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 | 15 | 14 | 17 | 13 | 14 | 14 | 15 | 14 | 11 | 12 |
N.S. |
1 | 0.93 | 1.13 | 0.87 | 0.93 | 0.93 | 1.00 | 0.93 | 0.73 | 0.80 |
time (sec) |
N/A | 0.219 | 0.001 | 0.062 | 0.028 | 0.055 | 0.022 | 0.111 | 0.218 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 31 | 31 | 30 | 35 | 29 | 29 | 0 | 29 | 29 |
N.S. |
1 | 1.15 | 1.15 | 1.11 | 1.30 | 1.07 | 1.07 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.446 | 0.031 | 9.765 | 0.168 | 0.074 | 0.708 | 0.000 | 0.220 | 2.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 44 | 60 | 37 | 50 | 49 | 103 | 46 | 108 |
N.S. |
1 | 0.00 | 1.42 | 1.94 | 1.19 | 1.61 | 1.58 | 3.32 | 1.48 | 3.48 |
time (sec) |
N/A | 0.000 | 0.130 | 1.365 | 0.364 | 0.073 | 0.200 | 0.198 | 0.216 | 2.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 5 | 5 | 6 | 5 | 5 | 5 | 6 | 5 | 5 |
N.S. |
1 | 0.45 | 0.45 | 0.55 | 0.45 | 0.45 | 0.45 | 0.55 | 0.45 | 0.45 |
time (sec) |
N/A | 0.206 | 0.001 | 0.053 | 0.023 | 0.061 | 0.041 | 0.110 | 0.186 | 1.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 37 | 55 | 43 | 44 | 0 | 90 | 43 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.62 | 1.26 | 1.29 | 0.00 | 2.65 | 1.26 | 0.00 |
time (sec) |
N/A | 0.000 | 0.159 | 0.092 | 0.292 | 0.076 | 0.000 | 0.312 | 0.185 | 0.000 |
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 | 26 | 0 | 26 | 31 | 45 | 29 | 26 | 26 | 116 | 32 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.73 | 1.12 | 1.00 | 1.00 | 4.46 | 1.23 |
time (sec) |
N/A | 0.000 | 0.146 | 1.694 | 0.221 | 0.075 | 0.793 | 0.274 | 200.020 | 1.876 |
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 | 24 | 20 | 18 | 17 | 23 | 22 | 20 | 22 | 17 |
N.S. |
1 | 1.14 | 0.95 | 0.86 | 0.81 | 1.10 | 1.05 | 0.95 | 1.05 | 0.81 |
time (sec) |
N/A | 0.178 | 0.004 | 0.106 | 0.025 | 0.064 | 0.081 | 0.107 | 0.205 | 0.064 |
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 | 23 | 25 | 30 | 24 | 76 | 38 | 29 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 1.30 | 1.04 | 3.30 | 1.65 | 1.26 | 0.91 |
time (sec) |
N/A | 0.000 | 1.130 | 0.227 | 0.092 | 0.067 | 0.111 | 0.115 | 0.216 | 0.135 |
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 | 30 | 29 | 25 | 28 | 0 | 27 | 20 | 0 | 30 | 23 |
N.S. |
1 | 0.97 | 0.83 | 0.93 | 0.00 | 0.90 | 0.67 | 0.00 | 1.00 | 0.77 |
time (sec) |
N/A | 0.462 | 1.513 | 1.055 | 0.000 | 0.085 | 0.120 | 0.000 | 0.221 | 1.827 |
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 | 19 | 18 | 16 | 16 | 0 | 43 | 17 | 46 | 54 | 20 |
N.S. |
1 | 0.95 | 0.84 | 0.84 | 0.00 | 2.26 | 0.89 | 2.42 | 2.84 | 1.05 |
time (sec) |
N/A | 1.476 | 0.020 | 0.435 | 0.000 | 0.077 | 0.092 | 0.113 | 0.213 | 0.133 |
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 | 16 | 59 | 58 | 53 | 56 | 47 | 49 | 56 | 49 | 27 |
N.S. |
1 | 3.69 | 3.62 | 3.31 | 3.50 | 2.94 | 3.06 | 3.50 | 3.06 | 1.69 |
time (sec) |
N/A | 0.322 | 0.011 | 0.552 | 0.028 | 0.069 | 0.085 | 0.115 | 0.215 | 1.540 |
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 | 25 | 25 | 38 | 39 | 17 | 41 | 42 | 28 |
N.S. |
1 | 0.00 | 0.76 | 0.76 | 1.15 | 1.18 | 0.52 | 1.24 | 1.27 | 0.85 |
time (sec) |
N/A | 0.000 | 0.175 | 9.779 | 0.068 | 0.066 | 0.111 | 0.118 | 0.204 | 1.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 41 | 36 | 28 | 35 | 33 | 26 | 33 | 35 | 33 |
N.S. |
