Parse Expression

var fSegmentNoBrackets = sExpression => {
  var aValues = [];
  var sRemainder = String(sExpression).replace(/\s+/g,'').replace(/([\+\-\*\/])([^\+\-\*\/]+)/g,(match,sign,val) => {
    aValues.push({
      sign: sign,
      val: val,
      exp: val,
    });
    return '';
  });

  if (sRemainder) {
    throw new Error(`Unexpected ${sRemainder}`);
  }
  return aValues
};

var fSegmentExpression = sExpression => {
  var aValues = [];
  var aSegments = String(sExpression).replace(/\s+/g,'').split('(');
  var sPre = aSegments.shift();
  aSegments.forEach(sSegment => {
    sSegment = sPre + '(' + sSegment;
    var nOpenBrackets = (sSegment.match(/\(/g) || []).length;
    var nCloseBrackets = (sSegment.match(/\)/g) || []).length;
    if (nOpenBrackets > nCloseBrackets) {
      sPre = sSegment;
    } else if (nOpenBrackets < nCloseBrackets) {
      throw new Error(`More Close Brackets Than Open Brackets. ${sSegment}`);
    } else {
      var match = sSegment.match(/^([^\(]*)([\+\-\*\/])\((.+)\)/);
      if (match) {
        aValues.push(...fSegmentNoBrackets(match[1]),{
          sign: match[2],
          val: fSegmentNoBrackets(match[3]),
          exp: `(${match[3]})`,
        });
      } else {
        throw new Error(`Expected Sign Before Expression. Got ${sSegment}`);
      }

      sPre = (sSegment.match(/[^)]+$/) || [''])[0];
    }
  });

  if (sPre.match(/\(/)) {
    throw new Error(`More Open Brackets Than Open Brackets. ${sPre}`);
  }

  aValues.push(...fSegmentNoBrackets(sPre));

  return aValues;
};

var fGenerateOperation = (oExpression1,oExpression2) => {
  var oOperation = {
    sign: oExpression1.sign,
    operation: oExpression2.sign,
    val1: oExpression1.val && oExpression1.val.constructor === Array ? fFormatExpression(oExpression1.val) : oExpression1,
    val2: oExpression2.val && oExpression2.val.constructor === Array ? fFormatExpression(oExpression2.val) : oExpression2,
  };
  oOperation.exp = `(${oOperation.val1.exp}${oOperation.operation}${oOperation.val2.exp})`;

  if (oExpression2.sign !== '-') oExpression2.sign = '+';

  return oOperation;
};

var fFormatExpression = aExpressions => {
  if (aExpressions.constructor === Array) {
    [['^'],['*','/'],['+','-']].forEach(aSigns => {

      aExpressions.forEach((oExpression,i) => {
        while (aExpressions[i+1] && aSigns.indexOf(aExpressions[i+1].sign) > -1) {
          aExpressions[i] = fGenerateOperation(aExpressions[i],aExpressions[i+1]);
          aExpressions.splice(i+1,1);
        }
      });

    });
  }
  return aExpressions[0];
};

var main = sExpression => fFormatExpression(fSegmentExpression(sExpression));

/* ---------- EXAMPLE ---------- */
console.log(main('+1*(+2+1)'));