Very cool. The tinkerer in me wanted to see how quickly I could come up with a function that wouldn't be approximated well.
Math.cos(x * Math.exp(Math.cos(x * x))) is the best I got so far as it is highly composite, which leads to rapid oscillations and steep gradients that can't easily be approximated by Chebyshev.
Math.cos(x * Math.exp(Math.cos(x * x))) is the best I got so far as it is highly composite, which leads to rapid oscillations and steep gradients that can't easily be approximated by Chebyshev.