1 | 1.52 | 1.33 | 1.04 | 1.30 | 1.22 | 0.96 | 1.22 | 1.30 | 1.22 |
time (sec) |
N/A | 1.479 | 0.337 | 0.685 | 0.153 | 0.074 | 0.133 | 0.117 | 0.194 | 1.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 28 | 332 | 27 | 22 | 603 | 26 | 27 |
N.S. |
1 | 0.00 | 0.90 | 0.97 | 11.45 | 0.93 | 0.76 | 20.79 | 0.90 | 0.93 |
time (sec) |
N/A | 0.000 | 0.242 | 13.155 | 0.986 | 0.069 | 0.219 | 0.442 | 0.220 | 2.223 |
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 | 33 | 23 | 20 | 19 | 19 | 19 | 19 | 27 | 19 |
N.S. |
1 | 1.43 | 1.00 | 0.87 | 0.83 | 0.83 | 0.83 | 0.83 | 1.17 | 0.83 |
time (sec) |
N/A | 0.264 | 0.182 | 0.155 | 0.031 | 0.069 | 0.108 | 0.109 | 0.247 | 0.103 |
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 | 19 | 19 | 19 | 21 | 21 | 19 | 21 | 19 | 28 |
N.S. |
1 | 0.73 | 0.73 | 0.73 | 0.81 | 0.81 | 0.73 | 0.81 | 0.73 | 1.08 |
time (sec) |
N/A | 0.503 | 1.939 | 0.125 | 0.074 | 0.062 | 0.074 | 0.121 | 0.220 | 1.638 |
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 | 45 | 34 | 25 | 37 | 23 | 22 | 32 | 41 | 32 |
N.S. |
1 | 1.73 | 1.31 | 0.96 | 1.42 | 0.88 | 0.85 | 1.23 | 1.58 | 1.23 |
time (sec) |
N/A | 0.431 | 0.113 | 0.335 | 0.061 | 0.066 | 0.067 | 0.104 | 0.227 | 0.086 |
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 | 32 | 132 | 22 | 21 | 34 | 34 | 32 | 34 | 37 | 36 |
N.S. |
1 | 4.12 | 0.69 | 0.66 | 1.06 | 1.06 | 1.00 | 1.06 | 1.16 | 1.12 |
time (sec) |
N/A | 0.691 | 0.085 | 5.561 | 0.091 | 0.076 | 3.155 | 0.225 | 3.846 | 0.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 25 | 24 | 25 | 29 | 17 | 25 | 24 | 24 |
N.S. |
1 | 0.00 | 0.86 | 0.83 | 0.86 | 1.00 | 0.59 | 0.86 | 0.83 | 0.83 |
time (sec) |
N/A | 0.000 | 0.259 | 0.770 | 0.075 | 0.075 | 0.398 | 0.132 | 0.246 | 1.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 14 | 14 | 14 | 0 | 13 | 0 | 0 | 14 | 13 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.00 | 0.72 | 0.00 | 0.00 | 0.78 | 0.72 |
time (sec) |
N/A | 0.949 | 0.123 | 0.626 | 0.000 | 0.067 | 0.000 | 0.000 | 0.215 | 1.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 23 | 38 | 28 | 51 | 31 | 32 | 23 | 32 |
N.S. |
1 | 0.00 | 1.15 | 1.90 | 1.40 | 2.55 | 1.55 | 1.60 | 1.15 | 1.60 |
time (sec) |
N/A | 0.000 | 0.187 | 0.148 | 0.167 | 0.075 | 0.275 | 0.117 | 0.228 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 40 | 37 | 67 | 42 | 39 | 35 | 37 | 0 |
N.S. |
1 | 0.00 | 1.43 | 1.32 | 2.39 | 1.50 | 1.39 | 1.25 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.706 | 0.708 | 0.174 | 0.074 | 0.481 | 0.120 | 0.205 | 0.000 |
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 | 21 | 0 | 21 | 18 | 39 | 38 | 41 | 39 | 43 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 1.86 | 1.81 | 1.95 | 1.86 | 2.05 | 0.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.382 | 0.120 | 0.069 | 0.159 | 0.189 | 0.215 | 0.000 |
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 | 30 | 0 | 30 | 32 | 27 | 27 | 68 | 29 | 32 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 0.90 | 0.90 | 2.27 | 0.97 | 1.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.442 | 4.200 | 0.075 | 0.074 | 0.198 | 0.136 | 0.215 | 0.000 |
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 | 28 | 0 | 49 | 72 | 52 | 56 | 60 | 74 | 76 | 56 |
N.S. |
1 | 0.00 | 1.75 | 2.57 | 1.86 | 2.00 | 2.14 | 2.64 | 2.71 | 2.00 |
time (sec) |
