how many numbers can you create with five 2s?

gistfile1.txt

<script>

  function fac(num) {
    if(!Number.isInteger(num)) {
      return NaN;
    }
    if(num > 10) {
      return Infinity;
    }
    if (num === 0 || num === 1)
      return 1;
    for (var i = num - 1; i >= 1; i--) {
      num *= i;
    }
    return num;
  }
  function bnot(num) {
    return ~num
  }

  function add(a, b){ return a + b }
  add.print = (a, b) => "("+a+"+"+b+")";

  function sub(a, b){ return a - b }
  sub.print = (a, b) => "("+a+"-"+b+")";

  function mul(a, b){ return a * b };
  mul.print = (a, b) => "("+a+"*"+b+")";

  function div(a, b){ return a / b };
  div.print = (a, b) => "("+a+"/"+b+")";

  function band(a, b) { return a & b }
  band.print = (a, b) => "("+a+"&"+b+")";

  function mod(a, b) { return a % b };
  mod.print = (a, b) => "("+a+"%"+b+")";

  function pow(a, b) { return Math.pow(a, b) }
  pow.print = (a, b) => "("+a + "^"+ b+")"

  var operations = [
    add,sub,mul, div,
    // power
    pow,
    band,
    mod
  ];
  var unaryOperations = [
    {
      test: (value)=> Number.isInteger(value) && value < 5,
      operation: fac,
      print: (child) => "(!"+child+")"
    },
    {
      test: () => true,
      operation: bnot,
      print: (child) => "(~"+child+")"
    }
  ];
  function unaryAnswers(result) {
    return unaryOperations.filter(op => op.test(result.value))
    .map( (op) => {
      return {
        value: op.operation(result.value),
        equation: op.print(result.equation)
      }
    })
  }

  var cache = {};


  function answers(roots, parent){
    if(roots.length === 1) {
      return [{
        value: roots[0],
        equation: ""+roots[0]
      }]
    }
    if(cache[roots.join(",")]) {
      return cache[roots.join(",")];
    }

    var allResults =[];
    if(roots.length === 2) {
      for( let operation of operations) {

        var equation = operation.print( roots[0], roots[1] );

        var value = operation(roots[0], roots[1]);
        let result = {
          value: value,
          equation: equation
        };

        allResults.push(result);
        allResults.push(...unaryAnswers(result));

        // should we try factorial?

      }

    } else {
      console.log("calculating for", roots.length);
      for(let i = 1; i < roots.length; i++) {
        console.log(parent, roots.slice(0,i).length, roots.slice(i).length)
        var leftResults = answers( roots.slice(0,i), roots.length);
        var rightResults = answers( roots.slice(i), roots.length);
        // try every operation on left and right given every result

        for(let leftResult of leftResults) {
          for( let rightResult of rightResults) {
            for( let operation of operations) {

              var equation = operation.print(
                leftResult.equation , rightResult.equation);

              var value = operation(leftResult.value, rightResult.value);
              let result = {
                value: value,
                equation: equation
              };
              allResults.push(result);
              allResults.push(...unaryAnswers(result));
            }
          }
        }
      }
    }
    cache[roots.join(",")] = allResults;
    return allResults;
  }

  var grouped = {};


  answers([2,2,2,2, 2] ).forEach(function(answer){
    if(!grouped[answer.value]) {
      grouped[answer.value] = [];
    }
    grouped[answer.value].push(answer);
  })

  answers([22,2,2,2] ).forEach(function(answer){
    if(!grouped[answer.value]) {
      grouped[answer.value] = [];
    }
    grouped[answer.value].push(answer);
  })

  answers([2,2,2,22] ).forEach(function(answer){
    if(!grouped[answer.value]) {
      grouped[answer.value] = [];
    }
    grouped[answer.value].push(answer);
  })

  setTimeout(function(){

    answers([22,2,22] ).forEach(function(answer){
      if(!grouped[answer.value]) {
        grouped[answer.value] = [];
      }
      grouped[answer.value].push(answer);
    })



    answers([2, 22,22] ).forEach(function(answer){
      if(!grouped[answer.value]) {
        grouped[answer.value] = [];
      }
      grouped[answer.value].push(answer);
    })

    console.log(grouped);
    for(var i = 0; i < 200; i++) {
      if(!grouped[i]){
        console.log(i)
      }
    }

  },100)






</script>