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 | B | A | A | B | F | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 27 | 25 | 60 | 24 | 22 | 5629 | 149 | 25 |
N.S. |
1 | 0.93 | 0.93 | 0.86 | 2.07 | 0.83 | 0.76 | 194.10 | 5.14 | 0.86 |
time (sec) |
N/A | 0.369 | 0.163 | 0.441 | 0.268 | 0.069 | 0.420 | 0.250 | 0.320 | 1.318 |
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 | 25 | 31 | 35 | 20 | 43 | 27 | 24 |
N.S. |
1 | 1.70 | 0.85 | 0.93 | 1.15 | 1.30 | 0.74 | 1.59 | 1.00 | 0.89 |
time (sec) |
N/A | 1.050 | 1.338 | 0.503 | 0.103 | 0.066 | 0.184 | 0.118 | 0.254 | 0.429 |
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 | 12 | 12 | 11 | 12 | 12 | 8 | 13 | 12 | 10 |
N.S. |
1 | 0.50 | 0.50 | 0.46 | 0.50 | 0.50 | 0.33 | 0.54 | 0.50 | 0.42 |
time (sec) |
N/A | 0.151 | 0.002 | 0.086 | 0.024 | 0.070 | 0.030 | 0.114 | 0.235 | 0.065 |
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 | 25 | 0 | 43 | 37 | 59 | 48 | 54 | 62 | 34 | 51 |
N.S. |
1 | 0.00 | 1.72 | 1.48 | 2.36 | 1.92 | 2.16 | 2.48 | 1.36 | 2.04 |
time (sec) |
N/A | 0.000 | 0.170 | 0.425 | 0.078 | 0.066 | 0.174 | 0.120 | 0.225 | 1.416 |
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 | 20 | 56 | 20 | 21 | 24 | 19 | 19 | 0 | 31 | 25 |
N.S. |
1 | 2.80 | 1.00 | 1.05 | 1.20 | 0.95 | 0.95 | 0.00 | 1.55 | 1.25 |
time (sec) |
N/A | 0.241 | 0.028 | 0.177 | 0.111 | 0.072 | 0.098 | 0.000 | 0.212 | 1.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 38 | 20 | 32 | 29 | 19 | 19 | 0 | 20 | 0 |
N.S. |
1 | 1.90 | 1.00 | 1.60 | 1.45 | 0.95 | 0.95 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.294 | 0.062 | 0.688 | 0.159 | 0.066 | 0.145 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 54 | 25 | 53 | 27 | 59 | 31 | 0 |
N.S. |
1 | 0.00 | 0.93 | 1.93 | 0.89 | 1.89 | 0.96 | 2.11 | 1.11 | 0.00 |
time (sec) |
N/A | 0.000 | 0.042 | 1.694 | 0.147 | 0.071 | 75.661 | 0.229 | 0.221 | 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 | 14 | 0 | 14 | 17 | 13 | 21 | 19 | 16 | 17 | 14 |
N.S. |
1 | 0.00 | 1.00 | 1.21 | 0.93 | 1.50 | 1.36 | 1.14 | 1.21 | 1.00 |
time (sec) |
N/A | 0.000 | 0.025 | 0.081 | 0.088 | 0.064 | 0.103 | 0.116 | 0.857 | 1.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 73 | 21 | 24 | 60 | 21 | 272 | 67 | 22 | 29 |
N.S. |
1 | 2.61 | 0.75 | 0.86 | 2.14 | 0.75 | 9.71 | 2.39 | 0.79 | 1.04 |
time (sec) |
N/A | 0.262 | 0.012 | 0.246 | 0.027 | 0.066 | 0.451 | 0.110 | 0.203 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 132 | 324 | 196 | 196 | 218 | 0 | 330 | 117946 |
N.S. |
1 | 0.00 | 5.08 | 12.46 | 7.54 | 7.54 | 8.38 | 0.00 | 12.69 | 4536.38 |
time (sec) |
N/A | 0.000 | 0.142 | 4.312 | 1.061 | 0.089 | 2.347 | 0.000 | 0.388 | 118.651 |
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 | 25 | 18 | 17 | 41 | 16 | 17 | 16 | 18 | 16 |
N.S. |
1 | 0.86 | 0.62 | 0.59 | 1.41 | 0.55 | 0.59 | 0.55 | 0.62 | 0.55 |
time (sec) |
N/A | 0.383 | 0.024 | 0.170 | 0.036 | 0.066 | 0.056 | 0.111 | 0.244 | 1.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 53 | 120 | 73 | 119 | 109 | 0 | 79 | 386 |
N.S. |
1 | 0.00 | 1.47 | 3.33 | 2.03 | 3.31 | 3.03 | 0.00 | 2.19 | 10.72 |
time (sec) |
N/A | 0.000 | 0.569 | 18.520 | 0.120 | 0.077 | 0.573 | 0.000 | 0.289 | 1.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | B | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 1682 | 42 | 53 | 161 | 45 | 112 | 53 | 64 | 0 |
