Communicating mental math

Through introspection, can we communicate how we solve math problems in our own minds? Here's an attempt for a simple procedure. Allowing $$=$$ to denote assignment, this is how I would find the distance between two coordinates in my head.

\begin{align} & a = x_2 - x_1 \\[0.5em] & b = a^2 \\[0.5em] & c = y_2 - y_1 \\[0.5em] & d = c^2 \\[0.5em] & e = b + d \\[0.5em] & \sqrt{e} \end{align}

Notice that I am only holding two variables in my head at any given time. Because the procedure is constant, and I have practiced it often enough, I can recall it easily.