N/A | 0.000 | 0.115 | 8.787 | 0.084 | 0.078 | 0.672 | 0.180 | 0.224 | 2.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 164 | 50 | 63 | 217 | 78 | 63 | 87 | 92 | 70 |
N.S. |
1 | 4.21 | 1.28 | 1.62 | 5.56 | 2.00 | 1.62 | 2.23 | 2.36 | 1.79 |
time (sec) |
N/A | 1.429 | 0.061 | 5.113 | 0.074 | 0.067 | 0.232 | 0.114 | 0.212 | 1.864 |
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 | 147 | 42 | 34 | 33 | 33 | 41 | 0 | 42 | 36 |
N.S. |
1 | 5.25 | 1.50 | 1.21 | 1.18 | 1.18 | 1.46 | 0.00 | 1.50 | 1.29 |
time (sec) |
N/A | 0.821 | 0.085 | 0.432 | 0.176 | 0.070 | 0.193 | 0.000 | 0.227 | 1.807 |
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 | 27 | 27 | 19 | 19 | 27 | 20 | 19 | 22 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.70 | 0.70 | 1.00 | 0.74 | 0.70 | 0.81 | 0.70 |
time (sec) |
N/A | 0.161 | 0.013 | 0.124 | 0.032 | 0.072 | 0.075 | 0.112 | 0.256 | 1.535 |
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 | 23 | 23 | 31 | 31 | 31 | 38 | 43 | 86 |
N.S. |
1 | 0.00 | 0.85 | 0.85 | 1.15 | 1.15 | 1.15 | 1.41 | 1.59 | 3.19 |
time (sec) |
N/A | 0.000 | 0.554 | 0.907 | 0.133 | 0.075 | 0.129 | 0.141 | 0.240 | 1.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 37 | 33 | 34 | 34 | 31 | 34 | 522 | 85 |
N.S. |
1 | 0.00 | 1.23 | 1.10 | 1.13 | 1.13 | 1.03 | 1.13 | 17.40 | 2.83 |
time (sec) |
N/A | 0.000 | 0.038 | 0.918 | 0.080 | 0.076 | 0.902 | 0.155 | 0.244 | 2.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 56 | 61 | 56 | 53 | 53 | 61 | 59 | 123 | 0 |
N.S. |
1 | 2.00 | 2.18 | 2.00 | 1.89 | 1.89 | 2.18 | 2.11 | 4.39 | 0.00 |
time (sec) |
N/A | 2.538 | 0.141 | 2.957 | 3.994 | 0.086 | 0.446 | 56.319 | 0.275 | 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 | 28 | 0 | 23 | 21 | 20 | 20 | 15 | 40 | 21 | 22 |
N.S. |
1 | 0.00 | 0.82 | 0.75 | 0.71 | 0.71 | 0.54 | 1.43 | 0.75 | 0.79 |
time (sec) |
N/A | 0.000 | 0.304 | 0.352 | 0.092 | 0.066 | 0.071 | 0.123 | 0.218 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 29 | 96 | 30 | 32 | 22 | 34 | 120 | 28 |
N.S. |
1 | 0.00 | 1.04 | 3.43 | 1.07 | 1.14 | 0.79 | 1.21 | 4.29 | 1.00 |
time (sec) |
N/A | 0.000 | 0.110 | 15.236 | 0.109 | 0.081 | 0.646 | 0.139 | 0.290 | 1.901 |
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 | 36 | 20 | 17 | 16 | 23 | 15 | 16 | 19 | 18 |
N.S. |
1 | 1.64 | 0.91 | 0.77 | 0.73 | 1.05 | 0.68 | 0.73 | 0.86 | 0.82 |
time (sec) |
N/A | 0.238 | 1.901 | 0.408 | 0.073 | 0.073 | 0.092 | 0.111 | 0.233 | 1.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 24 | 0 | 45 | 19 | 0 | 72 | 23 |
N.S. |
1 | 0.00 | 0.93 | 0.83 | 0.00 | 1.55 | 0.66 | 0.00 | 2.48 | 0.79 |
time (sec) |
N/A | 0.000 | 0.050 | 1.016 | 0.000 | 0.072 | 0.421 | 0.000 | 52.208 | 1.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 26 | 25 | 25 | 22 | 0 | 26 | 34 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.96 | 0.96 | 0.85 | 0.00 | 1.00 | 1.31 |
time (sec) |
N/A | 0.847 | 0.093 | 0.772 | 0.034 | 0.068 | 0.157 | 0.000 | 0.264 | 1.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 17 | 17 | 16 | 16 | 14 | 16 | 17 | 16 |
N.S. |
1 | 0.00 | 0.94 | 0.94 | 0.89 | 0.89 | 0.78 | 0.89 | 0.94 | 0.89 |
time (sec) |
N/A | 0.000 | 0.201 | 0.301 | 0.093 | 0.075 | 0.132 | 0.128 | 0.238 | 1.745 |
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 | 39 | 33 | 27 | 33 | 35 | 26 | 33 | 28 | 29 |
N.S. |
1 | 1.62 | 1.38 | 1.12 | 1.38 | 1.46 | 1.08 | 1.38 | 1.17 | 1.21 |
time (sec) |
