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In the real world rarely a problem can be solved using just a single algorithm, more often a solution is a chain of algorithms where the output of the former is the input for the follower.
|Polynomial approximation: here the convergence required six monomials and 70.000 iterations.
The final results has obtained via "fine-tuning" and it took 5000 iterations.
(In red the original function, in orange the approximation)