JavaScript 2D distance in the usual way and a faster approximation

fast_distance.js

// Usual function
function distance(p1,p2){
	var dx = p2.x-p1.x;
	var dy = p2.y-p1.y;
	return Math.sqrt(dx*dx + dy*dy);
}
// Faster approximation
function distanceApprox(p1,p2){
	// Approximation by using octagons approach
	var x = p2.x-p1.x;
	var y = p2.y-p1.y;
	return 1.426776695*Math.min(0.7071067812*(Math.abs(x)+Math.abs(y)), Math.max (Math.abs(x), Math.abs(y)));	
}

Update: The "faster" approximation is actually slower: https://jsperf.com/js-distance/

I'll investigate and write a blog post on this.