0.023 | 0.119 | 0.174 | 1.427 |
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 | 31 | 35 | 26 | 22 | 27 | 29 | 31 | 66 | 32 | 21 |
N.S. |
1 | 1.13 | 0.84 | 0.71 | 0.87 | 0.94 | 1.00 | 2.13 | 1.03 | 0.68 |
time (sec) |
N/A | 0.398 | 0.051 | 0.266 | 0.046 | 0.069 | 0.095 | 0.118 | 0.178 | 0.094 |
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 | 31 | 31 | 22 | 21 | 36 | 26 | 21 | 27 | 22 |
N.S. |
1 | 1.03 | 1.03 | 0.73 | 0.70 | 1.20 | 0.87 | 0.70 | 0.90 | 0.73 |
time (sec) |
N/A | 0.182 | 0.042 | 0.108 | 0.042 | 0.071 | 0.116 | 0.111 | 0.183 | 1.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 38 | 31 | 26 | 126 | 26 | 27 | 42 | 29 | 0 |
N.S. |
1 | 1.46 | 1.19 | 1.00 | 4.85 | 1.00 | 1.04 | 1.62 | 1.12 | 0.00 |
time (sec) |
N/A | 1.545 | 0.060 | 0.851 | 0.092 | 0.074 | 0.139 | 0.125 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 265 | 243 | 28 | 54 | 27 | 24 | 27 | 27 | 41 |
N.S. |
1 | 13.25 | 12.15 | 1.40 | 2.70 | 1.35 | 1.20 | 1.35 | 1.35 | 2.05 |
time (sec) |
N/A | 0.701 | 0.051 | 1.471 | 0.040 | 0.066 | 0.084 | 0.122 | 0.178 | 0.158 |
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 | 45 | 49 | 29 | 30 | 37 | 46 | 45 | 45 |
N.S. |
1 | 0.00 | 1.80 | 1.96 | 1.16 | 1.20 | 1.48 | 1.84 | 1.80 | 1.80 |
time (sec) |
N/A | 0.000 | 0.055 | 1.651 | 0.106 | 0.073 | 0.423 | 0.216 | 0.178 | 1.729 |
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 | 31 | 27 | 43 | 36 | 27 | 28 | 33 | 28 |
N.S. |
1 | 0.00 | 1.15 | 1.00 | 1.59 | 1.33 | 1.00 | 1.04 | 1.22 | 1.04 |
time (sec) |
N/A | 0.000 | 0.428 | 0.925 | 0.148 | 0.070 | 0.073 | 0.118 | 0.181 | 1.582 |
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 | 26 | 60 | 45 | 42 | 42 | 37 | 42 | 39 | 42 | 42 |
N.S. |
1 | 2.31 | 1.73 | 1.62 | 1.62 | 1.42 | 1.62 | 1.50 | 1.62 | 1.62 |
time (sec) |
N/A | 0.256 | 0.015 | 0.326 | 0.030 | 0.069 | 0.099 | 0.112 | 0.182 | 1.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 30 | 26 | 23 | 22 | 52 | 19 | 0 | 29 | 24 |
N.S. |
1 | 1.15 | 1.00 | 0.88 | 0.85 | 2.00 | 0.73 | 0.00 | 1.12 | 0.92 |
time (sec) |
N/A | 0.276 | 0.295 | 0.575 | 0.035 | 0.076 | 0.182 | 0.000 | 0.194 | 1.558 |
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 | 38 | 37 | 49 | 39 | 32 | 5401 | 40 | 40 |
N.S. |
1 | 0.00 | 1.23 | 1.19 | 1.58 | 1.26 | 1.03 | 174.23 | 1.29 | 1.29 |
time (sec) |
N/A | 0.000 | 0.074 | 11.273 | 0.233 | 0.070 | 0.521 | 1.806 | 0.202 | 3.067 |
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 | 1292 | 207 | 323 | 1726 | 333 | 366 | 351 | 500 | 183 |
N.S. |
1 | 53.83 | 8.62 | 13.46 | 71.92 | 13.88 | 15.25 | 14.62 | 20.83 | 7.62 |
time (sec) |
N/A | 16.278 | 0.183 | 203.115 | 0.101 | 0.081 | 0.977 | 0.145 | 0.164 | 2.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 45 | 43 | 45 | 44 | 0 | 100 | 50 |
N.S. |
1 | 0.00 | 0.97 | 1.55 | 1.48 | 1.55 | 1.52 | 0.00 | 3.45 | 1.72 |
time (sec) |
N/A | 0.000 | 0.457 | 1.467 | 0.266 | 0.071 | 0.228 | 0.000 | 77.202 | 1.716 |
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 | 36 | 50 | 34 | 27 | 26 | 33 | 20 | 26 | 52 | 26 |
