def THRESHOLD: Double = 0.0001

def sqr(x: Double): Double = x * x

def sqrt_stream(value: Double): LazyList[Double] = {
  def helper(target: Double, approx: Double): LazyList[Double] = {
    approx #:: helper(target, approx - (sqr(approx) - target) / (2 * approx))
  }
  helper(value, value)
}

sqrt_stream(2).take(10).toList

def threshold(list: LazyList[Double], thresh: Double) = {
  list.zip(list.drop(1)).filter(p => math.abs(p._2 - p._1) < thresh).head._2
}

threshold(sqrt_stream(2), 1e-15)