N.S. |
1 | 54.26 | 1.35 | 1.71 | 5.19 | 1.45 | 3.61 | 1.71 | 2.06 | 0.00 |
time (sec) |
N/A | 7.125 | 0.100 | 0.147 | 0.171 | 0.078 | 0.280 | 0.125 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 39 | 74 | 38 | 54 | 39 | 0 | 114 | 48 |
N.S. |
1 | 0.00 | 1.50 | 2.85 | 1.46 | 2.08 | 1.50 | 0.00 | 4.38 | 1.85 |
time (sec) |
N/A | 0.000 | 0.108 | 4.704 | 0.092 | 0.072 | 0.997 | 0.000 | 200.038 | 1.655 |
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 | 31 | 24 | 35 | 25 | 19 | 25 | 33 | 22 |
N.S. |
1 | 0.00 | 1.07 | 0.83 | 1.21 | 0.86 | 0.66 | 0.86 | 1.14 | 0.76 |
time (sec) |
N/A | 0.000 | 0.325 | 0.215 | 0.094 | 0.070 | 0.095 | 0.127 | 1.230 | 1.330 |
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 | 17 | 17 | 16 | 18 | 18 | 19 | 18 | 17 | 18 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.75 | 0.75 | 0.79 | 0.75 | 0.71 | 0.75 |
time (sec) |
N/A | 0.526 | 0.092 | 0.306 | 0.082 | 0.066 | 0.065 | 0.114 | 0.205 | 1.705 |
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 | 114 | 91 | 101 | 86 | 89 | 92 | 94 | 107 | 99 |
N.S. |
1 | 4.56 | 3.64 | 4.04 | 3.44 | 3.56 | 3.68 | 3.76 | 4.28 | 3.96 |
time (sec) |
N/A | 0.613 | 0.600 | 2.105 | 0.038 | 0.064 | 0.097 | 0.115 | 0.230 | 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 | 28 | 19 | 19 | 19 | 18 | 18 | 17 | 18 | 36 | 20 |
N.S. |
1 | 0.68 | 0.68 | 0.68 | 0.64 | 0.64 | 0.61 | 0.64 | 1.29 | 0.71 |
time (sec) |
N/A | 0.170 | 0.026 | 0.114 | 0.039 | 0.075 | 0.046 | 0.115 | 0.257 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 23 | 21 | 17 | 17 | 0 | 33 | 19 | 17 |
N.S. |
1 | 0.00 | 1.05 | 0.95 | 0.77 | 0.77 | 0.00 | 1.50 | 0.86 | 0.77 |
time (sec) |
N/A | 0.000 | 0.593 | 36.625 | 0.084 | 0.069 | 0.000 | 0.146 | 0.244 | 1.497 |
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 | 20 | 18 | 22 | 36 | 34 | 19 | 21 | 34 | 21 |
N.S. |
1 | 1.05 | 0.95 | 1.16 | 1.89 | 1.79 | 1.00 | 1.11 | 1.79 | 1.11 |
time (sec) |
N/A | 1.059 | 0.169 | 0.934 | 0.166 | 0.070 | 0.100 | 0.173 | 0.229 | 1.458 |
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 | 23 | 16 | 16 | 11 | 16 | 16 | 12 | 16 | 14 | 10 |
N.S. |
1 | 0.70 | 0.70 | 0.48 | 0.70 | 0.70 | 0.52 | 0.70 | 0.61 | 0.43 |
time (sec) |
N/A | 0.156 | 0.000 | 0.033 | 0.031 | 0.054 | 0.027 | 0.113 | 0.220 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 59 | 42 | 112 | 40 | 37 | 0 | 78 | 92 |
N.S. |
1 | 0.00 | 1.84 | 1.31 | 3.50 | 1.25 | 1.16 | 0.00 | 2.44 | 2.88 |
time (sec) |
N/A | 0.000 | 0.201 | 2.797 | 0.359 | 0.073 | 0.724 | 0.000 | 0.239 | 2.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 48 | 64 | 51 | 51 | 46 | 73 | 0 | 0 |
N.S. |
1 | 0.00 | 2.00 | 2.67 | 2.12 | 2.12 | 1.92 | 3.04 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.060 | 1.214 | 0.090 | 0.064 | 0.163 | 0.206 | 0.415 | 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 | 25 | 13 | 13 | 14 | 13 | 13 | 10 | 14 | 13 | 13 |
N.S. |
1 | 0.52 | 0.52 | 0.56 | 0.52 | 0.52 | 0.40 | 0.56 | 0.52 | 0.52 |
time (sec) |
N/A | 0.232 | 0.001 | 0.030 | 0.028 | 0.063 | 0.029 | 0.111 | 0.249 | 1.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 350 | 34 | 95 | 105 | 88 | 326 | 0 | 90 | 173 |
N.S. |
1 | 10.29 | 1.00 | 2.79 | 3.09 | 2.59 | 9.59 | 0.00 | 2.65 | 5.09 |
time (sec) |
N/A | 7.453 | 0.195 | 0.049 | 0.151 | 0.081 | 0.447 | 0.000 | 0.225 | 1.871 |
