Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be a differentiable function with $f ( 0 ) = 1$ and satisfying the equation
$$f ( x + y ) = f ( x ) f ^ { \prime } ( y ) + f ^ { \prime } ( x ) f ( y ) \text { for all } x , y \in \mathbb { R }$$
Then, the value of $\log _ { e } ( f ( 4 ) )$ is $\_\_\_\_$ .