Here's an example NASM (x86-64) program that calculates the distance between two points using the given pseudo-code.
section .data
format db "%lf", 0 ; format specifier for scanf and printf
section .bss
x1 resq 1
x2 resq 1
y1 resq 1
y2 resq 1
v1 resq 1
v2 resq 1
section .text
extern sqrt, printf, scanf
global main
%macro GET 1
mov rdi, format
mov rsi, %1
call scanf
%endmacro
%macro ASSIGN 2
mov %1, %2
%endmacro
%macro SUB 2
mov rax, %1
sub rax, %2
mov %1, rax
%endmacro
%macro MULT 2
mov rax, %1
imul rax, %2
mov %1, rax
%endmacro
%macro ADD 2
mov rax, %1
add rax, %2
mov %1, rax
%endmacro
%macro SQRT 1
movsd xmm0, %1
call sqrt
movsd %1, xmm0
%endmacro
%macro PRINTSTR 1
mov rdi, format
mov rsi, %1
call printf
%endmacro
%macro PRINTINT 1
mov rdi, format
mov rax, %1
call printf
%endmacro
main