N/A | 0.290 | 0.005 | 0.081 | 0.032 | 0.058 | 0.028 | 0.113 | 0.244 | 1.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 34 | 37 | 32 | 42 | 0 | 40 | 34 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 1.16 | 1.00 | 1.31 | 0.00 | 1.25 | 1.06 |
time (sec) |
N/A | 0.000 | 0.152 | 0.157 | 0.113 | 0.074 | 0.297 | 0.000 | 0.252 | 2.465 |
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 | 24 | 24 | 23 | 25 | 20 | 23 | 24 | 62 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 0.82 | 0.89 | 0.71 | 0.82 | 0.86 | 2.21 |
time (sec) |
N/A | 0.000 | 0.100 | 2.166 | 0.167 | 0.066 | 0.161 | 0.307 | 0.243 | 2.113 |
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 | 26 | 50 | 22 | 34 | 31 | 31 | 31 | 93 | 33 | 21 |
N.S. |
1 | 1.92 | 0.85 | 1.31 | 1.19 | 1.19 | 1.19 | 3.58 | 1.27 | 0.81 |
time (sec) |
N/A | 0.484 | 0.353 | 0.805 | 0.028 | 0.066 | 0.081 | 0.112 | 0.260 | 1.545 |
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 | 19 | 21 | 19 | 22 | 22 | 21 | 17 | 60 | 22 | 22 |
N.S. |
1 | 1.11 | 1.00 | 1.16 | 1.16 | 1.11 | 0.89 | 3.16 | 1.16 | 1.16 |
time (sec) |
N/A | 0.439 | 0.024 | 2.139 | 0.164 | 0.064 | 0.098 | 0.135 | 0.241 | 2.493 |
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 | 36 | 29 | 30 | 35 | 36 | 31 | 37 | 38 | 30 |
N.S. |
1 | 1.33 | 1.07 | 1.11 | 1.30 | 1.33 | 1.15 | 1.37 | 1.41 | 1.11 |
time (sec) |
N/A | 0.254 | 0.026 | 0.610 | 0.036 | 0.065 | 0.116 | 0.105 | 0.257 | 1.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 30 | 88 | 90 | 42 | 42 | 0 | 54 | 186 | 54 |
N.S. |
1 | 1.03 | 3.03 | 3.10 | 1.45 | 1.45 | 0.00 | 1.86 | 6.41 | 1.86 |
time (sec) |
N/A | 0.589 | 0.028 | 4.545 | 0.070 | 0.068 | 0.000 | 0.133 | 0.269 | 1.833 |
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 | 36 | 25 | 36 | 36 | 22 | 31 | 35 | 31 |
N.S. |
1 | 0.00 | 1.24 | 0.86 | 1.24 | 1.24 | 0.76 | 1.07 | 1.21 | 1.07 |
time (sec) |
N/A | 0.000 | 4.976 | 0.351 | 0.092 | 0.070 | 0.197 | 0.119 | 0.233 | 1.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 17 | 15 | 13 | 17 | 14 | 20 | 19 | 23 |
N.S. |
1 | 0.90 | 0.81 | 0.71 | 0.62 | 0.81 | 0.67 | 0.95 | 0.90 | 1.10 |
time (sec) |
N/A | 0.724 | 0.090 | 0.335 | 0.121 | 0.060 | 0.080 | 0.103 | 0.206 | 1.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 25 | 24 | 24 | 20 | 0 | 0 | 71 | 28 |
N.S. |
1 | 0.00 | 1.25 | 1.20 | 1.20 | 1.00 | 0.00 | 0.00 | 3.55 | 1.40 |
time (sec) |
N/A | 0.000 | 6.130 | 0.154 | 0.246 | 0.086 | 0.000 | 0.000 | 197.610 | 1.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 16 | 13 | 15 | 19 | 48 | 19 | 19 | 50 | 35 |
N.S. |
1 | 0.94 | 0.76 | 0.88 | 1.12 | 2.82 | 1.12 | 1.12 | 2.94 | 2.06 |
time (sec) |
N/A | 0.551 | 0.106 | 0.456 | 0.148 | 0.069 | 0.061 | 0.115 | 0.189 | 1.715 |
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 | 24 | 25 | 31 | 25 | 24 | 22 | 22 | 147 | 24 | 325 |
N.S. |
1 | 1.04 | 1.29 | 1.04 | 1.00 | 0.92 | 0.92 | 6.12 | 1.00 | 13.54 |
time (sec) |
N/A | 0.343 | 0.012 | 0.291 | 0.037 | 0.063 | 0.289 | 0.105 | 0.191 | 0.199 |
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 | 28 | 25 | 22 | 34 | 24 | 24 | 24 | 26 | 21 |
N.S. |
1 | 1.47 | 1.32 | 1.16 | 1.79 | 1.26 | 1.26 | 1.26 | 1.37 | 1.11 |
time (sec) |
N/A | 0.243 | 0.037 | 0.393 | 0.066 | 0.070 | 0.070 | 0.112 | 0.194 | 1.596 |
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 | 13 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 9 | 9 |
