I have been doing a lot of procedural animation, lately. Making a humanoid walk, and swing a torch at spiders.
I also needed a proper way to catch a fall, with the legs. Because I already had the Inverse Kinematics sorted, I just needed to shift the pelvis down, and up, after a fall.
To do this convincingly, I need to drop down hard at the start, then ease at the nadir, and ease again on the way back to the zenith. For this, piecewise functions come to the rescue. I ended up using this: