object Main extends App {
  def sqrt(x: Double) = {
    def square(num: Double): Double =
      num * num
    def sqrtIter(guess: Double): Double = 
      if (isGoodEnough(guess)) guess 
      else sqrtIter(improve(guess))
    def improve(guess: Double) =
      (guess + x / guess) / 2
    def isGoodEnough(guess: Double) =
      math.abs(square(guess) - x) < 0.000000000000001 * x
    sqrtIter(1.0)
  }
  Seq(
    math.sqrt(2),
    sqrt(2),
    math.sqrt(0.001),
    math.sqrt(0.1e-20),
    math.sqrt(1.0e20),
    math.sqrt(1.0e50),
    sqrt(0.001),
    sqrt(0.1e-20),
    sqrt(1.0e20),
    sqrt(1.0e50)
  ).foreach(println)
}

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