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 | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 28 | 24 | 26 | 24 | 28 | 25 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.33 | 1.14 | 1.24 | 1.14 | 1.33 | 1.19 | 1.05 |
time (sec) |
N/A | 0.000 | 0.134 | 0.394 | 0.104 | 0.071 | 0.141 | 0.145 | 0.212 | 1.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 130 | 227 | 0 | 169 | 212 | 759 | 289 | 269 |
N.S. |
1 | 0.00 | 5.00 | 8.73 | 0.00 | 6.50 | 8.15 | 29.19 | 11.12 | 10.35 |
time (sec) |
N/A | 0.000 | 0.185 | 0.049 | 0.000 | 0.078 | 0.411 | 0.163 | 0.208 | 3.904 |
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 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.40 | 0.40 | 0.50 | 0.40 | 0.40 | 0.30 | 0.50 | 0.40 | 0.40 |
time (sec) |
N/A | 0.143 | 0.000 | 0.033 | 0.027 | 0.057 | 0.028 | 0.114 | 0.208 | 0.014 |
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 | 19 | 129 | 34 | 32 | 136 | 31 | 27 | 31 | 164 | 23 |
N.S. |
1 | 6.79 | 1.79 | 1.68 | 7.16 | 1.63 | 1.42 | 1.63 | 8.63 | 1.21 |
time (sec) |
N/A | 0.783 | 0.061 | 2.316 | 0.599 | 0.066 | 0.078 | 0.156 | 0.235 | 1.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 38 | 77 | 77 | 42 | 49 | 83 | 259 |
N.S. |
1 | 0.00 | 1.03 | 1.27 | 2.57 | 2.57 | 1.40 | 1.63 | 2.77 | 8.63 |
time (sec) |
N/A | 0.000 | 0.045 | 1.565 | 0.080 | 0.075 | 0.125 | 0.192 | 0.222 | 1.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 23 | 51 | 25 | 36 | 54 | 28 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 2.12 | 1.04 | 1.50 | 2.25 | 1.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.092 | 0.454 | 0.247 | 0.068 | 0.263 | 0.115 | 0.229 | 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 | 29 | 30 | 37 | 28 | 49 | 31 | 24 | 34 | 36 | 30 |
N.S. |
1 | 1.03 | 1.28 | 0.97 | 1.69 | 1.07 | 0.83 | 1.17 | 1.24 | 1.03 |
time (sec) |
N/A | 0.375 | 0.006 | 0.373 | 0.041 | 0.070 | 0.143 | 0.109 | 0.204 | 1.371 |
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 | 25 | 23 | 26 | 36 | 27 | 38 | 32 | 100 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 1.04 | 1.44 | 1.08 | 1.52 | 1.28 | 4.00 |
time (sec) |
N/A | 0.000 | 0.166 | 0.585 | 0.130 | 0.066 | 0.096 | 0.132 | 0.221 | 1.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 26 | 20 | 43 | 17 | 43 | 29 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 0.91 | 1.95 | 0.77 | 1.95 | 1.32 | 0.91 |
time (sec) |
N/A | 0.230 | 0.020 | 0.164 | 0.031 | 0.078 | 0.114 | 0.125 | 0.202 | 1.351 |
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 | 28 | 0 | 21 | 20 | 25 | 19 | 17 | 18 | 104 | 17 |
N.S. |
1 | 0.00 | 0.75 | 0.71 | 0.89 | 0.68 | 0.61 | 0.64 | 3.71 | 0.61 |
time (sec) |
N/A | 0.000 | 0.158 | 0.406 | 0.072 | 0.071 | 0.201 | 0.114 | 0.241 | 1.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 22 | 28 | 60 | 24 | 24 | 0 | 27 | 0 |
N.S. |
1 | 0.00 | 0.85 | 1.08 | 2.31 | 0.92 | 0.92 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.445 | 12.536 | 0.147 | 0.081 | 0.171 | 0.000 | 0.240 | 0.000 |
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 | 25 | 26 | 24 | 25 | 25 | 41 | 25 | 25 | 20 |
N.S. |
1 | 1.09 | 1.13 | 1.04 | 1.09 | 1.09 | 1.78 | 1.09 | 1.09 | 0.87 |
time (sec) |
N/A | 0.257 | 0.002 | 0.068 | 0.040 | 0.064 | 0.026 | 0.105 | 0.214 | 1.281 |
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 | 24 | 22 | 21 | 21 | 19 | 21 | 44 | 59 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.88 | 0.88 | 0.79 | 0.88 | 1.83 | 2.46 |
