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) < 0.001 * 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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