You are given an initial integer and a target integer. You may change the initial number by doing any of the operations $+2, -2, \times 2, \div 2$, any number of times in any order, to get the target number. For example, from $16$ to $40$, you may do $+2, +2, +2, +2, +2, +2, +2, +2, +2, +2, +2, +2$, or $\div 2, \div 2, +2, +2, +2, \times 2, \times 2$. The only restriction is that no intermediate operation may result on a fraction.
Is there a feasible algorithm (say, it takes $O(n \log n)$ time for a maximum absolute input of $n$) to find the shortest solution for a given pair of integers?