mean BigFloat precision

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

No repository file or test is named. Start by running the provided Julia testprecision example with BigFloat, then trace the ForwardDiff.gradient and ReverseDiff.gradient entry points to compare their precision handling; done means determining whether the discrepancy is expected and documenting or correcting the behavior.