AutoFastDifferentiation not working with NamedTuple context

Issue

AutoFastDifferentiation is not able to deal with a NamedTuple context which could happen when the parameters of an optimization is a NamedTuple.

The error message:

ERROR: MethodError: no method matching variablize(::@NamedTuple{v1::Float64, v2::Float64}, ::Symbol) 
Closest candidates are:
  variablize(::AbstractArray, ::Symbol)
  variablize(::Number, ::Symbol)

MWE

Example taken from Optimization.jl, and modified to have a NamedTuple as p and use AutoFastDifferentiation

using Optimization
import FastDifferentiation

rosenbrock(u, p) = (p.v1 - u[1])^2 + p.v2 * (u[2] - u[1]^2)^2
u0 = zeros(2)
p = (v1=1.0, v2=100.0)

optf = OptimizationFunction(rosenbrock, AutoFastDifferentiation())
prob = OptimizationProblem(optf, u0, p)

sol = solve(prob, Optimization.LBFGS())

AutoForwardDiff works fine.

Start with the AutoFastDifferentiation path and the variablize methods shown in the error, then reproduce the provided Optimization.jl MWE with a NamedTuple parameter context. Done means the MWE runs successfully with AutoFastDifferentiation, without the missing-method error; compare its behavior with AutoForwardDiff.