One small change I'd recommend is for the graph visualization, have a separate source node for each x, x^2, x^4 used. A single x source clutters the graph and hides the structure.
> have a separate source node for each x, x^2, x^4 used
Do you mean a graph like this R&W? https://thomasahle.com/fast-polynomials/#ex=bessel&mode=Q&me... there are nodes labeled x2, x4, x8; but it's the output of multiplications, and we want to make the number of mults visually clear.
For completeness: To apply my original idea to R&W9 you would have 5 nodes labeled x, each with one arrow out, two nodes labeled x^2, each with no arrows in and one arrow out, one node labeled x^4 with no arrows in and one arrow out, one node labeled x^8 with no arrows in and one arrow out. Three missing mults, but way fewer crossings, not what you want.