Select ALL the following statements that are NOT a purpose function of the $C++$ compiler: $[5$ points$]$

$($a$)$ Translating $C++$ program source code into machine code $($assembly$).$

$($b$)$ Managing memory allocation during the execution of a $C++$ program.

$($c$)$ Identifying and reporting syntax errors in the $C++$ code.

$($d$)$ Optimizing the code for better performance during the compilation process.

$($e$)$ Converting machine code into high level pseudocode specific to the computer's architecture.