time (sec) |
N/A | 0.000 | 0.561 | 0.621 | 0.079 | 0.065 | 0.131 | 0.132 | 0.341 | 1.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | F | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 129 | 70 | 108 | 110 | 622 | 259 | 0 |
N.S. |
1 | 0.00 | 0.00 | 4.16 | 2.26 | 3.48 | 3.55 | 20.06 | 8.35 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.016 | 0.959 | 0.084 | 3.209 | 0.202 | 200.044 | 0.000 |
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 | 20 | 20 | 18 | 17 | 0 | 14 | 15 | 27 | 21 | 17 |
N.S. |
1 | 1.00 | 0.90 | 0.85 | 0.00 | 0.70 | 0.75 | 1.35 | 1.05 | 0.85 |
time (sec) |
N/A | 0.279 | 0.014 | 0.082 | 0.000 | 0.067 | 0.080 | 0.112 | 0.206 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 90 | 57 | 58 | 147 | 64 | 63 | 57 | 80 | 62 |
N.S. |
1 | 2.73 | 1.73 | 1.76 | 4.45 | 1.94 | 1.91 | 1.73 | 2.42 | 1.88 |
time (sec) |
N/A | 1.018 | 0.073 | 1.597 | 0.077 | 0.068 | 0.188 | 0.116 | 0.227 | 1.884 |
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 | 25 | 0 | 38 | 36 | 74 | 40 | 41 | 0 | 33 | 138 |
N.S. |
1 | 0.00 | 1.52 | 1.44 | 2.96 | 1.60 | 1.64 | 0.00 | 1.32 | 5.52 |
time (sec) |
N/A | 0.000 | 0.314 | 4.915 | 0.192 | 0.082 | 0.225 | 0.000 | 0.218 | 2.466 |
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 | 30 | 31 | 26 | 31 | 24 | 0 | 108 | 29 |
N.S. |
1 | 0.00 | 1.03 | 1.07 | 0.90 | 1.07 | 0.83 | 0.00 | 3.72 | 1.00 |
time (sec) |
N/A | 0.000 | 0.206 | 60.480 | 0.187 | 0.072 | 9.585 | 0.000 | 200.032 | 1.971 |
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 | 6 | 6 | 5 | 6 | 6 | 5 | 7 | 6 | 4 |
N.S. |
1 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 | 0.62 | 0.88 | 0.75 | 0.50 |
time (sec) |
N/A | 0.136 | 0.001 | 0.089 | 0.029 | 0.065 | 0.022 | 0.111 | 0.184 | 0.073 |
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 | 29 | 0 | 31 | 47 | 43 | 40 | 56 | 46 | 50 | 0 |
N.S. |
1 | 0.00 | 1.07 | 1.62 | 1.48 | 1.38 | 1.93 | 1.59 | 1.72 | 0.00 |
time (sec) |
N/A | 0.000 | 0.345 | 17.898 | 0.193 | 0.079 | 0.396 | 5.216 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 22 | 42 | 48 | 19 | 65 | 28 | 39 |
N.S. |
1 | 0.00 | 1.04 | 0.88 | 1.68 | 1.92 | 0.76 | 2.60 | 1.12 | 1.56 |
time (sec) |
N/A | 0.000 | 1.793 | 0.164 | 0.079 | 0.073 | 0.125 | 0.135 | 0.215 | 1.849 |
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 | 29 | 28 | 28 | 25 | 24 | 24 | 27 | 28 | 51 | 0 |
N.S. |
1 | 0.97 | 0.97 | 0.86 | 0.83 | 0.83 | 0.93 | 0.97 | 1.76 | 0.00 |
time (sec) |
N/A | 1.268 | 0.183 | 0.640 | 0.078 | 0.074 | 0.192 | 0.181 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 31 | 33 | 30 | 30 | 32 | 24 | 34 | 33 | 0 |
N.S. |
1 | 1.11 | 1.18 | 1.07 | 1.07 | 1.14 | 0.86 | 1.21 | 1.18 | 0.00 |
time (sec) |
N/A | 0.775 | 0.141 | 0.725 | 0.068 | 0.072 | 0.106 | 0.113 | 0.222 | 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 | 27 | 0 | 26 | 27 | 31 | 31 | 27 | 26 | 27 | 30 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 1.15 | 1.15 | 1.00 | 0.96 | 1.00 | 1.11 |
time (sec) |
N/A | 0.000 | 0.155 | 0.447 | 0.058 | 0.072 | 0.129 | 0.116 | 0.200 | 1.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 52 | 17 | 15 | 15 | 63 | 19 | 17 | 19 |
N.S. |
1 | 1.29 | 2.48 | 0.81 | 0.71 | 0.71 | 3.00 | 0.90 | 0.81 | 0.90 |
time (sec) |
