Trefethen Function

Here we consider the Trefethen function from the Problem 4 of the 100 Digit challenge.

\[f(x, y) = \exp(\sin(50 x)) + \sin(60 \exp(y)) + \sin(70 \sin(x)) + \sin(\sin(80 y)) - \sin(10 (x + y)) + (x^2 + y^2) / 4\]

This function has about \(2720\) critical points in \([-1, 1]^2\), which is slightly too much for us, at least for the moment, hence we subdivide the domain.

Here is the output of the critical points we are able to compute on the domain \([-.2, .2]^2\) with a polynomial approximant of degree 25.