I am confused about why you need to think that certain operations are/are not expensive, or why you think a table is faster.
I think they are expensive, and it won't be faster. Hence we're at an impasse. That block was predictable, and easily solve by taking the equation you have and testing against the reference code.
If you test it out, you'll know the answer. There's no need to think you know the answer when you can just measure it, and overrule any incorrect beliefs I may have.
As I said, I don't have a table of how fast each operation is. I don't think any of my assumptions were unreasonable, but I did explicitly state they were assumptions. And I don't have any way of testing it.
I am interested in function approximation mainly for finding functions for when there is no closed form solution, not so much tiny optimization.
I think they are expensive, and it won't be faster. Hence we're at an impasse. That block was predictable, and easily solve by taking the equation you have and testing against the reference code.
If you test it out, you'll know the answer. There's no need to think you know the answer when you can just measure it, and overrule any incorrect beliefs I may have.