N/A | 0.286 | 0.022 | 0.207 | 0.028 | 0.069 | 4.699 | 0.112 | 0.194 | 1.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | F | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 74 | 83 | 23 | 0 | 0 | 158 | 42 |
N.S. |
1 | 0.00 | 1.00 | 2.96 | 3.32 | 0.92 | 0.00 | 0.00 | 6.32 | 1.68 |
time (sec) |
N/A | 0.000 | 0.275 | 0.178 | 0.256 | 0.076 | 0.000 | 0.000 | 200.024 | 2.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F(-1) | B | A | A | F | B | B |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 173 | 46 | 0 | 74 | 42 | 42 | 0 | 46 | 87 |
N.S. |
1 | 6.65 | 1.77 | 0.00 | 2.85 | 1.62 | 1.62 | 0.00 | 1.77 | 3.35 |
time (sec) |
N/A | 0.729 | 1.347 | 0.000 | 0.260 | 0.079 | 14.724 | 0.000 | 0.216 | 2.008 |
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 | 27 | 17 | 17 | 14 | 13 | 13 | 12 | 15 | 13 | 15 |
N.S. |
1 | 0.63 | 0.63 | 0.52 | 0.48 | 0.48 | 0.44 | 0.56 | 0.48 | 0.56 |
time (sec) |
N/A | 0.599 | 0.036 | 0.164 | 0.059 | 0.070 | 0.058 | 0.119 | 0.194 | 1.793 |
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 | 29 | 31 | 39 | 30 | 27 | 29 | 82 | 50 |
N.S. |
1 | 0.00 | 1.21 | 1.29 | 1.62 | 1.25 | 1.12 | 1.21 | 3.42 | 2.08 |
time (sec) |
N/A | 0.000 | 0.945 | 5.307 | 0.157 | 0.076 | 0.388 | 0.314 | 0.205 | 2.062 |
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 | 22 | 49 | 22 | 18 | 69 | 31 | 22 | 27 | 35 | 21 |
N.S. |
1 | 2.23 | 1.00 | 0.82 | 3.14 | 1.41 | 1.00 | 1.23 | 1.59 | 0.95 |
time (sec) |
N/A | 0.651 | 0.214 | 0.235 | 0.102 | 0.069 | 0.052 | 0.126 | 0.200 | 1.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 43 | 59 | 63 | 49 | 0 | 53 | 65 | 87 |
N.S. |
1 | 0.00 | 1.48 | 2.03 | 2.17 | 1.69 | 0.00 | 1.83 | 2.24 | 3.00 |
time (sec) |
N/A | 0.000 | 0.082 | 0.285 | 0.068 | 0.069 | 0.000 | 0.180 | 0.215 | 1.994 |
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 | 26 | 23 | 36 | 36 | 17 | 22 | 38 | 22 |
N.S. |
1 | 0.00 | 0.96 | 0.85 | 1.33 | 1.33 | 0.63 | 0.81 | 1.41 | 0.81 |
time (sec) |
N/A | 0.000 | 0.118 | 0.733 | 0.068 | 0.077 | 0.050 | 0.112 | 0.214 | 1.891 |
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 | 27 | 1209 | 115 | 662 | 1976 | 94 | 107 | 141 | 197 | 107 |
N.S. |
1 | 44.78 | 4.26 | 24.52 | 73.19 | 3.48 | 3.96 | 5.22 | 7.30 | 3.96 |
time (sec) |
N/A | 2.884 | 0.066 | 0.020 | 0.154 | 0.077 | 0.207 | 0.151 | 0.218 | 2.242 |
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 | 24 | 0 | 27 | 21 | 42 | 36 | 15 | 42 | 478 | 22 |
N.S. |
1 | 0.00 | 1.12 | 0.88 | 1.75 | 1.50 | 0.62 | 1.75 | 19.92 | 0.92 |
time (sec) |
N/A | 0.000 | 3.366 | 0.329 | 0.079 | 0.074 | 0.076 | 0.128 | 0.227 | 1.873 |
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 | 31 | 43 | 37 | 42 | 37 | 42 | 40 | 160 |
N.S. |
1 | 0.00 | 1.29 | 1.79 | 1.54 | 1.75 | 1.54 | 1.75 | 1.67 | 6.67 |
time (sec) |
N/A | 0.000 | 0.342 | 0.401 | 0.072 | 0.074 | 0.141 | 0.113 | 0.218 | 2.099 |
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 | 108 | 108 | 94 | 360 | 100 | 112 | 371 | 170 | 93 |
N.S. |
1 | 4.50 | 4.50 | 3.92 | 15.00 | 4.17 | 4.67 | 15.46 | 7.08 | 3.88 |
time (sec) |
N/A | 1.972 | 0.470 | 12.276 | 0.050 | 0.080 | 0.194 | 0.122 | 0.192 | 0.415 |
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 | 40 | 41 | 46 | 46 | 36 | 50 | 45 | 32 |
N.S. |
1 | 0.00 | 1.43 | 1.46 | 1.64 | 1.64 | 1.29 | 1.79 | 1.61 | 1.14 |
time (sec) |
N/A | 0.000 | 3.961 | 0.415 | 0.136 | 0.074 | 0.178 | 0.156 | 0.209 | 1.993 |
