Cube root in Haskell

Cbrt.hs

--{-# LANGUAGE TemplateHaskell #-}
--import Test.QuickCheck
--import Test.QuickCheck.All

--prop_cbrt :: Double -> Bool
--prop_cbrt x = abs (x - cbrt x ^ 3) < 1e-12

--main = ($quickCheckAll)

module Cbrt (cbrt) where

--Newton's iteration.
newton :: Fractional a => (a -> a) -> (a -> a) -> a -> [a]
newton f f' x0 = iterate (\x -> x - f x / f' x) x0

--Assuming that a sequence of is converging to a fixed value, 
--take the first value that fails to improve in precision.
converge :: [Double] -> Double
converge xs = snd . head $ dropWhile ((< 0) . fst) $ zip deltaDeltas xs where
    deltaDeltas = zipWith (-) (tail deltas) deltas
    deltas = map abs $ zipWith (-) (tail xs) xs

--Alternative implementation
converge' :: [Double] -> Double
converge' (x0:x1:x2:xs) = if (change >= lastChange) then x2 else converge' (x1:x2:xs) where
    change     = abs (x2 - x1)
    lastChange = abs (x1 - x0)

--Given y find x such that x^3 == y using Newton's method.
cbrt' :: Double -> Double
cbrt' y = converge $ newton (\x -> x*x*x - y) (\x -> 3 * x*x) y

--Find the cube root of x.
cbrt :: Double -> Double
cbrt 0 = 0
cbrt x = if (abs x > 0.01)
            then cbrt' x
            else (1/) $ cbrt' (1 / x)