N.S. |
1 | 1.39 | 0.94 | 0.75 | 0.72 | 0.92 | 0.56 | 0.72 | 1.44 | 0.72 |
time (sec) |
N/A | 0.367 | 0.018 | 0.275 | 0.038 | 0.066 | 0.479 | 0.110 | 0.319 | 0.163 |
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 | 17 | 14 | 13 | 15 | 12 | 15 | 16 | 14 |
N.S. |
1 | 1.18 | 1.00 | 0.82 | 0.76 | 0.88 | 0.71 | 0.88 | 0.94 | 0.82 |
time (sec) |
N/A | 0.165 | 0.013 | 0.091 | 0.038 | 0.076 | 0.040 | 0.125 | 0.332 | 0.042 |
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 | 33 | 0 | 30 | 57 | 28 | 59 | 54 | 0 | 204 | 208 |
N.S. |
1 | 0.00 | 0.91 | 1.73 | 0.85 | 1.79 | 1.64 | 0.00 | 6.18 | 6.30 |
time (sec) |
N/A | 0.000 | 0.291 | 99.938 | 0.591 | 0.083 | 1.302 | 0.000 | 200.021 | 2.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 29 | 52 | 73 | 65 | 70 | 0 | 156 | 80 |
N.S. |
1 | 0.00 | 1.04 | 1.86 | 2.61 | 2.32 | 2.50 | 0.00 | 5.57 | 2.86 |
time (sec) |
N/A | 0.000 | 7.493 | 4.333 | 0.254 | 0.078 | 2.164 | 0.000 | 200.022 | 1.756 |
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 | 31 | 28 | 28 | 29 | 28 | 24 | 28 | 29 | 26 |
N.S. |
1 | 1.15 | 1.04 | 1.04 | 1.07 | 1.04 | 0.89 | 1.04 | 1.07 | 0.96 |
time (sec) |
N/A | 1.272 | 0.184 | 0.431 | 0.074 | 0.071 | 0.099 | 0.113 | 0.185 | 1.537 |
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 | 24 | 27 | 28 | 25 | 25 | 24 | 24 | 24 | 1105 | 28 |
N.S. |
1 | 1.12 | 1.17 | 1.04 | 1.04 | 1.00 | 1.00 | 1.00 | 46.04 | 1.17 |
time (sec) |
N/A | 2.700 | 5.099 | 1.214 | 0.125 | 0.074 | 0.521 | 0.182 | 0.899 | 1.767 |
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 | 24 | 17 | 15 | 20 | 14 | 19 | 14 | 15 | 19 |
N.S. |
1 | 1.41 | 1.00 | 0.88 | 1.18 | 0.82 | 1.12 | 0.82 | 0.88 | 1.12 |
time (sec) |
N/A | 0.183 | 0.020 | 0.106 | 0.033 | 0.069 | 0.049 | 0.111 | 0.195 | 1.417 |
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 | 23 | 22 | 22 | 39 | 43 | 43 | 41 | 38 | 40 | 24 |
N.S. |
1 | 0.96 | 0.96 | 1.70 | 1.87 | 1.87 | 1.78 | 1.65 | 1.74 | 1.04 |
time (sec) |
N/A | 0.199 | 0.007 | 0.168 | 0.106 | 0.076 | 0.054 | 0.119 | 0.197 | 1.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 31 | 52 | 0 | 51 | 42 | 100 | 175 | 84 |
N.S. |
1 | 0.00 | 0.84 | 1.41 | 0.00 | 1.38 | 1.14 | 2.70 | 4.73 | 2.27 |
time (sec) |
N/A | 0.000 | 0.262 | 125.046 | 0.000 | 0.076 | 9.817 | 0.338 | 200.026 | 2.205 |
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 | 35 | 43 | 40 | 33 | 0 | 45 | 37 | 55 | 64 | 30 |
N.S. |
1 | 1.23 | 1.14 | 0.94 | 0.00 | 1.29 | 1.06 | 1.57 | 1.83 | 0.86 |
time (sec) |
N/A | 0.578 | 0.138 | 0.365 | 0.000 | 0.069 | 0.109 | 0.111 | 0.180 | 1.481 |
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 | 22 | 29 | 22 | 26 | 0 | 23 | 22 | 0 | 26 | 21 |
N.S. |
1 | 1.32 | 1.00 | 1.18 | 0.00 | 1.05 | 1.00 | 0.00 | 1.18 | 0.95 |
time (sec) |
N/A | 0.485 | 0.158 | 0.268 | 0.000 | 0.065 | 0.070 | 0.000 | 0.186 | 0.143 |
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 | 87 | 59 | 60 | 51 | 51 | 58 | 51 | 87 | 46 |
N.S. |
1 | 3.48 | 2.36 | 2.40 | 2.04 | 2.04 | 2.32 | 2.04 | 3.48 | 1.84 |
