Manually preventing perturbation confusion

[ArnoStrouwen]

Some packages such as DifferentialEquations.jl require you to manually provide Dual numbers for trickier problems. When you have nested differentiation in such a situation you also need to provide ordering of the tags yourself. Could an example how to manually prevent perturbation confusion be provided?

using ForwardDiff
function f(u,p)
    u[1]^2*u[2]^2*p[1]^2
end
u0  = [2.0, 3.0]
p0 = [4.0]
dfdp = u->ForwardDiff.gradient(p->f(u,p),p0)
ForwardDiff.jacobian(dfdp,u0)
# ddf/dpdu1 = 2*u1*u2^2*2p1 = 2*2*3^2*2*4 = 288
# ddf/dpdu2 = u1^2*2*u2*2p1 = 2^2*2*3*2*4 = 192

using ForwardDiff:Dual
abstract type A end
abstract type B end
# ... define ordering on A and B here ...
u_test = [Dual{A}(2.0,1.0,0.0),Dual{A}(3.0,0.0,1.0)]
p_test = [Dual{B}(4.0,1.0)]
u_test[1]^2*u_test[2]^2*p_test[1]^2

[ChrisRackauckas]

The dual ordering is done via https://www.stochasticlifestyle.com/improved-forwarddiff-jl-stacktraces-with-package-tags/ which increments the tags and everything appropriately, so this isn't an issue.