N.S. |
1 | 0.85 | 0.85 | 0.77 | 0.69 | 0.69 | 0.62 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.142 | 0.000 | 0.112 | 0.027 | 0.068 | 0.021 | 0.109 | 0.183 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 21 | 25 | 29 | 22 | 29 | 28 | 21 |
N.S. |
1 | 1.08 | 1.00 | 0.81 | 0.96 | 1.12 | 0.85 | 1.12 | 1.08 | 0.81 |
time (sec) |
N/A | 0.520 | 0.353 | 0.665 | 0.076 | 0.066 | 0.123 | 0.122 | 0.179 | 2.109 |
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 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 9 | 11 |
N.S. |
1 | 0.52 | 0.52 | 0.48 | 0.43 | 0.43 | 0.38 | 0.43 | 0.43 | 0.52 |
time (sec) |
N/A | 0.426 | 0.036 | 0.272 | 0.061 | 0.062 | 0.057 | 0.113 | 0.178 | 1.598 |
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 | 19 | 26 | 17 | 20 | 0 | 14 | 19 | 14 | 18 | 17 |
N.S. |
1 | 1.37 | 0.89 | 1.05 | 0.00 | 0.74 | 1.00 | 0.74 | 0.95 | 0.89 |
time (sec) |
N/A | 0.780 | 0.159 | 0.346 | 0.000 | 0.067 | 0.079 | 0.111 | 0.181 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 27 | 29 | 32 | 27 | 27 | 27 | 0 | 0 |
N.S. |
1 | 1.19 | 1.04 | 1.12 | 1.23 | 1.04 | 1.04 | 1.04 | 0.00 | 0.00 |
time (sec) |
N/A | 1.333 | 0.065 | 1.596 | 0.230 | 0.066 | 0.160 | 0.510 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 14 | 14 | 14 | 18 | 18 | 15 | 18 | 19 | 13 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 1.00 | 1.00 | 0.83 | 1.00 | 1.06 | 0.72 |
time (sec) |
N/A | 1.289 | 0.117 | 0.375 | 0.087 | 0.068 | 0.103 | 0.111 | 0.191 | 1.837 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 24 | 23 | 24 | 27 | 26 | 27 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.04 | 1.00 | 1.04 | 1.17 | 1.13 | 1.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.131 | 0.530 | 0.085 | 0.071 | 0.126 | 0.162 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 64 | 35 | 37 | 91 | 39 | 41 | 55 | 39 | 46 |
N.S. |
1 | 1.94 | 1.06 | 1.12 | 2.76 | 1.18 | 1.24 | 1.67 | 1.18 | 1.39 |
time (sec) |
N/A | 0.562 | 0.355 | 0.651 | 0.160 | 0.066 | 0.124 | 0.120 | 0.195 | 1.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 39 | 19 | 38 | 37 | 24 | 34 | 28 | 82 | 23 |
N.S. |
1 | 2.05 | 1.00 | 2.00 | 1.95 | 1.26 | 1.79 | 1.47 | 4.32 | 1.21 |
time (sec) |
N/A | 0.375 | 0.082 | 0.350 | 0.259 | 0.067 | 0.201 | 0.114 | 0.189 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | A | A | F | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 497 | 0 | 40 | 39 | 0 | 30 | 92 |
N.S. |
1 | 0.00 | 0.96 | 17.75 | 0.00 | 1.43 | 1.39 | 0.00 | 1.07 | 3.29 |
time (sec) |
N/A | 0.000 | 0.180 | 0.270 | 0.000 | 0.067 | 0.689 | 0.000 | 0.187 | 2.125 |
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 | 33 | 25 | 25 | 23 | 24 | 36 | 20 | 186 | 53 | 22 |
N.S. |
1 | 0.76 | 0.76 | 0.70 | 0.73 | 1.09 | 0.61 | 5.64 | 1.61 | 0.67 |
time (sec) |
N/A | 1.076 | 0.021 | 2.329 | 0.157 | 0.065 | 0.187 | 0.246 | 0.185 | 1.618 |
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 | 34 | 0 | 30 | 34 | 144 | 147 | 63 | 178 | 198 | 0 |
N.S. |
1 | 0.00 | 0.88 | 1.00 | 4.24 | 4.32 | 1.85 | 5.24 | 5.82 | 0.00 |
time (sec) |
N/A | 0.000 | 0.107 | 2.828 | 0.291 | 0.073 | 0.297 | 0.177 | 0.194 | 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 | 20 | 20 | 17 | 16 | 16 | 15 | 16 | 15 | 15 |
N.S. |
1 | 0.80 | 0.80 | 0.68 | 0.64 | 0.64 | 0.60 | 0.64 | 0.60 | 0.60 |
time (sec) |
