Counting operations instead of degree in polynomial approximation

A famous problem in approximation theory is to approximate the function \left|x\right| as accurately as possible on the interval -1 \le x \le 1 , measured by maximum absolute error, using either polynomials or rational functions of fixed degree. Perhaps it seems silly to approximate a function as simple as this, but it serves as a useful test problem for probing how well non-smooth functions can…