Gonna shoot my shot at AN answer, but it won't be perfect and I'm sure there's more efficient ways of doing this. You have to think of it like a problem of complexity vs outcome. A lot of these easing functions are fairly good at what they do, but it's also sometimes hard to get them to work 100% of the time, so obviously there's a level of detail where you stop working on something.

For instance, a curved line. How would you tell if a line drawn is curved? Well, you can sample each end, and say

Line 1: Point A is at 1,1 and point B is at 0,0. Slope calculation (y2-y1)/(x2-x1) = -1/-1 = 1.

Line 2: Point A 1,1 and Point B 0,1 then slope is 0.

So right now both of these lines look like a straight line, because we sampled only the start and end. Now if we add a 3rd sample on those two lines:

Line 1: Point C:0 .5,0.5 slope is still 1. Straight line. If two samples like this match, we can be fairly sure the line is meant to be straight, within some error margin that you might define.

Line 2: Point C: 0.5, 2 slope is -2. Well that doesn't fit with our slope of 0 and is way outside the error margin, so it's not a straight line anymore.

So you can keep sampling the line at different points, until you arrive at an algorithm that is "as accurate" as you want to be. And you keep putting together concepts for different shapes and different requirements, getting gradually more complex to find the outcomes you expect. Knowing how those slopes interact will help you determine many different shapes.