N/A | 0.161 | 0.002 | 0.073 | 0.033 | 0.057 | 0.020 | 0.115 | 0.197 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 68 | 47 | 57 | 56 | 65 | 62 | 62 | 0 |
N.S. |
1 | 0.00 | 2.62 | 1.81 | 2.19 | 2.15 | 2.50 | 2.38 | 2.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.064 | 0.823 | 0.076 | 0.068 | 0.253 | 0.123 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 83 | 11 | 12 | 0 | 11 | 8 | 11 | 11 | 11 |
N.S. |
1 | 3.46 | 0.46 | 0.50 | 0.00 | 0.46 | 0.33 | 0.46 | 0.46 | 0.46 |
time (sec) |
N/A | 0.648 | 0.033 | 0.224 | 0.000 | 0.063 | 0.043 | 0.110 | 0.211 | 1.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 29 | 35 | 52 | 72 | 26 | 91 | 100 | 91 |
N.S. |
1 | 0.00 | 0.91 | 1.09 | 1.62 | 2.25 | 0.81 | 2.84 | 3.12 | 2.84 |
time (sec) |
N/A | 0.000 | 0.108 | 1.303 | 0.249 | 0.074 | 0.214 | 0.162 | 0.191 | 2.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 40 | 51 | 44 | 42 | 0 | 74 | 47 |
N.S. |
1 | 0.00 | 1.00 | 1.54 | 1.96 | 1.69 | 1.62 | 0.00 | 2.85 | 1.81 |
time (sec) |
N/A | 0.000 | 0.103 | 1.233 | 0.156 | 0.072 | 0.143 | 0.000 | 0.184 | 1.948 |
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 | 22 | 23 | 22 | 22 | 27 | 22 | 26 | 22 |
N.S. |
1 | 0.00 | 0.88 | 0.92 | 0.88 | 0.88 | 1.08 | 0.88 | 1.04 | 0.88 |
time (sec) |
N/A | 0.000 | 0.306 | 0.512 | 0.147 | 0.073 | 0.091 | 0.109 | 0.187 | 1.892 |
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 | 33 | 0 | 30 | 29 | 698 | 42 | 26 | 0 | 54 | 28 |
N.S. |
1 | 0.00 | 0.91 | 0.88 | 21.15 | 1.27 | 0.79 | 0.00 | 1.64 | 0.85 |
time (sec) |
N/A | 0.000 | 0.484 | 0.887 | 0.182 | 0.074 | 0.136 | 0.000 | 0.198 | 2.485 |
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 | 38 | 38 | 32 | 52 | 35 | 22 | 29 | 35 | 31 |
N.S. |
1 | 1.36 | 1.36 | 1.14 | 1.86 | 1.25 | 0.79 | 1.04 | 1.25 | 1.11 |
time (sec) |
N/A | 0.528 | 0.109 | 0.402 | 0.061 | 0.070 | 0.068 | 0.113 | 0.225 | 1.856 |
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 | 21 | 38 | 23 | 21 | 107 | 30 | 17 | 33 | 38 | 20 |
N.S. |
1 | 1.81 | 1.10 | 1.00 | 5.10 | 1.43 | 0.81 | 1.57 | 1.81 | 0.95 |
time (sec) |
N/A | 0.415 | 0.103 | 0.327 | 0.117 | 0.067 | 0.067 | 0.116 | 0.204 | 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 | 18 | 0 | 18 | 19 | 17 | 17 | 15 | 17 | 18 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 0.94 | 0.94 | 0.83 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.054 | 1.281 | 0.053 | 0.065 | 0.079 | 0.113 | 0.197 | 4.971 |
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 | 13 | 17 | 12 | 11 | 11 | 11 | 10 | 11 | 10 | 10 |
N.S. |
1 | 1.31 | 0.92 | 0.85 | 0.85 | 0.85 | 0.77 | 0.85 | 0.77 | 0.77 |
time (sec) |
N/A | 0.214 | 0.000 | 0.059 | 0.031 | 0.053 | 0.016 | 0.115 | 0.181 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | C | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 76 | 80 | 47 | 20 | 50 | 50 | 37 |
N.S. |
1 | 0.00 | 0.96 | 2.92 | 3.08 | 1.81 | 0.77 | 1.92 | 1.92 | 1.42 |
time (sec) |
N/A | 0.000 | 0.068 | 288.328 | 0.075 | 0.075 | 0.096 | 0.207 | 0.188 | 2.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 24 | 23 | 0 | 28 | 26 | 22 | 76 | 23 |
N.S. |
1 | 0.96 | 0.86 | 0.82 | 0.00 | 1.00 | 0.93 | 0.79 | 2.71 | 0.82 |
time (sec) |
N/A | 1.175 | 4.540 | 6.569 | 0.000 | 0.072 | 0.221 | 0.145 | 71.515 | 2.029 |
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 | 26 | 0 | 22 | 20 | 19 | 19 | 17 | 54 | 26 | 21 |
