Benchmarking Fibonacci. E-Graphs memoize computation.

using Metatheory
using Test

function fib end

fibo = @theory x y n begin
  x::Int + y::Int => x + y
  fib(n::Int) => (n < 2 ? n : :(fib($(n - 1)) + fib($(n - 2))))
end

params = SaturationParams(timeout = 60)

SaturationParams(60, 0x0000000000000000, 5000, 15000, nothing, Metatheory.EGraphs.var"#30#32"(), Metatheory.EGraphs.Schedulers.BackoffScheduler, (), false, true)

We run the saturation twice to see a result that does not include compilation time.

g = EGraph(:(fib(10)))
saturate!(g, fibo, params)

SaturationReport
=================
	Stop Reason: saturated
	Iterations: 16
	EGraph Size: 15 eclasses, 54 nodes
 ────────────────────────────────────────────────────────────────────
                            Time                    Allocations      
                   ───────────────────────   ────────────────────────
 Tot / % measured:      388ms /  11.8%           21.6MiB /   8.8%    

 Section   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────
 Search        16   30.2ms   65.9%  1.89ms   1.34MiB   70.2%  85.5KiB
   2           16   30.1ms   65.6%  1.88ms   1.29MiB   67.8%  82.6KiB
   1           16    113μs    0.2%  7.04μs   43.4KiB    2.2%  2.71KiB
 Apply         16   15.4ms   33.5%   961μs    511KiB   26.2%  32.0KiB
 Rebuild       16    255μs    0.6%  15.9μs   69.4KiB    3.6%  4.34KiB
 ────────────────────────────────────────────────────────────────────

That's fast!

z = EGraph(:(fib(10)))
saturate!(z, fibo, params)

SaturationReport
=================
	Stop Reason: saturated
	Iterations: 16
	EGraph Size: 15 eclasses, 54 nodes
 ────────────────────────────────────────────────────────────────────
                            Time                    Allocations      
                   ───────────────────────   ────────────────────────
 Tot / % measured:     1.49ms /  80.8%            575KiB /  87.3%    

 Section   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────
 Apply         16    832μs   69.3%  52.0μs    332KiB   66.1%  20.7KiB
 Rebuild       16    215μs   17.9%  13.5μs   69.4KiB   13.8%  4.34KiB
 Search        16    154μs   12.8%  9.60μs    101KiB   20.1%  6.30KiB
   1           16   73.0μs    6.1%  4.56μs   43.4KiB    8.6%  2.71KiB
   2           16   69.1μs    5.8%  4.32μs   53.2KiB   10.6%  3.33KiB
 ────────────────────────────────────────────────────────────────────

We can test that the result is correct.

@testset "Fibonacci" begin
  @test 55 == extract!(g, astsize)
end

Test.DefaultTestSet("Fibonacci", Any[], 1, false, false, true, 1.712763133436037e9, 1.71276313345246e9, false, "none")

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