The easing equations are great, but they can't be editable. What is the best thing about them: the user doesn't need to worry about the animation if some point change its location.
But there is an aspect of easing equations that still can be improved. They don't follow the normal of the curve. In an animation, this mean that they can break any previous movement of a object, instead of starting from it.
Currently, this is what happen if we change the bezier control point of the start point of an easing equation Cubic In:
For Bounce In:
You can see how the animation break when the easing start, because the first internal point of the easing curve doesn't follow the previous curve normal.
The proposed solution
To solve it, the first internal control point of an easing equation should be placed above the curve normal. This is what would be expected for Cubic:
An example of how this issue can break an animation is if we nest 2 easing equations, for instance a Back In followed by a Bounce Out. easing-back-in-bounce-out.blend
I'm not sure it's applicable to all easing modes. But it should be the default behaviour for those that it's applicable. I believe an option to disable it would be useless, since its easy to control the control point handler to get the the horizontal normal. And these options are actually new, so I would not be worried about breaking backward compatibility for the previous easing curves that will change now with follow normal by default.
The most important thing about the easing equation is that they allow easy, smooth and automatic animations. So I think the change proposed here is looking to allow it in a more complete way.