Triangle of power

An interesting approach to math notation removing trifold redundancy
and making relations between transformation rules visible
that are completely obfuscated in conventional math notation.

Here is a sligt variation with a T notation. It could also be made into a symmetric Y i.e. an upside down "🟀"

These transformations in ALDs?

(TODO: Investigate these directed acyclic graph (DAG) rewriting rules in the projection of annotated lambda diagrams)
Anyone one up for this? Math has no preverred evaluation direction.

Side-note:
Simplifying math as in a computer algebra system (CAS)
is more like relational/logical meta programming that straight forward purely functional programming and evaluation.
But before that random walk into all directions and ensuing combinatoric explosion
making heavily use of a tool-bag of heuristics for moving into an overall direction that is
one or more good simplified expressions.

External links

Youtube – 2016 – 3Blue1Brown (Grant Sanderson) – Triangle of power
This original comes from an answer to a math exchange post by Alex Jordan, which you can find here:
https://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots
Here's a sketch from the math redditer Cosmologicon showing how this might be usual with practical space considerations:
http://i.imgur.com/hAeJokq.jpg