gistfile1.txt

// (Math.exp(704.6589) / Math.expm1(704.6589) - 1) / Number.EPSILON
var isExpOK = Math.exp(704.6589) >= 1.0702171200481775e+306 * (1 - 16 * Math.pow(2, -52)) && 
              Math.exp(704.6589) <= 1.0702171200481775e+306 * (1 + 16 * Math.pow(2, -52));
// (Math.exp(704.6589) / Math.expm1(704.6589) - 1) / Number.EPSILON
var isExpOK = Math.exp(704.6589) >= 1.0702171200481775e+306 * (1 - 16 * Math.pow(2, -52)) && 
              Math.exp(704.6589) <= 1.0702171200481775e+306 * (1 + 16 * Math.pow(2, -52));
Math.exp = function (x) {
  var hi = 0.6931471805598903;
  var lo = 5.497923018708371e-14;
  var k = Math.floor(x / hi + 0.5);
  var t = Math.pow(2, k);
  var k2 = 0;
  if (t === 0) {
    k2 -= 1;
  }
  if (t === Infinity) {
    k2 += 1;
  }
  t = Math.pow(2, k - k2);
  if (t === 0 || t === Infinity) {
    return t;
  }
  var r = x - k * hi - k * lo;
  return (Math.expm1(r) + 1) * t * Math.pow(2, k2);
};
// 709.4758600739439

var test2 = function (v) {
  console.log((Math.exp(v)/nativeExp(v) - 1)/Number.EPSILON);
};
var test = function (v) {
  test2(v * (1 - Math.floor(4) * Number.EPSILON));
  test2(v);
  test2(v * (1 + Math.floor(4) * Number.EPSILON));
};
test(708);
test(-708);


Math.sqrt = function (value) {
  if (value < 0) {
    return NaN;
  }
  if (value === 0) {
    return value;
  }
  if (value === Infinity) {
    return Infinity;
  }
  var abs = Math.abs(value);
  var result = Math.exp(Math.log(abs) / 2);
  result = (abs / result + result) / 2;
  return result;
};