Graph presentation of equations instead of tree presentation

[AKHCE]

Hi,

My assumption is PySR converts equations into trees by using sequence-based list. For example, for equation 2*x+1, the tree is represented by a list like [+, 1, *, 2, x]. Did I get it correctly?

I am curious to know if you could conceive any benefit of using graph presentation of equations instead of using trees (i.e. sequence-based list). The reason I am bringing this up is that there is a rich history of graph theory, which might contribute to search engine.

Thank you so much in advance for sharing your thoughts,
Cheers

[MilesCranmer]

Hi @AKHCE,

PySR stores expressions as binary trees rather than sequences. The struct is defined here: https://github.com/SymbolicML/DynamicExpressions.jl/blob/46388518281b0be12479afcb3a3b8bdabc361ccd/src/Equation.jl#L57

Technically as of MilesCranmer/SymbolicRegression.jl#135, expressions are actually stored as acyclic graphs — which can let you have multiple parent nodes for a single child. That means you could in theory share a subexpression across an expression. However relevant utilities for that are not set up yet.

I’d be interested to know if you have any ideas for exploiting graph theory.

Cheers,
Miles