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 | 21 | 60 | 30 | 28 | 40 | 27 | 29 | 27 | 25 | 24 |
N.S. |
1 | 2.86 | 1.43 | 1.33 | 1.90 | 1.29 | 1.38 | 1.29 | 1.19 | 1.14 |
time (sec) |
N/A | 0.211 | 0.028 | 0.600 | 0.046 | 0.082 | 0.087 | 0.120 | 0.219 | 1.672 |
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 | 15 | 14 | 14 | 12 | 14 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 0.80 | 0.93 | 1.13 | 1.00 |
time (sec) |
N/A | 0.478 | 0.040 | 0.200 | 0.070 | 0.070 | 0.054 | 0.125 | 0.231 | 0.163 |
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 | 21 | 22 | 41 | 27 | 24 | 31 | 40 | 32 |
N.S. |
1 | 0.00 | 0.91 | 0.96 | 1.78 | 1.17 | 1.04 | 1.35 | 1.74 | 1.39 |
time (sec) |
N/A | 0.000 | 10.396 | 0.381 | 0.087 | 0.069 | 0.087 | 0.208 | 0.206 | 1.700 |
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 | 25 | 17 | 16 | 15 | 15 | 12 | 18 | 31 | 15 |
N.S. |
1 | 0.76 | 0.52 | 0.48 | 0.45 | 0.45 | 0.36 | 0.55 | 0.94 | 0.45 |
time (sec) |
N/A | 0.347 | 0.011 | 0.204 | 0.027 | 0.070 | 0.083 | 0.113 | 0.190 | 1.621 |
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 | 13 | 15 | 12 | 11 | 17 | 7 | 11 | 13 | 11 |
N.S. |
1 | 0.65 | 0.75 | 0.60 | 0.55 | 0.85 | 0.35 | 0.55 | 0.65 | 0.55 |
time (sec) |
N/A | 0.285 | 0.006 | 0.151 | 0.032 | 0.060 | 0.029 | 0.114 | 0.211 | 0.037 |
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 | 14 | 13 | 13 | 14 | 13 | 16 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.81 | 0.81 | 0.88 | 0.81 | 1.00 | 0.81 |
time (sec) |
N/A | 0.433 | 0.031 | 0.295 | 0.082 | 0.070 | 0.094 | 0.115 | 0.200 | 1.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 17 | 16 | 16 | 17 | 16 | 17 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.94 | 0.94 | 1.00 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.000 | 0.084 | 0.089 | 0.058 | 0.074 | 0.110 | 0.109 | 0.217 | 1.599 |
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 | 30 | 34 | 34 | 35 | 47 | 45 | 34 | 35 | 35 | 0 |
N.S. |
1 | 1.13 | 1.13 | 1.17 | 1.57 | 1.50 | 1.13 | 1.17 | 1.17 | 0.00 |
time (sec) |
N/A | 0.935 | 0.048 | 1.422 | 0.158 | 0.078 | 0.602 | 0.173 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 20 | 18 | 19 | 19 | 17 | 24 | 28 | 17 |
N.S. |
1 | 1.17 | 0.83 | 0.75 | 0.79 | 0.79 | 0.71 | 1.00 | 1.17 | 0.71 |
time (sec) |
N/A | 0.244 | 0.038 | 0.151 | 0.031 | 0.066 | 0.080 | 0.114 | 0.219 | 1.481 |
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 | 23 | 25 | 21 | 20 | 20 | 17 | 20 | 18 | 17 |
N.S. |
1 | 0.82 | 0.89 | 0.75 | 0.71 | 0.71 | 0.61 | 0.71 | 0.64 | 0.61 |
time (sec) |
N/A | 0.193 | 0.010 | 0.198 | 0.029 | 0.065 | 0.043 | 0.113 | 0.228 | 1.408 |
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 | 38 | 0 | 55 | 52 | 60 | 68 | 54 | 62 | 75 | 191 |
N.S. |
1 | 0.00 | 1.45 | 1.37 | 1.58 | 1.79 | 1.42 | 1.63 | 1.97 | 5.03 |
time (sec) |
N/A | 0.000 | 0.120 | 4.306 | 0.166 | 0.083 | 0.209 | 0.245 | 0.224 | 1.846 |
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 | 9 | 7 | 7 | 7 | 6 | 6 | 3 | 6 | 7 | 6 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.33 | 0.67 | 0.78 | 0.67 |
time (sec) |
N/A | 0.202 | 0.001 | 0.051 | 0.046 | 0.058 | 0.027 | 0.111 | 0.213 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 1114 | 1529 | 380 | 1957 | 362 | 1402 | 508 | 525 | 0 |
N.S. |
1 | 41.26 | 56.63 | 14.07 | 72.48 | 13.41 | 51.93 | 18.81 | 19.44 | 0.00 |
time (sec) |
