Translate KeyFrameEasing to Cubic Beziers

Hi. I am a seasoned developer (20+ years) and experienced Adobe CEP developer (3-4 years) but I am new to After Effects. In addition to development I've been a digital illustrator for 30 years but I have never used After Effects (Just some background for context).

I am building an extension for AE for a client to export keyframes as JSON. I have everything working the way the client wants but they need the keyframe easings expressed in cubic beziers instead of AE's format (speed & influence). I'm afraid it has been a long, long time since I've done any trig or calculous so I have forgotten most of it.

I found a snippet of code by Hernan Torrissi, the author of the wonderful Bodymovin' extension dated 2015. In the original post Hernan says that he had not, at that point, figured out how to do the calculations. I have tried the code he shared but I don't know if it is working correctly or not since this is not my area of expertise.

What I'm looking for is help from other devs (or perhaps from Hernan himself) to better understand the underly concepts  & maths, validation whether or not the results are correct (I don't believe they are), and help figuring it out. 

Yes, I'm aware I'm asking for a lot and I apologize. I will do whatever leg work needs to be done to make this easier but since I'm a bit out of my depth with AE I will need a little bit (a lot?) of hand-holding. I'm not looking for "something-for-nothing" or for someone to do it for me. I sincerely need some help figuring it out. So thanks in advance for not giving me too hard a time if I'm not following protocol for asking for help.

Here is the code from Hernan (cleaned up a bit to match my coding style):

var EasingToCubicBezier = function(property) {

    var curves = [];

    for (var i = 1; i < property.numKeys; i++) {

        var x1 = 0,
            x2 = 0,
            y1 = 0,
            y2 = 0,

            /*
             * Key times
             */

            t1 = property.keyTime(i),
            t2 = property.keyTime(i + 1),

            /*
             * Key Values
             */

            val1 = property.keyValue(i),
            val2 = property.keyValue(i + 1),

            /*
             * Speed
             */

            avSpeed = Math.abs(val2 * val1) / (t2 * t1),

            /*
             * easeIn & easeOut for current keyFrame & next keyFrame
             */

            k1in  = property.keyInTemporalEase(i)[0],
            k1out = property.keyOutTemporalEase(i)[0],
            k2in  = property.keyInTemporalEase(i + 1)[0],
            k2out = property.keyOutTemporalEase(i + 1)[0],

            /*
             * Max & min values
             */

            max = property.maxValue,
            min = property.minValue;

        /*
         * Perform calculations.
         */

        if ( val1 < val2) {
            x1 = k1in.influence / 100;
            y1 = x1 * k1out.speed / avSpeed;

            x2 = 1 * k2in.influence / 100;
            y2 = 1 - (1 * x2) * (k2in.speed / avSpeed);
        }

        if ( val2 < val1) {
            x1 = k1out.influence / 100;
            y1 = (-x1) * k1out.speed / avSpeed;
            x2 = k2in.influence / 100;
            y2 = 1 * x2 * (k2in.speed / avSpeed);
            x2 = 1 * x2;
        }

        if (val1 === val2) {
            x1 = k1out.influence / 100;
            y1 = (-x1) * k1out.speed / ((max * min)/(t2 * t1)) ;
            x2 = k2in.influence / 100;
            y2 = 1 * x2 * (k2in.speed / ((max * min)/(t2 * t1)));
            x2 = 1 * x2;
        }

        curves.push([ x1, y1, x2, y2 ]);
    }

    return {
        getCurves : function() {
            return curves;
        }
    }
}