How to improve CPU performance?

[Moelf]

consider this example from a Jax discussion:

Source code

function run_julia(height, width)
    y = range(-1.0f0, 0.0f0; length = height) # need Float32 because Jax defaults to it
    x = range(-1.5f0, 0.0f0; length = width)
    c = x' .+ y*im
    fractal = fill(Int32(20), height, width)

    # this checks if indicies are compatible between `c` and `fractal`
    @inbounds for idx in eachindex(c, fractal)
        _c = c[idx]
        z = _c
        m = true
        Base.Cartesian.@nexprs 20 i -> begin
            z = z^2 + _c
            az4 = abs2(z) > 4f0
            fractal[idx] = ifelse(m&az4, Int32(i), fractal[idx]) # 32-bit Int, same reason as above
            m &= (!az4)
        end
    end
    return fractal
end

using KernelAbstractions
    
@kernel function julia_kernel!(c, fractal)    
    I = @index(Global)    
    _c = c[I]    
    z = _c       
    @inbounds for i = 1:20    
        z = z^2 + _c    
        if abs2(z) > 4f0    
            fractal[I] = Int32(i)    
            break    
        end    
    end    
end

function run_julia_cpu_jaxstype(height, width)
    y = range(-1.0f0, 0.0f0; length = height)  
    x = range(-1.5f0, 0.0f0; length = width)  
    c = x' .+ y*im
    fractal = fill(Int32(20), height, width)     

    kernel! = julia_kernel!(CPU(), length(c)÷Threads.nthreads()) # we're using 1-thread here 
    event = kernel!(c, fractal; ndrange=length(c))
    wait(event) # not copying back, need to block here
    return fractal
end

we have

julia> Threads.nthreads()
1

julia> @benchmark run_julia(2000,3000)
BenchmarkTools.Trial: 100 samples with 1 evaluation.
 Range (min … max):  49.380 ms …  52.606 ms  ┊ GC (min … max): 0.37% … 1.04%
 Time  (median):     49.789 ms               ┊ GC (median):    0.98%
 Time  (mean ± σ):   49.982 ms ± 583.818 μs  ┊ GC (mean ± σ):  0.98% ± 0.07%

      ▅█▇▄   ▃
  ▃▁▅▇█████▃▇██▅▇▅▁▆▆▃▆▃▁▆▃▅▁▃▁▁▁▁▁▃▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▁▁▆ ▃
  49.4 ms         Histogram: frequency by time           52 ms <

 Memory estimate: 68.66 MiB, allocs estimate: 4.

julia> @benchmark run_julia_cpu_jaxstype(2000,3000)
BenchmarkTools.Trial: 29 samples with 1 evaluation.
 Range (min … max):  176.674 ms … 179.932 ms  ┊ GC (min … max): 0.27% … 0.08%
 Time  (median):     177.228 ms               ┊ GC (median):    0.26%
 Time  (mean ± σ):   177.528 ms ± 780.443 μs  ┊ GC (mean ± σ):  0.26% ± 0.03%

  ▃▃ ▃▃  ▃                  █
  ██▇██▇▁█▇▇▇▁▇▁▁▁▁▇▁▁▇▇▁▁▇▇█▇▁▇▇▁▁▁▁▁▁▁▁▁▁▁▁▁▇▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▇ ▁
  177 ms           Histogram: frequency by time          180 ms <

 Memory estimate: 68.67 MiB, allocs estimate: 28.