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:      498ms /   4.3%           72.0MiB /   2.7%    

 Section   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────
 Search        16   12.7ms   60.0%   794μs   1.32MiB   68.4%  84.4KiB
   2           16   12.5ms   59.2%   783μs   1.27MiB   66.0%  81.4KiB
   1           16    155μs    0.7%  9.69μs   43.4KiB    2.2%  2.71KiB
 Apply         16   8.21ms   38.8%   513μs    553KiB   28.0%  34.6KiB
 Rebuild       16    246μs    1.2%  15.4μs   69.7KiB    3.5%  4.35KiB
 ────────────────────────────────────────────────────────────────────

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:     1.64ms /  82.2%            577KiB /  87.2%    

 Section   ncalls     time    %tot     avg     alloc    %tot      avg
 ────────────────────────────────────────────────────────────────────
 Apply         16    866μs   64.1%  54.1μs    332KiB   66.0%  20.8KiB
 Search        16    270μs   20.0%  16.9μs    102KiB   20.2%  6.35KiB
   1           16    131μs    9.7%  8.20μs   43.4KiB    8.6%  2.71KiB
   2           16    123μs    9.1%  7.69μs   53.2KiB   10.6%  3.33KiB
 Rebuild       16    214μs   15.9%  13.4μs   69.7KiB   13.8%  4.35KiB
 ────────────────────────────────────────────────────────────────────

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, 1.699628935438294e9, 1.699628935455287e9, false)

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