math.r3

REBOL []

math: context [
	eps: 1E-15
	
	steps: 0
	
	math-init: func [] [
		steps: 0
	]
	
	derive: func [
		f [function!]
		x [decimal!]
		/local d1 d2 d3 d4
	] [
		d1: negate f x + (2 * eps)
		d2: 8 * (f x + eps)
		d3: -8 * (f x - eps)
		d4: f x - (2 * eps)
		(d1 + d2 + d3 + d4) / (12 * eps)
	]
	
	newton: func [
		f     [function!]
		guess [decimal!]
		/local x
	] [
		math-init
		x: guess
		until [
			steps: steps + 1
			x: x - ((f x) / (derive :f x))
			(abs f x) < eps
		]
		x
	]
]