N/A | 7.840 | 2.730 | 173.258 | 0.253 | 0.094 | 2.762 | 0.161 | 0.219 | 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 | 36 | 34 | 27 | 36 | 36 | 29 | 36 | 31 | 27 |
N.S. |
1 | 1.44 | 1.36 | 1.08 | 1.44 | 1.44 | 1.16 | 1.44 | 1.24 | 1.08 |
time (sec) |
N/A | 0.166 | 0.003 | 0.110 | 0.032 | 0.061 | 0.022 | 0.108 | 0.212 | 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 | 16 | 13 | 13 | 13 | 12 | 12 | 15 | 32 | 33 | 11 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.75 | 0.75 | 0.94 | 2.00 | 2.06 | 0.69 |
time (sec) |
N/A | 0.157 | 0.019 | 0.119 | 0.032 | 0.069 | 0.088 | 0.107 | 0.238 | 1.561 |
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 | 27 | 29 | 23 | 23 | 37 | 27 | 37 | 54 | 26 | 20 |
N.S. |
1 | 1.07 | 0.85 | 0.85 | 1.37 | 1.00 | 1.37 | 2.00 | 0.96 | 0.74 |
time (sec) |
N/A | 0.224 | 0.015 | 0.382 | 0.063 | 0.067 | 0.066 | 0.122 | 0.202 | 1.524 |
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 | 28 | 0 | 0 | 68 | 75 | 72 | 68 | 70 | 75 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.43 | 2.68 | 2.57 | 2.43 | 2.50 | 2.68 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.037 | 0.225 | 0.086 | 0.556 | 0.477 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | B | B | B | B | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 31 | 0 | 153 | 132 | 134 | 165 | 186 | 8404 |
N.S. |
1 | 0.00 | 1.29 | 0.00 | 6.38 | 5.50 | 5.58 | 6.88 | 7.75 | 350.17 |
time (sec) |
N/A | 0.000 | 5.044 | 0.000 | 0.262 | 0.076 | 0.271 | 0.171 | 0.195 | 9.045 |
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 | 19 | 13 | 13 | 14 | 13 | 13 | 10 | 13 | 25 | 13 |
N.S. |
1 | 0.68 | 0.68 | 0.74 | 0.68 | 0.68 | 0.53 | 0.68 | 1.32 | 0.68 |
time (sec) |
N/A | 0.261 | 0.005 | 0.134 | 0.037 | 0.063 | 0.179 | 0.116 | 0.207 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 33 | 33 | 56 | 53 | 51 | 150 | 0 | 56 |
N.S. |
1 | 0.00 | 1.06 | 1.06 | 1.81 | 1.71 | 1.65 | 4.84 | 0.00 | 1.81 |
time (sec) |
N/A | 0.000 | 0.127 | 7.336 | 0.169 | 0.078 | 0.573 | 0.381 | 2.229 | 1.963 |
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 | 20 | 0 | 25 | 22 | 25 | 27 | 17 | 27 | 27 | 23 |
N.S. |
1 | 0.00 | 1.25 | 1.10 | 1.25 | 1.35 | 0.85 | 1.35 | 1.35 | 1.15 |
time (sec) |
N/A | 0.000 | 1.702 | 0.224 | 0.087 | 0.068 | 0.056 | 0.121 | 0.193 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 24 | 26 | 21 | 24 | 0 | 83 | 29 |
N.S. |
1 | 0.00 | 0.00 | 1.33 | 1.44 | 1.17 | 1.33 | 0.00 | 4.61 | 1.61 |
time (sec) |
N/A | 0.000 | 0.000 | 5.070 | 0.174 | 0.068 | 0.563 | 0.000 | 200.027 | 1.687 |
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 | 27 | 0 | 45 | 274 | 873 | 60 | 60 | 0 | 198 | 217 |
N.S. |
1 | 0.00 | 1.67 | 10.15 | 32.33 | 2.22 | 2.22 | 0.00 | 7.33 | 8.04 |
time (sec) |
N/A | 0.000 | 0.197 | 0.742 | 0.789 | 0.083 | 0.709 | 0.000 | 0.240 | 2.594 |
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 | 33 | 35 | 35 | 32 | 67 | 34 | 27 | 34 | 151 | 31 |
N.S. |
1 | 1.06 | 1.06 | 0.97 | 2.03 | 1.03 | 0.82 | 1.03 | 4.58 | 0.94 |
time (sec) |
N/A | 2.685 | 0.102 | 1.065 | 0.186 | 0.071 | 0.092 | 0.131 | 0.220 | 1.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 29 | 49 | 28 | 29 | 51 | 547 | 28 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 2.23 | 1.27 | 1.32 | 2.32 | 24.86 | 1.27 |
time (sec) |
N/A | 0.000 | 0.000 | 1.523 | 0.146 | 0.072 | 0.253 | 0.246 | 0.233 | 1.893 |
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 | 48 | 43 | 37 | 36 | 36 | 39 | 36 | 76 | 36 |