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 | 34 | 36 | 29 | 29 | 22 | 29 | 34 | 30 |
N.S. |
1 | 0.00 | 1.06 | 1.12 | 0.91 | 0.91 | 0.69 | 0.91 | 1.06 | 0.94 |
time (sec) |
N/A | 0.000 | 0.071 | 0.457 | 0.087 | 0.077 | 0.094 | 0.141 | 0.220 | 1.684 |
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 | 20 | 0 | 17 | 15 | 14 | 49 | 12 | 0 | 17 | 14 |
N.S. |
1 | 0.00 | 0.85 | 0.75 | 0.70 | 2.45 | 0.60 | 0.00 | 0.85 | 0.70 |
time (sec) |
N/A | 0.000 | 0.031 | 0.103 | 0.041 | 0.067 | 0.100 | 0.000 | 0.208 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 35 | 59 | 37 | 36 | 57 | 63 | 58 |
N.S. |
1 | 0.00 | 0.00 | 1.17 | 1.97 | 1.23 | 1.20 | 1.90 | 2.10 | 1.93 |
time (sec) |
N/A | 0.000 | 0.000 | 0.982 | 0.290 | 0.066 | 0.521 | 0.120 | 0.217 | 4.106 |
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 | 25 | 49 | 28 | 20 | 25 | 20 | 20 | 20 | 21 | 20 |
N.S. |
1 | 1.96 | 1.12 | 0.80 | 1.00 | 0.80 | 0.80 | 0.80 | 0.84 | 0.80 |
time (sec) |
N/A | 0.266 | 0.026 | 0.286 | 0.061 | 0.065 | 0.089 | 0.126 | 0.212 | 1.351 |
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 | 18 | 18 | 16 | 18 | 44 | 17 | 14 | 17 | 17 | 16 |
N.S. |
1 | 1.00 | 0.89 | 1.00 | 2.44 | 0.94 | 0.78 | 0.94 | 0.94 | 0.89 |
time (sec) |
N/A | 0.405 | 0.025 | 0.270 | 0.100 | 0.067 | 0.064 | 0.131 | 0.224 | 1.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 27 | 42 | 37 | 43 | 78 | 77 | 45 | 0 |
N.S. |
1 | 0.00 | 1.29 | 2.00 | 1.76 | 2.05 | 3.71 | 3.67 | 2.14 | 0.00 |
time (sec) |
N/A | 0.000 | 15.928 | 0.294 | 0.137 | 0.069 | 0.214 | 0.127 | 0.228 | 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 | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.128 | 0.000 | 0.020 | 0.031 | 0.063 | 0.032 | 0.117 | 0.221 | 0.008 |
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 | 32 | 26 | 25 | 32 | 24 | 22 | 25 | 20 | 25 |
N.S. |
1 | 1.39 | 1.13 | 1.09 | 1.39 | 1.04 | 0.96 | 1.09 | 0.87 | 1.09 |
time (sec) |
N/A | 0.327 | 0.070 | 0.378 | 0.135 | 0.068 | 0.121 | 0.146 | 0.223 | 1.486 |
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 | 32 | 35 | 30 | 30 | 36 | 30 | 36 | 33 |
N.S. |
1 | 0.00 | 1.10 | 1.21 | 1.03 | 1.03 | 1.24 | 1.03 | 1.24 | 1.14 |
time (sec) |
N/A | 0.000 | 0.108 | 45.959 | 0.142 | 0.075 | 1.123 | 29.911 | 0.217 | 2.047 |
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 | 28 | 30 | 24 | 21 | 156 | 37 | 34 | 74 | 30 | 81 |
N.S. |
1 | 1.07 | 0.86 | 0.75 | 5.57 | 1.32 | 1.21 | 2.64 | 1.07 | 2.89 |
time (sec) |
N/A | 0.500 | 0.025 | 0.221 | 0.196 | 0.065 | 0.117 | 0.114 | 0.237 | 0.230 |
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 | 40 | 18 | 18 | 23 | 21 | 22 | 23 | 25 | 17 |
N.S. |
1 | 1.25 | 0.56 | 0.56 | 0.72 | 0.66 | 0.69 | 0.72 | 0.78 | 0.53 |
time (sec) |
N/A | 0.378 | 0.022 | 0.303 | 0.028 | 0.061 | 0.420 | 0.112 | 0.229 | 1.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | B | B | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 29 | 806 | 55 | 75 | 78 | 60 | 77 | 87 |
N.S. |
1 | 0.00 | 1.12 | 31.00 | 2.12 | 2.88 | 3.00 | 2.31 | 2.96 | 3.35 |
time (sec) |
N/A | 0.000 | 0.354 | 0.135 | 0.177 | 0.074 | 0.325 | 0.188 | 0.224 | 1.609 |
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 | 40 | 27 | 25 | 24 | 24 | 24 | 24 | 25 | 28 |
N.S. |
1 | 1.33 | 0.90 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.83 | 0.93 |
time (sec) |