time (sec) |
N/A | 1.022 | 0.474 | 0.450 | 0.040 | 0.068 | 0.064 | 0.111 | 0.184 | 1.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 41 | 26 | 20 | 0 | 23 | 24 | 23 | 26 | 19 |
N.S. |
1 | 2.05 | 1.30 | 1.00 | 0.00 | 1.15 | 1.20 | 1.15 | 1.30 | 0.95 |
time (sec) |
N/A | 1.142 | 0.146 | 0.500 | 0.000 | 0.070 | 0.111 | 0.111 | 0.190 | 1.517 |
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 | 33 | 0 | 42 | 43 | 55 | 42 | 42 | 56 | 54 | 37 |
N.S. |
1 | 0.00 | 1.27 | 1.30 | 1.67 | 1.27 | 1.27 | 1.70 | 1.64 | 1.12 |
time (sec) |
N/A | 0.000 | 0.083 | 0.060 | 0.113 | 0.071 | 0.148 | 0.144 | 0.204 | 1.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 109 | 73 | 32 | 48 | 72 | 46 | 90 | 58 | 48 |
N.S. |
1 | 4.19 | 2.81 | 1.23 | 1.85 | 2.77 | 1.77 | 3.46 | 2.23 | 1.85 |
time (sec) |
N/A | 0.463 | 0.027 | 1.057 | 0.029 | 0.067 | 3.424 | 0.125 | 0.194 | 0.242 |
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 | 16 | 16 | 16 | 15 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 1.562 | 0.185 | 3.306 | 0.451 | 0.067 | 0.068 | 0.150 | 0.187 | 1.642 |
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 | 18 | 17 | 15 | 14 | 13 | 13 | 12 | 14 | 13 | 13 |
N.S. |
1 | 0.94 | 0.83 | 0.78 | 0.72 | 0.72 | 0.67 | 0.78 | 0.72 | 0.72 |
time (sec) |
N/A | 0.165 | 0.001 | 0.050 | 0.031 | 0.056 | 0.041 | 0.107 | 0.195 | 1.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 101 | 82 | 29 | 74 | 74 | 88 | 74 | 84 | 74 |
N.S. |
1 | 3.61 | 2.93 | 1.04 | 2.64 | 2.64 | 3.14 | 2.64 | 3.00 | 2.64 |
time (sec) |
N/A | 0.226 | 0.034 | 0.256 | 0.033 | 0.066 | 0.031 | 0.114 | 0.179 | 1.453 |
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 | 24 | 0 | 24 | 22 | 21 | 23 | 20 | 44 | 40 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.88 | 0.96 | 0.83 | 1.83 | 1.67 | 0.96 |
time (sec) |
N/A | 0.000 | 0.079 | 0.450 | 0.123 | 0.074 | 54.414 | 0.127 | 0.190 | 1.571 |
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 | 26 | 15 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 1.18 | 0.68 | 0.59 | 0.55 | 0.55 | 0.55 | 0.55 | 0.59 | 0.55 |
time (sec) |
N/A | 0.280 | 0.007 | 0.117 | 0.054 | 0.062 | 0.046 | 0.118 | 0.194 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 48 | 48 | 35 | 33 | 33 | 37 | 39 | 368 | 37 |
N.S. |
1 | 2.18 | 2.18 | 1.59 | 1.50 | 1.50 | 1.68 | 1.77 | 16.73 | 1.68 |
time (sec) |
N/A | 1.768 | 0.029 | 0.589 | 0.165 | 0.079 | 0.170 | 0.160 | 29.961 | 1.630 |
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 | 16 | 0 | 14 | 14 | 13 | 13 | 10 | 30 | 16 | 0 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.81 | 0.81 | 0.62 | 1.88 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.053 | 0.303 | 0.114 | 0.066 | 1.149 | 0.131 | 0.202 | 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 | 18 | 18 | 19 | 18 | 18 | 14 | 19 | 18 | 18 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.95 | 0.95 | 0.74 | 1.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.172 | 0.001 | 0.045 | 0.029 | 0.063 | 0.027 | 0.112 | 0.187 | 0.031 |