$\newcommand{\cost}{\operatorname{cost}}$My cost-metric is in following form
\begin{equation} \cost(x,y) = A(x,y_1) \times \sum_{i}b_i B_i(x,y_i)\tag{1} \end{equation}
where $A$ and $B$'s follow normal distribution. For my computer implementation, I am thinking of taking $\log(\cdot)$ to avoid computing exponential. By taking log of (1), I get
\begin{equation} \log(\cost(x,y)) = \log(A(x,y_1)) + \log\left(\sum_i b_i B_i(x,y_i)\right) \end{equation}
which simplifies first term but second term remains unchanged. Can I bring $\log(\cdot)$ inside the summation?