N/A | 0.215 | 0.007 | 0.148 | 0.030 | 0.068 | 0.059 | 0.109 | 0.201 | 1.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 75 | 80 | 32 | 22 | 36 | 36 | 25 |
N.S. |
1 | 0.00 | 0.86 | 2.68 | 2.86 | 1.14 | 0.79 | 1.29 | 1.29 | 0.89 |
time (sec) |
N/A | 0.000 | 0.503 | 1.022 | 0.187 | 0.072 | 0.123 | 0.134 | 0.223 | 1.430 |
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 | 34 | 36 | 25 | 22 | 22 | 20 | 22 | 29 | 23 |
N.S. |
1 | 1.31 | 1.38 | 0.96 | 0.85 | 0.85 | 0.77 | 0.85 | 1.12 | 0.88 |
time (sec) |
N/A | 1.539 | 0.044 | 0.300 | 0.197 | 0.064 | 0.081 | 0.117 | 0.226 | 1.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 85 | 45 | 39 | 42 | 48 | 39 | 71 | 56 | 39 |
N.S. |
1 | 2.93 | 1.55 | 1.34 | 1.45 | 1.66 | 1.34 | 2.45 | 1.93 | 1.34 |
time (sec) |
N/A | 0.732 | 0.021 | 0.290 | 0.036 | 0.062 | 1.973 | 0.112 | 0.232 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 35 | 26 | 0 | 32 | 20 | 58 | 37 | 20 |
N.S. |
1 | 0.00 | 1.46 | 1.08 | 0.00 | 1.33 | 0.83 | 2.42 | 1.54 | 0.83 |
time (sec) |
N/A | 0.000 | 0.130 | 0.152 | 0.000 | 0.070 | 0.139 | 0.119 | 0.242 | 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 | 15 | 20 | 22 | 17 | 22 | 16 | 22 | 16 | 15 | 11 |
N.S. |
1 | 1.33 | 1.47 | 1.13 | 1.47 | 1.07 | 1.47 | 1.07 | 1.00 | 0.73 |
time (sec) |
N/A | 0.204 | 0.005 | 0.076 | 0.027 | 0.065 | 0.050 | 0.114 | 0.241 | 1.349 |
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 | 23 | 20 | 17 | 19 | 19 | 18 | 15 | 16 | 187 | 18 |
N.S. |
1 | 0.87 | 0.74 | 0.83 | 0.83 | 0.78 | 0.65 | 0.70 | 8.13 | 0.78 |
time (sec) |
N/A | 0.395 | 0.218 | 0.217 | 0.076 | 0.069 | 0.153 | 0.127 | 0.233 | 1.565 |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 6 | 6 | 6 |
N.S. |
1 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 | 0.38 | 0.46 | 0.46 | 0.46 |
time (sec) |
N/A | 0.142 | 0.000 | 0.029 | 0.036 | 0.063 | 0.044 | 0.104 | 0.217 | 1.240 |
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 | 21 | 0 | 136 | 85 | 87 | 135 | 95 | 84 | 84 | 132 |
N.S. |
1 | 0.00 | 6.48 | 4.05 | 4.14 | 6.43 | 4.52 | 4.00 | 4.00 | 6.29 |
time (sec) |
N/A | 0.000 | 5.100 | 0.097 | 0.110 | 0.075 | 0.637 | 0.698 | 0.252 | 1.728 |
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 | 14 | 14 | 20 | 20 | 15 | 20 | 18 | 16 |
N.S. |
1 | 0.95 | 0.67 | 0.67 | 0.95 | 0.95 | 0.71 | 0.95 | 0.86 | 0.76 |
time (sec) |
N/A | 0.160 | 0.002 | 0.045 | 0.046 | 0.052 | 0.025 | 0.114 | 0.204 | 1.639 |
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 | 34 | 27 | 25 | 30 | 24 | 26 | 24 | 27 | 24 |
N.S. |
1 | 1.62 | 1.29 | 1.19 | 1.43 | 1.14 | 1.24 | 1.14 | 1.29 | 1.14 |
time (sec) |
N/A | 0.248 | 0.046 | 0.375 | 0.031 | 0.066 | 0.104 | 0.112 | 0.219 | 0.098 |
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 | 23 | 0 | 28 | 36 | 25 | 37 | 31 | 37 | 37 | 37 |
N.S. |
1 | 0.00 | 1.22 | 1.57 | 1.09 | 1.61 | 1.35 | 1.61 | 1.61 | 1.61 |
time (sec) |
N/A | 0.000 | 0.061 | 0.770 | 0.092 | 0.067 | 0.191 | 0.209 | 0.226 | 1.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | B | B | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 27 | 149 | 27 | 46 | 42 | 108 | 182 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 5.52 | 1.00 | 1.70 | 1.56 | 4.00 | 6.74 |
time (sec) |
N/A | 0.000 | 0.000 | 23.524 | 0.336 | 0.065 | 1.177 | 0.606 | 200.023 | 1.716 |
