I'm implementing the Finite Different 2nd and 3rd derivatives in my research and naturally I'm looking for the most efficient approach.
From https://en.wikipedia.org/wiki/Finite_difference#cite_ref-WilmottHowison1995_1-0 I found a more efficient formula that takes 2 function evaluations out of the picture. But I'm not sure what simplification or substitution was implemented. Can anyone help me out? See the Image below.