Write docs on how to write rules to run different computations at different times

[oxinabox]

With #30
this might be a great example

function rrule(::typeof(/), A::AbstractVecOrMat{<:Real}, B::AbstractVecOrMat{<:Real})
    # Compute C (return value differently) to just calling `A/B`
    # so we have some parts precomputed 
    # that we need to use for computing the pullback

    Aᵀ, dA_pb = rrule(adjoint, A)
    Bᵀ, dB_pb = rrule(adjoint, B)
    Cᵀ, dS_pb = rrule(\, Bᵀ, Aᵀ)
    C, dC_pb = rrule(adjoint, Cᵀ)
    
    function slash_pullback(Ȳ)
         # These two run no matter which partial you want
         # but they don't run if you only want the result (C)

        _, dC = dC_pb(Ȳ)
        _, dAᵀ, dBᵀ = dS_pb(dC)

        # Each of these only run if you want that particular partial
        ∂A = @thunk last(dA_pb(dAᵀ))
        ∂B = @thunk last(dA_pb(dBᵀ))

        (NO_FIELDS, ∂A, ∂B)
    end
    return C, slash_pullback
end

[simeonschaub]

If we replaced adjoint with transpose, I believe this should even be correct for complex input.

[oxinabox]

A better example would not call rrule internally,
and also would have more obvious work happenning in the thunk

[nickrobinson251]

related: JuliaDiff/ChainRules.jl#103
but does not add a specific example like suggested here