use core::quantities

@name("Numerical differentiation")
@url("https://en.wikipedia.org/wiki/Numerical_differentiation")
@description("Compute the numerical derivative of the function $f$ at point $x$ using the central difference method.")
@example("fn polynomial(x) = x² - x - 1\ndiff(polynomial, 1)", "Compute the derivative of $f(x) = x² -x -1$ at $x=1$.")
@example("fn distance(t) = 0.5 g0 t²\nfn velocity(t) = diff(distance, t)\nvelocity(2 s)", "Compute the free fall velocity after $t=2 s$.")
fn diff<X: Dim, Y: Dim>(f: Fn[(X) -> Y], x: X) -> Y / X =
  (f(x + Δx) - f(x - Δx)) / 2 Δx
  where
    Δx = 1e-10 × unit_of(x)