javascript - How does this recursion work?

Question

This is an example from Eloquent Javascript:

By starting from the number 1 and repeatedly either adding 5 or multiplying by 3, an infinite amount of new numbers can be produced. How would you write a function that, given a number, tries to find a sequence of additions and multiplications that produce that number?

I'm having trouble understanding how the recursion is working here, wondering if someone could write out a couple times how find is getting called or some other explanation.

function findSequence(goal) {
  function find(start, history) {
    if (start == goal)
      return history;
    else if (start > goal)
      return null;
    else
      return find(start + 5, "(" + history + " + 5)") ||
             find(start * 3, "(" + history + " * 3)");
  }
  return find(1, "1");
}

console.log(findSequence(24)); // => (((1 * 3) + 5) * 3)

Answer 1

The function runs a rather simple brute force search with backtracking: at each invocation level it tries adding 5 to the number, and see if starting from the resultant number gets you to the goal. If it does, the result is returned; otherwise, the number is multiplied by 3, and the search for the goal continues from that new number. As the recursion goes along, the textual representation of the expression producing the number is passed to the next invocation levels.

The search for 14 goes as follows:

(1,  "1")
(5,  "1+5")
(10, "(1+5)+5")
(15, "((1+5)+5)+5") <<= Fail
(30, "((1+5)+5)*3") <<= Fail
(15, "(1+5)*3") <<= Fail
(3,  "1*3")
(8,  "(1*3)+5")
(13, "((1*3)+5)+5")
(18, "(((1*3)+5)+5)+5") <<= Fail
(39, "(((1*3)+5)+5)*3") <<= Fail
(24,  "((1*3)+5)*3") <<= Fail
(9, "(1*3)*3")
(14, "((1*3)*3)+5) <<= Success!