If you have access to modern processors (CPUs, GPUs) then a lookup table makes no sense. The polynomial is faster, more accurate, and needs less space to store precomputed values.
As an example, the LUT will get you in the ballpark of the answer, and then you compute a polynomial to calculate the delta and add the two together.
You can always find a polynomial that is extremely accurate, but it likely will be higher order, etc. A LUT + polynomial is faster. A pure LUT is the fastest, but takes too much memory.
Would be interesting to see benchmarks. On to my list of things I have a low chance of completing...