Safe bisection algorithm in Haskell.

bisection.hs

bisection :: (Double -> Double) -> Double -> Double -> Double -> Maybe Double
bisection f a b err
  | err < 1e-15           = Nothing
  | abs (b - a) / 2 < err = Nothing
  | a < b                 = bis a b
  | otherwise             = bis b a
  where
    bis a b
      | d < err || f m == 0.0 = Just m
      | f a * f m < 0.0       = bis a m
      | f m * f b < 0.0       = bis m b
      | otherwise             = Nothing
      where
        d = (b - a) / 2
        m = (b + a) / 2

I prefer to explicitly type it to ensure precision is high enough.