N.S. |
1 | 0.00 | 0.85 | 0.77 | 0.73 | 0.73 | 0.65 | 2.08 | 1.00 | 0.81 |
time (sec) |
N/A | 0.000 | 0.756 | 0.428 | 0.074 | 0.068 | 0.284 | 0.190 | 0.240 | 2.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 50 | 0 | 48 | 0 | 119 | 39 | 145 |
N.S. |
1 | 0.00 | 0.93 | 1.79 | 0.00 | 1.71 | 0.00 | 4.25 | 1.39 | 5.18 |
time (sec) |
N/A | 0.000 | 0.039 | 4.392 | 0.000 | 0.071 | 0.000 | 0.135 | 0.211 | 2.151 |
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 | 21 | 21 | 26 | 26 | 22 | 26 | 40 | 29 |
N.S. |
1 | 0.00 | 0.78 | 0.78 | 0.96 | 0.96 | 0.81 | 0.96 | 1.48 | 1.07 |
time (sec) |
N/A | 0.000 | 2.397 | 0.217 | 0.087 | 0.065 | 0.088 | 0.132 | 0.767 | 1.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 28 | 14 | 14 | 13 | 15 | 14 | 13 | 14 | 17 |
N.S. |
1 | 1.87 | 0.93 | 0.93 | 0.87 | 1.00 | 0.93 | 0.87 | 0.93 | 1.13 |
time (sec) |
N/A | 0.208 | 0.035 | 0.099 | 0.038 | 0.065 | 0.062 | 0.103 | 0.189 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | B | A | A | B | B | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 1299 | 1485 | 32 | 82 | 30 | 29 | 64 | 32 | 32 |
N.S. |
1 | 72.17 | 82.50 | 1.78 | 4.56 | 1.67 | 1.61 | 3.56 | 1.78 | 1.78 |
time (sec) |
N/A | 3.862 | 0.396 | 0.515 | 0.111 | 0.074 | 0.128 | 0.152 | 0.205 | 5.014 |
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 | 20 | 25 | 21 | 23 | 27 | 28 | 26 | 23 | 31 | 23 |
N.S. |
1 | 1.25 | 1.05 | 1.15 | 1.35 | 1.40 | 1.30 | 1.15 | 1.55 | 1.15 |
time (sec) |
N/A | 0.220 | 0.010 | 0.145 | 0.030 | 0.059 | 0.122 | 0.111 | 0.198 | 1.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 27 | 27 | 22 | 23 | 23 | 26 | 0 | 30 | 24 |
N.S. |
1 | 0.87 | 0.87 | 0.71 | 0.74 | 0.74 | 0.84 | 0.00 | 0.97 | 0.77 |
time (sec) |
N/A | 0.470 | 5.064 | 0.531 | 0.118 | 0.067 | 0.480 | 0.000 | 0.210 | 1.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 30 | 41 | 0 | 96 | 39 | 92 | 47 | 40 |
N.S. |
1 | 0.00 | 0.94 | 1.28 | 0.00 | 3.00 | 1.22 | 2.88 | 1.47 | 1.25 |
time (sec) |
N/A | 0.000 | 5.036 | 0.562 | 0.000 | 0.076 | 0.105 | 0.119 | 0.302 | 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 | 37 | 0 | 32 | 28 | 32 | 31 | 26 | 29 | 30 | 31 |
N.S. |
1 | 0.00 | 0.86 | 0.76 | 0.86 | 0.84 | 0.70 | 0.78 | 0.81 | 0.84 |
time (sec) |
N/A | 0.000 | 0.349 | 0.290 | 0.068 | 0.075 | 0.174 | 0.126 | 0.201 | 2.085 |
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 | 22 | 3 | 3 | 4 | 3 | 3 | 3 | 4 | 3 | 3 |
N.S. |
1 | 0.14 | 0.14 | 0.18 | 0.14 | 0.14 | 0.14 | 0.18 | 0.14 | 0.14 |
time (sec) |
N/A | 0.211 | 0.001 | 0.057 | 0.026 | 0.063 | 0.040 | 0.106 | 0.193 | 1.697 |
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 | 23 | 23 | 21 | 20 | 24 | 19 | 21 | 23 | 20 |
N.S. |
1 | 0.85 | 0.85 | 0.78 | 0.74 | 0.89 | 0.70 | 0.78 | 0.85 | 0.74 |
time (sec) |
N/A | 0.233 | 0.005 | 0.088 | 0.025 | 0.064 | 0.046 | 0.114 | 0.218 | 1.746 |
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 | 33 | 0 | 32 | 130 | 436 | 200 | 369 | 0 | 286 | 316 |
N.S. |
1 | 0.00 | 0.97 | 3.94 | 13.21 | 6.06 | 11.18 | 0.00 | 8.67 | 9.58 |
time (sec) |
N/A | 0.000 | 0.107 | 0.173 | 0.123 | 0.078 | 0.462 | 0.000 | 0.208 | 2.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 145 | 15 | 14 | 21 | 13 | 12 | 13 | 13 | 13 |
N.S. |
1 | 6.30 | 0.65 | 0.61 | 0.91 | 0.57 | 0.52 | 0.57 | 0.57 | 0.57 |
time (sec) |
