This is a "diary" that records my thoughts when trying to debug the
forest manipulations.  Basically the forests are wrongly "merged", and
produce weird clones.

Right now I have finished refactoring most of the codes, but still
fail to perceive why the forests behave in that way.  I even finished
a proto-type of my procedural macros which help me reduce
boiler-plates but are not necessary.

Right now I think I need more refined control over the details of the
forests manipulations.  To be more precise, I need to be able to
observe, step by step, how the chain-rule machine manipulated the
forests.  This means in particular to be able to produce graphs of
half-way forests whenever I want.  I have not yet figured out how to
do this exactly.

The rough plan is to compress all steps of graphs into an "incremental
format" that stores not just forests information, but how they were
created, and allow the users to re-create the forests step by step.

Simply put, this is just another feature that I would like to have for
the end-users, but postponed to later since that was not essential for
my developments.  Now this seems to be quite important for me to
properly observe the forests, so it is perhaps time to implement this
feature first.