Why are my higher order functions a million times slower than they should be?

General Usage Performance
6

Ah, ok. The thing is that Julia does not specialize for the function type if the function is not called from withing the function. Thus, the fix is:

ulia> function slow(f::F, x) where F # annotate F type here !
           y = apply(f, x)
           for _ in eachindex(y)
               
           end
       end
slow (generic function with 1 method)

julia> function run()
           for f in [slow, fast]
               x = rand(10^6)
               @time f(identity, x)
           end
       end
run (generic function with 1 method)

julia> run()
  0.003013 seconds (3.17 k allocations: 170.994 KiB, 99.51% compilation time)
  0.000002 seconds

julia> run()
  0.000009 seconds
  0.000005 seconds

This is actually the performance tip to be considered here (a tricky one, I learnt this the hard way as well):

https://docs.julialang.org/en/v1/manual/performance-tips/#Be-aware-of-when-Julia-avoids-specializing

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