Compiling an assignment of a symbolic expression to a name will not make
it run faster.
You can compile a function this way:
f (x) := (1/2)*exp(-(1/4)*(sqrt(k[1]^2+k[2]^2+k[3]^2)-m)^2 / (sigma))
/ (Pi^(3/2));
compile(f);
You don't need a separate file, a special command to compile files, a
separate "compile-time"
operation, etc. The compiler is there all the time.
You might mean %pi instead of Pi, by the way.
RJF