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If you use memoization, your algorithm will have $O(n^2)$ running time, instead of $O(2^n)$ running time. See also https://en.wikipedia.org/wiki/Numerical_differentiation#Higher_derivatives. You might check the value of $dx$ you are using (see https://en.wikipedia.org/wiki/Numerical_differentiation#Step_size); and check whether you are experiencing ...


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