forwbackw.jl

function f(x)
    y = x
    zz = zeros(typeof(y[1]),10)
    zz[1] = sum(x)
    for i in 2:10
        zz[i] = zz[i-1] +   0.01 * sum(sin.(y))
    end
    sum(zz)^2
end

function f2(x)
    y = x
    z = copy(y)
    A = rand(length(x),length(x))
    for i in 2:10
        for j in 1:length(z)
            z[i] = z[i] + sin(dot(@view(A[i,:]),x))/1000
        end
    end
    sum(z)^2
end

function f3(x)
    y = x
    z = copy(y)
    r = 1:length(x)
    A = rand(length(x),length(x))
    for i in 2:10
        z = z + sin.(A*x)/1000
    end
#    println("eval f")
    sum(z)^2
end

using LinearAlgebra
using ForwardDiff
using ReverseDiff

N = 1_000
x = rand(N)
@time ForwardDiff.gradient(f2,rand(1000));
@time ReverseDiff.gradient(f3,rand(1000));