Deepcopy output rather than copy

[willtebbutt]

@gdalle could you see if this branch sorts your problem out? If so, I'll merge it, as I don't think it does any harm on my end.

[gdalle]

It probably slows things down and makes them type unstable. Is it really a deep copy that you need? Why even copy?

[github-actions]

Performance Ratio:

┌────────────────────────────┬────────┬─────────┬─────────────┬─────────┐
│                      Label │  Tapir │  Zygote │ ReverseDiff │  Enzyme │
│                     String │ String │  String │      String │  String │
├────────────────────────────┼────────┼─────────┼─────────────┼─────────┤
│                        sum │   98.6 │   0.357 │        2.32 │    0.54 │
│                       _sum │   25.7 │   485.0 │        26.7 │   0.121 │
│                   kron_sum │  171.0 │    3.42 │       233.0 │    20.8 │
│              kron_view_sum │  221.0 │    9.97 │       229.0 │     7.3 │
│      naive_map_sin_cos_exp │   8.62 │ missing │        8.86 │    2.77 │
│            map_sin_cos_exp │   10.7 │    1.82 │        7.56 │    3.44 │
│      broadcast_sin_cos_exp │   10.1 │    2.64 │        1.68 │    2.86 │
│                 simple_mlp │   23.0 │     3.1 │        11.3 │    3.63 │
│                     gp_lml │   42.7 │    4.16 │     missing │ missing │
│ turing_broadcast_benchmark │   19.3 │ missing │        37.9 │ missing │
└────────────────────────────┴────────┴─────────┴─────────────┴─────────┘

[gdalle]

See JuliaDiff/DifferentiationInterface.jl#126 for the new issue ^^

[gdalle]

Related:

• copy not implemented for String JuliaLang/julia#31995
• Define copy for immutable values JuliaLang/julia#45143

[gdalle]

Probably worth closing for now? Maybe in favor of a custom _copy that handles the nothing case as suggested in JuliaDiff/DifferentiationInterface.jl#126 (comment)?
I'm usually not a fan of these manual patches, but I think it's justified by the relevance of DifferentiationInterface for testing Tapir