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 | 37 | 0 | 34 | 34 | 96 | 96 | 42 | 104 | 94 | 45 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 2.59 | 2.59 | 1.14 | 2.81 | 2.54 | 1.22 |
time (sec) |
N/A | 0.000 | 4.980 | 1.444 | 0.125 | 0.069 | 0.134 | 0.131 | 0.217 | 1.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 30 | 32 | 56 | 56 | 26 | 75 | 147 | 29 |
N.S. |
1 | 0.00 | 1.07 | 1.14 | 2.00 | 2.00 | 0.93 | 2.68 | 5.25 | 1.04 |
time (sec) |
N/A | 0.000 | 0.068 | 14.888 | 0.118 | 0.072 | 1.327 | 0.974 | 200.022 | 1.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | C | C | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 75 | 59 | 68 | 120 | 34 | 44 | 44 | 64 | 28 |
N.S. |
1 | 2.34 | 1.84 | 2.12 | 3.75 | 1.06 | 1.38 | 1.38 | 2.00 | 0.88 |
time (sec) |
N/A | 0.577 | 0.041 | 0.638 | 0.116 | 0.071 | 0.126 | 0.115 | 0.211 | 1.390 |
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 | 16 | 35 | 28 | 22 | 31 | 24 | 24 | 25 | 31 | 23 |
N.S. |
1 | 2.19 | 1.75 | 1.38 | 1.94 | 1.50 | 1.50 | 1.56 | 1.94 | 1.44 |
time (sec) |
N/A | 0.375 | 0.095 | 0.232 | 0.035 | 0.072 | 0.077 | 0.119 | 0.205 | 0.092 |
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 | 23 | 31 | 27 | 72 | 55 | 55 | 88 | 74 | 80 | 74 |
N.S. |
1 | 1.35 | 1.17 | 3.13 | 2.39 | 2.39 | 3.83 | 3.22 | 3.48 | 3.22 |
time (sec) |
N/A | 0.920 | 0.034 | 0.515 | 0.088 | 0.080 | 0.239 | 0.219 | 0.258 | 2.800 |
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 | 26 | 32 | 28 | 28 | 27 | 35 | 28 | 28 |
N.S. |
1 | 0.00 | 1.18 | 1.45 | 1.27 | 1.27 | 1.23 | 1.59 | 1.27 | 1.27 |
time (sec) |
N/A | 0.000 | 0.176 | 0.351 | 0.084 | 0.071 | 0.182 | 0.110 | 0.234 | 1.558 |
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 | 27 | 30 | 27 | 21 | 20 | 22 | 19 | 22 | 52 | 21 |
N.S. |
1 | 1.11 | 1.00 | 0.78 | 0.74 | 0.81 | 0.70 | 0.81 | 1.93 | 0.78 |
time (sec) |
N/A | 0.379 | 0.408 | 0.223 | 0.138 | 0.067 | 0.163 | 0.117 | 200.021 | 0.118 |
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 | 20 | 21 | 25 | 29 | 27 | 34 | 26 | 24 | 37 | 0 |
N.S. |
1 | 1.05 | 1.25 | 1.45 | 1.35 | 1.70 | 1.30 | 1.20 | 1.85 | 0.00 |
time (sec) |
N/A | 0.301 | 0.028 | 0.196 | 0.036 | 0.066 | 0.099 | 0.113 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 20 | 0 | 19 | 0 | 19 | 21 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.95 | 0.00 | 0.95 | 1.05 | 0.95 |
time (sec) |
N/A | 0.553 | 0.157 | 0.383 | 0.000 | 0.073 | 0.000 | 0.186 | 0.228 | 1.657 |
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 | 30 | 55 | 26 | 26 | 66 | 25 | 22 | 25 | 26 | 25 |
N.S. |
1 | 1.83 | 0.87 | 0.87 | 2.20 | 0.83 | 0.73 | 0.83 | 0.87 | 0.83 |
time (sec) |
N/A | 0.345 | 0.174 | 0.072 | 0.030 | 0.071 | 0.057 | 0.112 | 0.216 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 57 | 28 | 25 | 30 | 39 | 53 | 25 | 26 | 24 |
N.S. |
1 | 2.04 | 1.00 | 0.89 | 1.07 | 1.39 | 1.89 | 0.89 | 0.93 | 0.86 |
time (sec) |
N/A | 0.947 | 0.235 | 3.785 | 0.189 | 0.084 | 0.406 | 0.139 | 0.243 | 1.926 |
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 | 33 | 22 | 27 | 35 | 38 | 20 | 41 | 39 | 32 |
N.S. |
1 | 1.18 | 0.79 | 0.96 | 1.25 | 1.36 | 0.71 | 1.46 | 1.39 | 1.14 |
time (sec) |
N/A | 1.897 | 2.471 | 0.484 | 0.137 | 0.071 | 0.069 | 0.111 | 0.208 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 51 | 45 | 37 | 39 | 41 | 56 | 39 | 38 | 39 |
N.S. |
1 | 2.43 | 2.14 | 1.76 | 1.86 | 1.95 | 2.67 | 1.86 | 1.81 | 1.86 |
time (sec) |