N.S. |
1 | 1.85 | 1.65 | 1.42 | 1.38 | 1.38 | 1.50 | 1.38 | 2.92 | 1.38 |
time (sec) |
N/A | 0.223 | 0.067 | 0.229 | 0.037 | 0.072 | 0.114 | 0.120 | 0.274 | 1.503 |
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 | 21 | 18 | 20 | 22 | 20 | 22 | 25 | 21 |
N.S. |
1 | 1.12 | 0.88 | 0.75 | 0.83 | 0.92 | 0.83 | 0.92 | 1.04 | 0.88 |
time (sec) |
N/A | 0.410 | 0.524 | 0.234 | 0.136 | 0.070 | 0.172 | 0.118 | 0.231 | 1.567 |
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 | 16 | 16 | 15 | 16 | 16 | 17 | 16 | 16 | 14 |
N.S. |
1 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 | 0.85 | 0.80 | 0.80 | 0.70 |
time (sec) |
N/A | 0.419 | 0.100 | 0.162 | 0.068 | 0.092 | 0.073 | 0.115 | 0.242 | 1.552 |
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 | 24 | 41 | 37 | 27 | 36 | 37 | 37 | 38 | 25 | 31 |
N.S. |
1 | 1.71 | 1.54 | 1.12 | 1.50 | 1.54 | 1.54 | 1.58 | 1.04 | 1.29 |
time (sec) |
N/A | 0.348 | 0.018 | 0.304 | 0.027 | 0.067 | 0.288 | 0.132 | 0.229 | 0.174 |
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 | 20 | 28 | 21 | 23 | 24 | 27 | 57 | 19 |
N.S. |
1 | 0.00 | 0.71 | 1.00 | 0.75 | 0.82 | 0.86 | 0.96 | 2.04 | 0.68 |
time (sec) |
N/A | 0.000 | 0.246 | 2.645 | 0.083 | 0.075 | 0.072 | 0.141 | 0.519 | 1.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 38 | 0 | 67 | 36 | 0 | 23 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.46 | 0.00 | 2.58 | 1.38 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.218 | 0.739 | 0.000 | 0.079 | 0.195 | 0.000 | 0.219 | 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 | 29 | 91 | 91 | 77 | 297 | 76 | 65 | 76 | 80 | 101 |
N.S. |
1 | 3.14 | 3.14 | 2.66 | 10.24 | 2.62 | 2.24 | 2.62 | 2.76 | 3.48 |
time (sec) |
N/A | 3.644 | 0.033 | 0.809 | 0.144 | 0.067 | 0.130 | 0.137 | 0.236 | 1.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-1) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 72 | 186 | 180 | 130 | 133 | 0 | 418 | 135 |
N.S. |
1 | 0.00 | 2.18 | 5.64 | 5.45 | 3.94 | 4.03 | 0.00 | 12.67 | 4.09 |
time (sec) |
N/A | 0.000 | 0.183 | 1.143 | 0.141 | 0.078 | 0.373 | 0.000 | 200.025 | 3.080 |
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 | 19 | 31 | 15 | 13 | 250 | 17 | 19 | 22 | 18 | 14 |
N.S. |
1 | 1.63 | 0.79 | 0.68 | 13.16 | 0.89 | 1.00 | 1.16 | 0.95 | 0.74 |
time (sec) |
N/A | 0.431 | 0.121 | 0.079 | 0.094 | 0.083 | 0.092 | 0.112 | 0.255 | 1.522 |
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 | 22 | 54 | 42 | 39 | 54 | 32 | 34 | 35 | 36 | 26 |
N.S. |
1 | 2.45 | 1.91 | 1.77 | 2.45 | 1.45 | 1.55 | 1.59 | 1.64 | 1.18 |
time (sec) |
N/A | 0.325 | 0.025 | 1.392 | 0.026 | 0.070 | 0.080 | 0.111 | 0.193 | 1.630 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 32 | 210 | 33 | 31 | 29 | 1340 | 58 | 0 |
N.S. |
1 | 1.20 | 1.07 | 7.00 | 1.10 | 1.03 | 0.97 | 44.67 | 1.93 | 0.00 |
time (sec) |
N/A | 1.739 | 0.127 | 0.089 | 1.003 | 0.075 | 1.464 | 3.440 | 0.238 | 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 | 23 | 37 | 37 | 34 | 31 | 37 | 40 | 22 |
N.S. |
1 | 0.00 | 0.96 | 1.54 | 1.54 | 1.42 | 1.29 | 1.54 | 1.67 | 0.92 |
time (sec) |
N/A | 0.000 | 0.110 | 10.400 | 0.076 | 0.071 | 0.440 | 0.160 | 0.230 | 2.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 40 | 103 | 74 | 412 | 83 | 0 | 337 | 87 |
N.S. |
1 | 0.00 | 1.29 | 3.32 | 2.39 | 13.29 | 2.68 | 0.00 | 10.87 | 2.81 |
time (sec) |
