mean BigFloat precision

[edljk]

I observed a loss of precision using ReverseDiff with respect to ForwardDiff on the following simple example:

julia> testprecision()
type precision eps(T)     = 1.7272337110188889250772703725600799142232e-77 

ForwardDiff error         = 0.0000000000000000000000000000000000000000e+00 
ReverseDiff error         = 8.6560832651618551196119417711416155844212e-19

Is it expected? Thanks!

using Statistics, LinearAlgebra
using ForwardDiff, ReverseDiff, Printf

setprecision(2 ^ 8)

function testprecision(n::Int64 = 1_000, T::DataType = BigFloat)
    x = rand(T, n)
    f(x) = mean(x .^ 3) 
    gf = ForwardDiff.gradient(f, x)
    gr = ReverseDiff.gradient(f, x)
    gth = 3 * x .^ 2 / n 
    @printf "type precision eps(T)     = %4.40e \n\n" eps(T)
    @printf "ForwardDiff error         = %4.40e \n" norm(gf - gth)
    @printf "ReverseDiff error         = %4.40e \n" norm(gr - gth)
    nothing
end