equality saturation

[shashi]

simple, performance conscious port of the egg algorithm. Simplify works with it.

[github-actions]

Benchmark Results

	master	2d8eeb2...	t[master]/t[2d8eeb2...]
overhead/acrule/a+2	1.31 ± 0.42 μs	1.31 ± 0.27 μs	1
overhead/acrule/a+2+b	1.31 ± 0.46 μs	1.3 ± 0.29 μs	1.01
overhead/acrule/a+b	0.464 ± 0.073 μs	0.472 ± 0.049 μs	0.981
overhead/acrule/noop:Int	0.0318 ± 0.0002 μs	0.0371 ± 0.0038 μs	0.856
overhead/acrule/noop:Sym	0.0696 ± 0.0088 μs	0.0643 ± 0.013 μs	1.08
overhead/rule/noop:Int	0.0507 ± 0.016 μs	0.0507 ± 0.0038 μs	1
overhead/rule/noop:Sym	0.0933 ± 0.021 μs	0.0875 ± 0.016 μs	1.07
overhead/rule/noop:Term	0.0853 ± 0.022 μs	0.0884 ± 0.017 μs	0.964
overhead/ruleset/noop:Int	0.199 ± 0.011 μs	0.186 ± 0.043 μs	1.07
overhead/ruleset/noop:Sym	0.254 ± 0.021 μs	0.243 ± 0.062 μs	1.05
overhead/ruleset/noop:Term	6.32 ± 0.68 μs	6.49 ± 1.3 μs	0.974
overhead/simplify/noop:Int	0.277 ± 0.021 μs	0.273 ± 0.049 μs	1.01
overhead/simplify/noop:Sym	0.316 ± 0.032 μs	0.315 ± 0.074 μs	1
overhead/simplify/noop:Term	0.0894 ± 0.0071 ms	0.0776 ± 0.017 ms	1.15
overhead/simplify/randterm (+, *):serial	0.214 ± 0.011 s	0.208 ± 0.01 s	1.03
overhead/simplify/randterm (+, *):thread	0.13 ± 0.02 s	0.122 ± 0.022 s	1.07
overhead/simplify/randterm (/, *):serial	0.503 ± 0.044 ms	0.476 ± 0.097 ms	1.06
overhead/simplify/randterm (/, *):thread	0.593 ± 0.074 ms	0.548 ± 0.11 ms	1.08
overhead/substitute/a	0.115 ± 0.018 ms	0.119 ± 0.0081 ms	0.967
overhead/substitute/a,b	0.108 ± 0.018 ms	0.108 ± 0.0074 ms	0.995
overhead/substitute/a,b,c	30.4 ± 3.4 μs	0.0327 ± 0.0023 ms	0.93
polyform/easy_iszero	0.0718 ± 0.0057 ms	0.0663 ± 0.017 ms	1.08
polyform/isone	3.5 ± 0 ns	3.2 ± 0.2 ns	1.09
polyform/iszero	2.67 ± 0.38 ms	2.49 ± 0.36 ms	1.07
polyform/simplify_fractions	3.74 ± 0.42 ms	3.45 ± 0.5 ms	1.08
time_to_load	7.03 ± 0.2 s	7.31 ± 0.18 s	0.961

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).

[shashi]

Tasks:

• Only rules of depth 1 are working right now...
• acrules will not explore different order of applications, for example 2+1+5 will always be 3+5 then 8, never 2+6 then 8
• need some way to back off and break for infinite loops Why reasonable rules can create infinite loops egraphs-good/egg#60 && https://julialang.slack.com/archives/C8R5HJMSN/p1683499144970229