N/A | 0.000 | 0.471 | 111.262 | 2.109 | 0.086 | 3.502 | 0.000 | 200.042 | 3.499 |
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 | 12 | 12 | 12 | 11 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.83 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.139 | 0.000 | 0.092 | 0.028 | 0.080 | 0.015 | 0.108 | 0.255 | 1.727 |
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 | 32 | 30 | 32 | 29 | 31 | 29 | 31 | 52 | 33 |
N.S. |
1 | 1.19 | 1.11 | 1.19 | 1.07 | 1.15 | 1.07 | 1.15 | 1.93 | 1.22 |
time (sec) |
N/A | 0.695 | 0.405 | 0.793 | 0.260 | 0.064 | 0.121 | 0.154 | 5.493 | 1.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 33 | 75 | 42 | 73 | 71 | 97 | 110 | 74 |
N.S. |
1 | 0.00 | 1.22 | 2.78 | 1.56 | 2.70 | 2.63 | 3.59 | 4.07 | 2.74 |
time (sec) |
N/A | 0.000 | 0.116 | 1.711 | 8.484 | 0.077 | 0.628 | 3.642 | 0.234 | 3.500 |
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 | 23 | 46 | 29 | 29 | 32 | 41 | 49 | 41 |
N.S. |
1 | 0.00 | 0.88 | 1.77 | 1.12 | 1.12 | 1.23 | 1.58 | 1.88 | 1.58 |
time (sec) |
N/A | 0.000 | 0.137 | 0.095 | 0.333 | 0.075 | 17.068 | 0.123 | 0.343 | 3.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 36 | 40 | 35 | 57 | 27 | 0 | 169 | 33 |
N.S. |
1 | 0.00 | 0.97 | 1.08 | 0.95 | 1.54 | 0.73 | 0.00 | 4.57 | 0.89 |
time (sec) |
N/A | 0.000 | 0.668 | 0.502 | 0.225 | 0.085 | 0.340 | 0.000 | 0.265 | 1.708 |
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 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 10 | 8 |
N.S. |
1 | 0.64 | 0.64 | 0.64 | 0.57 | 0.57 | 0.50 | 0.57 | 0.71 | 0.57 |
time (sec) |
N/A | 0.155 | 0.002 | 0.073 | 0.026 | 0.057 | 0.038 | 0.108 | 0.229 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 56 | 67 | 65 | 72 | 75 | 80 | 165 | 201 |
N.S. |
1 | 0.00 | 2.33 | 2.79 | 2.71 | 3.00 | 3.12 | 3.33 | 6.88 | 8.38 |
time (sec) |
N/A | 0.000 | 0.074 | 163.047 | 0.677 | 0.065 | 0.276 | 0.391 | 200.041 | 2.283 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 2527 | 30 | 29 | 191 | 29 | 24 | 37 | 44 | 33 |
N.S. |
1 | 84.23 | 1.00 | 0.97 | 6.37 | 0.97 | 0.80 | 1.23 | 1.47 | 1.10 |
time (sec) |
N/A | 7.932 | 0.813 | 1.188 | 1.009 | 0.067 | 0.130 | 0.121 | 0.214 | 1.879 |
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 | 22 | 0 | 54 | 44 | 188 | 57 | 53 | 73 | 76 | 59 |
N.S. |
1 | 0.00 | 2.45 | 2.00 | 8.55 | 2.59 | 2.41 | 3.32 | 3.45 | 2.68 |
time (sec) |
N/A | 0.000 | 0.086 | 4.679 | 0.156 | 0.069 | 0.143 | 0.145 | 0.198 | 1.848 |
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 | 38 | 33 | 34 | 48 | 25 | 26 | 26 | 46 | 28 |
N.S. |
1 | 1.31 | 1.14 | 1.17 | 1.66 | 0.86 | 0.90 | 0.90 | 1.59 | 0.97 |
time (sec) |
N/A | 0.547 | 0.047 | 0.932 | 0.082 | 0.069 | 0.142 | 0.114 | 0.224 | 1.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 18 | 22 | 16 | 70 | 17 | 0 | 22 | 18 |
N.S. |
1 | 0.00 | 0.78 | 0.96 | 0.70 | 3.04 | 0.74 | 0.00 | 0.96 | 0.78 |
time (sec) |
N/A | 0.000 | 0.190 | 0.353 | 0.175 | 0.072 | 0.106 | 0.000 | 2.672 | 1.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 30 | 30 | 31 | 0 | 50 | 30 | 68 |
N.S. |
1 | 0.00 | 0.93 | 1.11 | 1.11 | 1.15 | 0.00 | 1.85 | 1.11 | 2.52 |
time (sec) |
N/A | 0.000 | 0.308 | 185.603 | 0.191 | 0.074 | 0.000 | 0.124 | 0.210 | 2.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | B | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 43 | 44 | 52 | 54 | 45 | 46 | 42 |
N.S. |