N/A | 0.188 | 0.020 | 0.371 | 0.028 | 0.063 | 0.702 | 0.111 | 0.201 | 0.045 |
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 | 28 | 19 | 19 | 23 | 28 | 17 | 23 | 31 | 23 |
N.S. |
1 | 1.17 | 0.79 | 0.79 | 0.96 | 1.17 | 0.71 | 0.96 | 1.29 | 0.96 |
time (sec) |
N/A | 0.318 | 0.009 | 0.199 | 0.030 | 0.064 | 0.074 | 0.114 | 0.201 | 1.342 |
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 | 26 | 0 | 27 | 21 | 531 | 531 | 275 | 713 | 742 | 0 |
N.S. |
1 | 0.00 | 1.04 | 0.81 | 20.42 | 20.42 | 10.58 | 27.42 | 28.54 | 0.00 |
time (sec) |
N/A | 0.000 | 20.148 | 164.996 | 1.141 | 0.094 | 0.686 | 0.640 | 0.234 | 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 | 22 | 76 | 84 | 59 | 100 | 51 | 61 | 58 | 65 | 62 |
N.S. |
1 | 3.45 | 3.82 | 2.68 | 4.55 | 2.32 | 2.77 | 2.64 | 2.95 | 2.82 |
time (sec) |
N/A | 0.420 | 0.053 | 0.914 | 0.035 | 0.067 | 0.127 | 0.115 | 0.214 | 1.286 |
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 | 17 | 27 | 27 | 26 | 53 | 21 | 32 | 27 | 35 | 25 |
N.S. |
1 | 1.59 | 1.59 | 1.53 | 3.12 | 1.24 | 1.88 | 1.59 | 2.06 | 1.47 |
time (sec) |
N/A | 0.636 | 0.043 | 0.382 | 0.090 | 0.065 | 0.246 | 0.114 | 0.228 | 1.481 |
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 | 25 | 1229 | 25 | 24 | 98 | 22 | 17 | 29 | 62 | 21 |
N.S. |
1 | 49.16 | 1.00 | 0.96 | 3.92 | 0.88 | 0.68 | 1.16 | 2.48 | 0.84 |
time (sec) |
N/A | 5.470 | 0.443 | 0.955 | 0.530 | 0.067 | 0.114 | 0.118 | 0.211 | 1.495 |
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 | 23 | 38 | 44 | 45 | 47 | 66 | 63 | 43 | 74 | 38 |
N.S. |
1 | 1.65 | 1.91 | 1.96 | 2.04 | 2.87 | 2.74 | 1.87 | 3.22 | 1.65 |
time (sec) |
N/A | 0.344 | 0.017 | 0.366 | 0.029 | 0.064 | 0.432 | 0.112 | 0.213 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 58 | 21 | 56 | 20 | 17 | 20 | 31 | 20 |
N.S. |
1 | 0.00 | 2.76 | 1.00 | 2.67 | 0.95 | 0.81 | 0.95 | 1.48 | 0.95 |
time (sec) |
N/A | 0.000 | 0.481 | 1.720 | 0.095 | 0.071 | 0.155 | 0.279 | 0.216 | 1.434 |
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 | 28 | 60 | 25 | 28 | 92 | 28 | 34 | 40 | 27 | 26 |
N.S. |
1 | 2.14 | 0.89 | 1.00 | 3.29 | 1.00 | 1.21 | 1.43 | 0.96 | 0.93 |
time (sec) |
N/A | 0.551 | 0.051 | 0.345 | 0.073 | 0.071 | 0.109 | 0.108 | 0.205 | 1.292 |
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 | 21 | 0 | 21 | 46 | 65 | 47 | 49 | 56 | 39 | 41 |
N.S. |
1 | 0.00 | 1.00 | 2.19 | 3.10 | 2.24 | 2.33 | 2.67 | 1.86 | 1.95 |
time (sec) |
N/A | 0.000 | 0.227 | 0.893 | 0.138 | 0.065 | 0.288 | 0.154 | 0.216 | 1.506 |
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 | 19 | 0 | 19 | 29 | 26 | 28 | 27 | 28 | 29 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.53 | 1.37 | 1.47 | 1.42 | 1.47 | 1.53 | 1.53 |
time (sec) |
N/A | 0.000 | 0.020 | 0.515 | 0.144 | 0.076 | 0.379 | 0.149 | 0.249 | 1.488 |
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 | 7 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 0.71 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.422 | 0.001 | 0.040 | 0.032 | 0.067 | 0.052 | 0.112 | 0.206 | 1.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 54 | 52 | 81 | 75 | 107 | 90 | 0 | 143 | 94 |
N.S. |
1 | 1.69 | 1.62 | 2.53 | 2.34 | 3.34 | 2.81 | 0.00 | 4.47 | 2.94 |
time (sec) |
N/A | 1.118 | 0.056 | 0.685 | 0.032 | 0.069 | 1.091 | 0.000 | 0.217 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 43 | 0 | 42 | 0 | 34 | 50 | 101 |
