cubic.js

http://jsfiddle.net/rjxh7h0y/1/

// https://github.com/arian/cubic-bezier

var bezier = function(x1, y1, x2, y2, epsilon){

	var curveX = function(t){
		var v = 1 - t;
		return 3 * v * v * t * x1 + 3 * v * t * t * x2 + t * t * t;
	};

	var curveY = function(t){
		var v = 1 - t;
		return 3 * v * v * t * y1 + 3 * v * t * t * y2 + t * t * t;
	};

	var derivativeCurveX = function(t){
		var v = 1 - t;
		return 3 * (2 * (t - 1) * t + v * v) * x1 + 3 * (- t * t * t + 2 * v * t) * x2;
	};

	return function(t){

		var x = t, t0, t1, t2, x2, d2, i;

		// First try a few iterations of Newton's method -- normally very fast.
		for (t2 = x, i = 0; i < 8; i++){
			x2 = curveX(t2) - x;
			if (Math.abs(x2) < epsilon) return curveY(t2);
			d2 = derivativeCurveX(t2);
			if (Math.abs(d2) < 1e-6) break;
			t2 = t2 - x2 / d2;
		}

		t0 = 0, t1 = 1, t2 = x;

		if (t2 < t0) return curveY(t0);
		if (t2 > t1) return curveY(t1);

		// Fallback to the bisection method for reliability.
		while (t0 < t1){
			x2 = curveX(t2);
			if (Math.abs(x2 - x) < epsilon) return curveY(t2);
			if (x > x2) t0 = t2;
			else t1 = t2;
			t2 = (t1 - t0) * .5 + t0;
		}

		// Failure
		return curveY(t2);

	};
};
var duration = 200;
    var epsilon = (1000 / 60 / duration) / 4;
    var timingFunction = bezier(0.2, 0.9, 0.3, 0.4, epsilon);
    
   console.log(  timingFunction(0.01) );