thanks for this:
Here is another one:
It takes scene-referred linear whatever 
and outputs display-referred linear whatever
It is already formulated so it can be directly applied to images and addresses the whole SDR/HDR problem space.
It is the most simple form I could think of, and it could be expressed in actual a single line instead of the two lines rendering code (which I added for readability).
Invertablitiy is trivial.
It is based around the Michaelis-Menten equation.
It has a gamma model for surround compensation as well,
If you look at it in desmos it does not look like a typical sigmoid, this is because Desmos does not have log ranging axis.