perf: avoid double function call in ReverseDiff value_and_gradient

[gdalle]

Personal musings: The behavior of ReverseDiff is very confusing, even on ImmutableDiffResult. I encountered a Heisenbug which seems to depend on the compilation path (disappears when I add a print statement), where value_and_gradient! suddenly becomes incorrect when called inside value_gradient_and_hessian!. But only for a compiled tape. And the :gradient tests for value_and_gradient! still pass. What a mess.

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[gdalle]

So, in the current state of the PR, value_and_gradient! works but not alongside a Hessian computation... unless we print something? I'm going crazy.

julia> DifferentiationInterface.value_gradient_and_hessian!(
           f,
           zeros(2),
           zeros(2, 2),
           SecondOrder(AutoFiniteDiff(), AutoReverseDiff(; compile=true)),
           ones(2),
       )
(0.0, [2.0, 2.0], [2.0 0.0; 0.0 2.0])

julia> DifferentiationInterface.value_gradient_and_hessian!(
           f,
           zeros(2),
           zeros(2, 2),
           SecondOrder(AutoFiniteDiff(), AutoReverseDiff(; compile=true)),
           ones(2),
       )
(0.0, [2.0, 2.0], [2.0 0.0; 0.0 2.0])

julia> using DifferentiationInterface, FiniteDiff, ReverseDiff

julia> DifferentiationInterface.value_and_gradient!(
           f,
           zeros(2),
           AutoReverseDiff(; compile=true),
           ones(2),
       )
(2.0, [2.0, 2.0])

julia> DifferentiationInterface.value_gradient_and_hessian!(
           f,
           zeros(2),
           zeros(2, 2),
           SecondOrder(AutoFiniteDiff(), AutoReverseDiff(; compile=true)),
           ones(2),
       )
(0.0, [2.0, 2.0], [2.0 0.0; 0.0 2.0])

julia> # now we just add a log

julia> DifferentiationInterface.value_and_gradient!(
           f,
           zeros(2),
           AutoReverseDiff(; compile=true),
           ones(2),
       )
[ Info: I'm here
(2.0, [2.0, 2.0])

julia> DifferentiationInterface.value_gradient_and_hessian!(
           f,
           zeros(2),
           zeros(2, 2),
           SecondOrder(AutoFiniteDiff(), AutoReverseDiff(; compile=true)),
           ones(2),
       )
[ Info: I'm here
(2.0, [2.0, 2.0], [2.0 0.0; 0.0 2.0])

[gdalle]

I further boiled it down to whether I do y, grad or y, _ in the assignment. Still have no clue what's going on.

EDIT: pure-ReverseDiff example available at JuliaDiff/ReverseDiff.jl#269

using DifferentiationInterface  # version from this branch
import DifferentiationInterface as DI
using ReverseDiff: ReverseDiff

backend = AutoReverseDiff(; compile=true)
f(x) = sum(abs2, x)
x = ones(2)

prep = prepare_gradient(f, backend, zero(x))

function value_and_gradient_nested!(f, grad, prep, backend, x)
    y, _ = value_and_gradient!(f, grad, prep, backend, x)
    return y, grad
end

julia> value_and_gradient!(f, zeros(2), prep, backend, x)
(2.0, [2.0, 2.0])

julia> value_and_gradient_nested!(f, zeros(2), prep, backend, x)  # wrong
(0.0, [2.0, 2.0])

This behavior only happens with the compiled tape mode of ReverseDiff. I think it might be because the compiler struggles to figure out that ReverseDiff mutates the value of y in the MutableDiffResult?