1 | 0.00 | 0.00 | 1.59 | 1.63 | 1.93 | 2.00 | 1.67 | 1.70 | 1.56 |
time (sec) |
N/A | 0.000 | 0.000 | 0.474 | 0.067 | 0.071 | 0.185 | 0.124 | 0.210 | 1.954 |
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 | 28 | 0 | 22 | 30 | 19 | 29 | 27 | 53 | 22 | 63 |
N.S. |
1 | 0.00 | 0.79 | 1.07 | 0.68 | 1.04 | 0.96 | 1.89 | 0.79 | 2.25 |
time (sec) |
N/A | 0.000 | 0.284 | 2.569 | 0.099 | 0.068 | 0.317 | 0.241 | 0.224 | 2.011 |
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 | 20 | 36 | 23 | 23 | 0 | 23 | 31 | 23 | 20 | 19 |
N.S. |
1 | 1.80 | 1.15 | 1.15 | 0.00 | 1.15 | 1.55 | 1.15 | 1.00 | 0.95 |
time (sec) |
N/A | 0.788 | 0.418 | 0.600 | 0.000 | 0.065 | 0.121 | 0.121 | 0.193 | 1.824 |
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 | 11 | 9 | 8 | 7 | 7 | 5 | 7 | 10 | 7 |
N.S. |
1 | 0.73 | 0.60 | 0.53 | 0.47 | 0.47 | 0.33 | 0.47 | 0.67 | 0.47 |
time (sec) |
N/A | 0.248 | 0.001 | 0.037 | 0.034 | 0.055 | 0.017 | 0.106 | 0.214 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 49 | 28 | 21 | 20 | 21 | 24 | 0 | 27 | 21 |
N.S. |
1 | 1.69 | 0.97 | 0.72 | 0.69 | 0.72 | 0.83 | 0.00 | 0.93 | 0.72 |
time (sec) |
N/A | 1.205 | 0.028 | 0.174 | 0.235 | 0.070 | 0.141 | 0.000 | 0.216 | 0.112 |
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 | 23 | 20 | 18 | 19 | 19 | 15 | 20 | 23 | 16 |
N.S. |
1 | 1.44 | 1.25 | 1.12 | 1.19 | 1.19 | 0.94 | 1.25 | 1.44 | 1.00 |
time (sec) |
N/A | 0.299 | 0.008 | 0.153 | 0.030 | 0.061 | 0.195 | 0.111 | 0.198 | 1.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 76 | 25 | 24 | 23 | 23 | 0 | 48 | 27 | 23 |
N.S. |
1 | 2.53 | 0.83 | 0.80 | 0.77 | 0.77 | 0.00 | 1.60 | 0.90 | 0.77 |
time (sec) |
N/A | 0.670 | 3.867 | 0.718 | 0.081 | 0.070 | 0.000 | 0.137 | 0.202 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 36 | 36 | 36 | 31 | 36 | 37 | 32 |
N.S. |
1 | 0.00 | 0.00 | 1.12 | 1.12 | 1.12 | 0.97 | 1.12 | 1.16 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.234 | 0.071 | 0.070 | 0.179 | 0.129 | 0.204 | 1.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 30 | 26 | 32 | 34 | 31 | 32 | 34 | 47 | 121 |
N.S. |
1 | 1.25 | 1.08 | 1.33 | 1.42 | 1.29 | 1.33 | 1.42 | 1.96 | 5.04 |
time (sec) |
N/A | 0.666 | 0.252 | 1.829 | 0.087 | 0.065 | 0.157 | 0.174 | 0.214 | 2.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | B | B | B | B | F | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 50 | 81 | 50 | 44 | 0 | 708 | 44 |
N.S. |
1 | 0.00 | 0.00 | 2.27 | 3.68 | 2.27 | 2.00 | 0.00 | 32.18 | 2.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.688 | 0.302 | 0.067 | 0.203 | 0.000 | 0.532 | 2.232 |
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 | 20 | 28 | 18 | 18 | 19 | 18 | 17 | 36 | 33 | 21 |
N.S. |
1 | 1.40 | 0.90 | 0.90 | 0.95 | 0.90 | 0.85 | 1.80 | 1.65 | 1.05 |
time (sec) |
N/A | 0.188 | 0.029 | 0.378 | 0.044 | 0.067 | 0.112 | 0.118 | 0.216 | 1.756 |
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 | 33 | 51 | 36 | 25 | 0 | 25 | 29 | 36 | 45 | 35 |
N.S. |
1 | 1.55 | 1.09 | 0.76 | 0.00 | 0.76 | 0.88 | 1.09 | 1.36 | 1.06 |
time (sec) |
N/A | 0.529 | 0.577 | 0.372 | 0.000 | 0.077 | 0.115 | 0.112 | 0.201 | 1.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 42 | 62 | 58 | 50 | 24 | 0 | 88 | 33 |
N.S. |
1 | 0.00 | 1.17 | 1.72 | 1.61 | 1.39 | 0.67 | 0.00 | 2.44 | 0.92 |
time (sec) |
N/A | 0.000 | 0.209 | 2.075 | 0.105 | 0.069 | 0.135 | 0.000 | 1.799 | 1.976 |