N/A | 0.994 | 0.018 | 0.085 | 0.071 | 0.068 | 0.050 | 0.120 | 0.194 | 1.898 |
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 | 39 | 25 | 29 | 30 | 28 | 24 | 30 | 37 | 21 |
N.S. |
1 | 1.30 | 0.83 | 0.97 | 1.00 | 0.93 | 0.80 | 1.00 | 1.23 | 0.70 |
time (sec) |
N/A | 0.517 | 0.187 | 0.365 | 0.111 | 0.080 | 0.134 | 0.120 | 0.208 | 1.934 |
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 | 24 | 22 | 17 | 16 | 22 | 14 | 20 | 32 | 18 |
N.S. |
1 | 0.86 | 0.79 | 0.61 | 0.57 | 0.79 | 0.50 | 0.71 | 1.14 | 0.64 |
time (sec) |
N/A | 0.292 | 0.007 | 0.062 | 0.024 | 0.057 | 0.046 | 0.112 | 0.214 | 0.058 |
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 | 13 | 13 | 13 | 11 | 14 | 12 | 14 | 17 | 11 |
N.S. |
1 | 0.93 | 0.93 | 0.93 | 0.79 | 1.00 | 0.86 | 1.00 | 1.21 | 0.79 |
time (sec) |
N/A | 0.547 | 0.048 | 0.359 | 0.200 | 0.076 | 0.744 | 0.111 | 0.200 | 1.886 |
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 | 14 | 14 | 13 | 12 | 16 | 15 | 14 | 14 | 14 |
N.S. |
1 | 0.82 | 0.82 | 0.76 | 0.71 | 0.94 | 0.88 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.566 | 0.069 | 0.279 | 0.070 | 0.070 | 0.072 | 0.115 | 0.209 | 1.943 |
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 | 42 | 32 | 39 | 39 | 26 | 36 | 38 | 36 |
N.S. |
1 | 0.00 | 1.35 | 1.03 | 1.26 | 1.26 | 0.84 | 1.16 | 1.23 | 1.16 |
time (sec) |
N/A | 0.000 | 6.601 | 0.184 | 0.088 | 0.071 | 0.187 | 0.116 | 0.244 | 1.970 |
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 | 16 | 15 | 14 | 14 | 12 | 14 | 16 | 14 |
N.S. |
1 | 0.00 | 0.84 | 0.79 | 0.74 | 0.74 | 0.63 | 0.74 | 0.84 | 0.74 |
time (sec) |
N/A | 0.000 | 0.114 | 0.116 | 0.078 | 0.072 | 0.097 | 0.116 | 0.199 | 1.827 |
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 | 26 | 24 | 20 | 20 | 60 | 25 | 15 | 25 | 28 | 27 |
N.S. |
1 | 0.92 | 0.77 | 0.77 | 2.31 | 0.96 | 0.58 | 0.96 | 1.08 | 1.04 |
time (sec) |
N/A | 1.241 | 0.161 | 0.490 | 0.114 | 0.067 | 0.080 | 0.127 | 0.210 | 1.950 |
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 | 24 | 0 | 23 | 22 | 27 | 46 | 19 | 0 | 33 | 21 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 1.12 | 1.92 | 0.79 | 0.00 | 1.38 | 0.88 |
time (sec) |
N/A | 0.000 | 0.161 | 1.198 | 0.098 | 0.074 | 0.175 | 0.000 | 0.222 | 1.892 |
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 | 35 | 0 | 53 | 133 | 117 | 120 | 129 | 0 | 154 | 49 |
N.S. |
1 | 0.00 | 1.51 | 3.80 | 3.34 | 3.43 | 3.69 | 0.00 | 4.40 | 1.40 |
time (sec) |
N/A | 0.000 | 0.082 | 2.629 | 0.221 | 0.073 | 0.264 | 0.000 | 0.227 | 2.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 188 | 26 | 33 | 0 | 41 | 32 | 43 | 47 | 0 |
N.S. |
1 | 8.17 | 1.13 | 1.43 | 0.00 | 1.78 | 1.39 | 1.87 | 2.04 | 0.00 |
time (sec) |
N/A | 0.729 | 0.191 | 4.841 | 0.000 | 0.072 | 0.125 | 0.118 | 0.210 | 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 | 23 | 23 | 23 | 23 | 0 | 31 | 20 | 23 | 23 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 1.35 | 0.87 | 1.00 | 1.00 | 0.96 |
time (sec) |
N/A | 2.461 | 0.086 | 178.938 | 0.000 | 0.078 | 0.947 | 0.169 | 0.201 | 2.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | F | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 114 | 45 | 87 | 70 | 60 | 0 | 381 | 0 |
N.S. |
1 | 0.00 | 3.93 | 1.55 | 3.00 | 2.41 | 2.07 | 0.00 | 13.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.115 | 5.092 | 0.195 | 0.072 | 0.289 | 0.000 | 0.238 | 0.000 |