Ways to optimize the runtime of x86 assembly subroutine for collatz conjecture [duplicate]

I'm trying to optimize the runtime of the code that I wrote for computing the number of iterations it takes to reach 1 in the collatz conjecture

Here is my psudeocode for this

int threexplusone(int x){ if(x == 1){ return 0; }else{ if(x % 2 == 0){ return (threexplusone(x/2)+1); }else{ return (threexplusone(3*x+1)+1); } } } 

Here is my assembly code

threexplusone: push rbx ;store the rbx to stack mov rax, 0 ;store the base case cmp rdi, 1 ;compare the input with 1 je done ;finished the loop if equal to 1 jmp threexplusone_recursive ;jump to the recursion threexplusone_recursive: push rax mov rdx,0 mov rax,rdi mov rbx,2 idiv rbx cmp rdx, 0 ;compare to check if the remainder is 0 mov rbx, rax pop rax je even ;start the even instruction odd: imul rdi,3 ;multiply x by 3 add rdi, 1 ;add x by 1 xor rax, rax call threexplusone ;do the recursion inc rax ;add the result by one jmp done even: sar rdi,1 ;divided the input by 2 xor rax,rax call threexplusone ;do the recursion inc rax ;add the result by one jmp done ; ; done: pop rbx ret 

What could be the possible way of optimizing this code？ Thanks