Here’s a relevant example: http://www.chebfun.org/examples/approx/EightShades.html http://www.chebfun.org/examples/approx/EightShades.html Here are the first

Here’s a relevant example: http://www.chebfun.org/examples/approx/EightShades.html http://www.chebfun.org/examples/approx/EightShades.html Here are the first 6 chapters of ATAP http://www.chebfun.org/ATAP/atap-first6chapters.pdf http://www.chebfun.org/ATAP/atap-first6chapters.pdf Also cf. https://people.maths.ox.ac.uk/trefethen/mythspaper.pdf https://people.maths.ox.ac.uk/trefethen/mythspaper.pdf * * * I’d say the bigger point is not about whether the error is marginally better or worse with a Chebyshev series vs. CF vs. Remez, etc., but rather that any of these will usually beat the others if you add just one more coefficient. Usually convergence speed matters more than picking a number of coefficients and then exactly optimizing to the last bit. And as you say, running the Remez algorithm is probably waste of time if you are trying to calculate a near-optimal approximation on the fly at runtime.