N.S. |
1 | 0.00 | 0.87 | 1.39 | 0.00 | 1.35 | 0.00 | 1.10 | 1.61 | 3.26 |
time (sec) |
N/A | 0.000 | 0.065 | 0.963 | 0.000 | 0.068 | 0.000 | 0.327 | 0.209 | 1.794 |
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 | 14 | 19 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.82 | 1.12 | 1.00 | 1.00 |
time (sec) |
N/A | 1.056 | 0.088 | 0.292 | 0.062 | 0.071 | 0.094 | 0.114 | 0.224 | 1.319 |
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 | 30 | 30 | 50 | 49 | 24 | 55 | 55 | 53 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 1.47 | 1.44 | 0.71 | 1.62 | 1.62 | 1.56 |
time (sec) |
N/A | 0.000 | 0.041 | 2.312 | 0.086 | 0.076 | 0.100 | 0.221 | 0.237 | 1.670 |
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 | 20 | 20 | 16 | 16 | 16 | 22 | 16 | 17 | 15 |
N.S. |
1 | 0.80 | 0.80 | 0.64 | 0.64 | 0.64 | 0.88 | 0.64 | 0.68 | 0.60 |
time (sec) |
N/A | 0.167 | 0.002 | 0.034 | 0.027 | 0.062 | 0.022 | 0.110 | 0.218 | 1.232 |
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 | 20 | 18 | 18 | 17 | 16 | 28 | 15 | 16 | 36 | 19 |
N.S. |
1 | 0.90 | 0.90 | 0.85 | 0.80 | 1.40 | 0.75 | 0.80 | 1.80 | 0.95 |
time (sec) |
N/A | 0.296 | 0.034 | 0.580 | 0.113 | 0.067 | 0.060 | 0.117 | 0.230 | 0.165 |
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 | 10 | 9 | 9 | 8 | 9 | 10 | 9 |
N.S. |
1 | 0.53 | 0.53 | 0.53 | 0.47 | 0.47 | 0.42 | 0.47 | 0.53 | 0.47 |
time (sec) |
N/A | 0.145 | 0.001 | 0.061 | 0.034 | 0.063 | 0.035 | 0.106 | 0.214 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 57 | 50 | 46 | 0 | 104 | 44 | 133 | 145 | 72 |
N.S. |
1 | 1.97 | 1.72 | 1.59 | 0.00 | 3.59 | 1.52 | 4.59 | 5.00 | 2.48 |
time (sec) |
N/A | 2.845 | 0.095 | 2.386 | 0.000 | 0.074 | 0.143 | 0.120 | 0.214 | 1.399 |
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 | 16 | 16 | 19 | 16 | 20 | 22 | 20 | 20 | 16 |
N.S. |
1 | 1.07 | 1.07 | 1.27 | 1.07 | 1.33 | 1.47 | 1.33 | 1.33 | 1.07 |
time (sec) |
N/A | 0.594 | 0.041 | 0.154 | 0.150 | 0.071 | 0.081 | 0.110 | 0.214 | 1.486 |
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 | 25 | 29 | 19 | 15 | 0 | 28 | 14 | 28 | 24 | 18 |
N.S. |
1 | 1.16 | 0.76 | 0.60 | 0.00 | 1.12 | 0.56 | 1.12 | 0.96 | 0.72 |
time (sec) |
N/A | 0.484 | 0.019 | 0.316 | 0.000 | 0.070 | 0.070 | 0.106 | 0.224 | 1.328 |
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 | 26 | 39 | 27 | 25 | 33 | 23 | 22 | 30 | 68 | 24 |
N.S. |
1 | 1.50 | 1.04 | 0.96 | 1.27 | 0.88 | 0.85 | 1.15 | 2.62 | 0.92 |
time (sec) |
N/A | 0.258 | 0.125 | 0.264 | 0.094 | 0.071 | 0.141 | 0.115 | 0.234 | 1.489 |
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 | 16 | 58 | 16 | 17 | 49 | 16 | 22 | 20 | 17 | 13 |
N.S. |
1 | 3.62 | 1.00 | 1.06 | 3.06 | 1.00 | 1.38 | 1.25 | 1.06 | 0.81 |
time (sec) |
N/A | 0.594 | 0.055 | 0.092 | 0.065 | 0.065 | 0.044 | 0.108 | 0.217 | 1.278 |
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 | 24 | 24 | 23 | 88 | 22 | 24 | 22 | 25 | 22 |
N.S. |
1 | 0.96 | 0.96 | 0.92 | 3.52 | 0.88 | 0.96 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.321 | 0.095 | 0.254 | 0.030 | 0.066 | 0.078 | 0.113 | 0.210 | 1.276 |
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 | 17 | 17 | 16 | 16 | 14 | 16 | 13 | 12 |
N.S. |
1 | 0.94 | 0.94 | 0.94 | 0.89 | 0.89 | 0.78 | 0.89 | 0.72 | 0.67 |
time (sec) |
