An attempt to calculate Ackermann in Scala... It keeps overflowing the stack near Ack(3,11)

ackermann.scala

package io.wausoft

import org.joda.time.{Seconds, DateTime}
import scala.collection.mutable

case class Ack(m: Int, n: Int)

object Program extends App {
  // Basic ackermann without cache, overflows at around Ack(3,11) after a few seconds
  def compute(a: Ack): Int = a match {
    case Ack(0, n) => n + 1
    case Ack(m, 0) => compute(Ack(m - 1, 1))
    case Ack(m, n) => compute(Ack(m - 1, compute(Ack(m, n - 1))))
  }

  // ackermann with cache, overflows at around Ack(3,11) instantly
  def computeWithCache(a: Ack, cache: mutable.Map[Ack, Int]): Int = if(cache contains a) {
    val res = cache(a)
    println(s"result from cache: $res")
    return res // explicit 'return' for readability
  } else {
    val res = a match {
      case Ack(0, n) => n + 1
      case Ack(m, 0) => computeWithCache(Ack(m - 1, 1), cache)
      case Ack(m, n) => computeWithCache(Ack(m - 1, computeWithCache(Ack(m, n - 1), cache)), cache)
    }
    cache += a -> res
    return res
  }

  // convenience method
  def getSeconds(start: DateTime, end: DateTime): Int = Seconds.secondsBetween(start, end).getSeconds

  val time = DateTime.now
  val cache = mutable.Map[Ack, Int]()

  for{ i <- 0 to 4
       j <- 0 until 20
  } println(s"result of ackermann($i, $j) => ${computeWithCache(Ack(i, j), cache)}. Time: ${getSeconds(time, DateTime.now)}")
}

build.sbt

name := "Ackermann"

version := "1.0"

libraryDependencies ++= Seq( "joda-time" % "joda-time"    % "2.3"
                           , "org.joda"  % "joda-convert" % "1.6"
                           )