FP Division by constant is optimized by a compiler into a multiply. Graphics processing typically happens on the GPU these days, and on all recent GPUs FPMUL belongs to the class of lowest-latency operations. That is, there are no other instructions that complete faster.
Only with things like -ffast-math enabled will compilers do the reciprocal. It can make a fair difference in some cases, but it's often better to selectively use it in code locations you know are acceptable by doing it manually in the code.
That's only valid to do if the reciprocal is representable exactly.
That's not totally true. It's sufficient to be exactly representable, but you only need the reciprocal rounding error to be small enough to guarantee the multiplication rounding step fixes it across the entire range of numerators. For IEEE754 f16 values, there are 28 such extra values, the positive and negative sides of 1705/x where x is a power of 2 at least as great as 2048.