N/A | 0.930 | 0.081 | 0.073 | 0.074 | 0.075 | 0.086 | 0.113 | 0.202 | 1.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 24 | 21 | 90 | 31 | 32 | 0 | 57 | 66 |
N.S. |
1 | 0.00 | 0.89 | 0.78 | 3.33 | 1.15 | 1.19 | 0.00 | 2.11 | 2.44 |
time (sec) |
N/A | 0.000 | 2.382 | 2.246 | 0.418 | 0.078 | 0.294 | 0.000 | 0.214 | 2.072 |
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 | 20 | 19 | 17 | 18 | 18 | 17 | 18 | 19 | 18 |
N.S. |
1 | 1.05 | 1.00 | 0.89 | 0.95 | 0.95 | 0.89 | 0.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.375 | 0.007 | 0.162 | 0.026 | 0.065 | 0.177 | 0.116 | 0.218 | 0.181 |
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 | 38 | 17 | 28 | 27 | 27 | 29 | 27 | 30 | 27 |
N.S. |
1 | 2.00 | 0.89 | 1.47 | 1.42 | 1.42 | 1.53 | 1.42 | 1.58 | 1.42 |
time (sec) |
N/A | 0.394 | 0.017 | 1.031 | 0.055 | 0.067 | 0.119 | 0.109 | 0.228 | 1.348 |
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 | 22 | 23 | 32 | 32 | 19 | 32 | 37 | 25 |
N.S. |
1 | 0.00 | 0.81 | 0.85 | 1.19 | 1.19 | 0.70 | 1.19 | 1.37 | 0.93 |
time (sec) |
N/A | 0.000 | 2.212 | 0.280 | 0.105 | 0.071 | 0.063 | 0.115 | 0.210 | 1.442 |
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 | 26 | 163 | 39 | 120 | 115 | 165 | 122 | 111 | 187 | 131 |
N.S. |
1 | 6.27 | 1.50 | 4.62 | 4.42 | 6.35 | 4.69 | 4.27 | 7.19 | 5.04 |
time (sec) |
N/A | 1.219 | 0.038 | 0.425 | 0.033 | 0.068 | 5.576 | 0.106 | 0.200 | 0.224 |
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 | 28 | 29 | 25 | 29 | 32 | 28 | 27 | 28 | 29 | 26 |
N.S. |
1 | 1.04 | 0.89 | 1.04 | 1.14 | 1.00 | 0.96 | 1.00 | 1.04 | 0.93 |
time (sec) |
N/A | 0.296 | 0.030 | 0.521 | 0.067 | 0.070 | 0.105 | 0.114 | 0.202 | 1.320 |
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 | 17 | 0 | 20 | 20 | 41 | 41 | 31 | 55 | 44 | 19 |
N.S. |
1 | 0.00 | 1.18 | 1.18 | 2.41 | 2.41 | 1.82 | 3.24 | 2.59 | 1.12 |
time (sec) |
N/A | 0.000 | 0.104 | 1.395 | 0.065 | 0.067 | 0.057 | 0.118 | 0.208 | 1.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | A | F(-2) | B | B | F(-1) |
verified | N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 89 | 79 | 120 | 43 | 0 | 90 | 49 | 0 |
N.S. |
1 | 0.00 | 2.70 | 2.39 | 3.64 | 1.30 | 0.00 | 2.73 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.190 | 9.568 | 0.197 | 0.082 | 0.000 | 2.326 | 0.244 | 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 | 25 | 44 | 34 | 33 | 36 | 36 | 39 | 36 | 38 | 38 |
N.S. |
1 | 1.76 | 1.36 | 1.32 | 1.44 | 1.44 | 1.56 | 1.44 | 1.52 | 1.52 |
time (sec) |
N/A | 0.205 | 0.007 | 0.079 | 0.034 | 0.059 | 0.020 | 0.117 | 0.216 | 0.060 |
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 | 26 | 27 | 30 | 26 | 24 | 26 | 26 | 26 |
N.S. |
1 | 0.00 | 1.08 | 1.12 | 1.25 | 1.08 | 1.00 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.000 | 0.098 | 0.410 | 0.154 | 0.063 | 0.110 | 0.126 | 0.214 | 1.451 |
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 | 19 | 19 | 14 | 18 | 13 | 14 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.95 | 0.68 | 0.74 | 0.68 | 0.79 | 0.68 |
time (sec) |
N/A | 0.150 | 0.002 | 0.091 | 0.029 | 0.059 | 0.027 | 0.108 | 0.205 | 0.060 |
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 | 23 | 18 | 20 | 16 | 0 | 24 | 14 | 24 | 27 | 17 |
N.S. |
1 | 0.78 | 0.87 | 0.70 | 0.00 | 1.04 | 0.61 | 1.04 | 1.17 | 0.74 |
time (sec) |
N/A | 0.471 | 0.179 | 0.339 | 0.000 | 0.068 | 0.054 | 0.114 | 0.201 | 1.432 |