Program synthesis/graph expressions

[MilesCranmer]

This is a working implementation of program synthesis in SymbolicRegression.jl via the use of nodes that are shared between multiple parents.

• Moving these TODOs to later:

  • Improving printing to be like a program, rather than like an expression
  • Consider optimizing the weight of forming connections and breaking connections
  • Consider whether we want to be smart at all about where we form connections across a tree
  • Create some unittests for these new mutations
  • Refactor existing mutations to be simpler (?)

• Try other settings for Optim.options:

  • Set f_calls_limit in Optim.options, rather than just iterations.

[github-actions]

Benchmark Results

	master	89daeff...	master/89daeff0c2f869...
search/multithreading	22.5 ± 0.78 s	26.4 ± 1.2 s	0.855
search/serial	32.3 ± 0.33 s	35.3 ± 0.19 s	0.914
utils/best_of_sample	1.02 ± 0.43 μs	0.922 ± 0.32 μs	1.11
utils/check_constraints_x10	12.4 ± 3.1 μs	11.5 ± 2.9 μs	1.08
utils/compute_complexity_x10/Float64	2.25 ± 0.12 μs	2.21 ± 0.12 μs	1.02
utils/compute_complexity_x10/Int64	2.31 ± 0.12 μs	2.21 ± 0.12 μs	1.04
utils/compute_complexity_x10/nothing	1.54 ± 0.12 μs	1.46 ± 0.11 μs	1.05
utils/optimize_constants_x10	29.7 ± 6.5 ms	0.032 ± 0.0071 s	0.927
time_to_load	1.27 ± 0.013 s	1.72 ± 0.0052 s	0.738

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[MilesCranmer]

Did a git bisect on the illegal instruction error that comes up from the deterministic test. It started on 3a33882.

Reported in JuliaLang/julia#53761

[MilesCranmer]

The function optimize_and_simplify_population seems to be accounting for the performance regression here, even though optimize_constants by itself seems fine. So perhaps the simplification method is hurting us here?