Broken Calculator - Reverse Greedy

Work backwards: transform $Y$ to $X$. The reverse operations are halve (if even) or add $1$. Greedy: if $Y > X$ and $Y$ is even, halve it.

If $Y$ is odd, add $1$ (makes it even for halving).

If $Y \leq X$, just add $X - Y$. Halving is powerful: it reduces $Y$ quickly. Adding is cheap but slow. Prioritize halving when possible. Why this is optimal: halving reduces $Y$ by a factor of $2$, which is exponentially faster than adding $1$.

If $Y$ is odd, you must add $1$ to make it even before halving. Once $Y \leq X$, halving would undershoot, so you switch to adding the difference.