perf: prepare inner gradient in HVP

[gdalle]

No description provided.

[codecov]

Codecov Report

Attention: Patch coverage is 81.90476% with 19 lines in your changes missing coverage. Please review.

Project coverage is 96.80%. Comparing base (0ea7f1d) to head (2471e24).
Report is 20 commits behind head on main.

Files with missing lines	Patch %	Lines
DifferentiationInterface/src/utils/traits.jl	84.21%	3 Missing ⚠️
...faceZygoteExt/DifferentiationInterfaceZygoteExt.jl	0.00%	2 Missing ⚠️
DifferentiationInterface/src/misc/zero_backends.jl	0.00%	2 Missing ⚠️
...reExt/DifferentiationInterfaceChainRulesCoreExt.jl	0.00%	1 Missing ⚠️
...ractorExt/DifferentiationInterfaceDiffractorExt.jl	0.00%	1 Missing ⚠️
...xt/DifferentiationInterfaceFiniteDifferencesExt.jl	0.00%	1 Missing ⚠️
...dDiffExt/DifferentiationInterfaceForwardDiffExt.jl	0.00%	1 Missing ⚠️
...erfaceGTPSAExt/DifferentiationInterfaceGTPSAExt.jl	0.00%	1 Missing ⚠️
...MooncakeExt/DifferentiationInterfaceMooncakeExt.jl	0.00%	1 Missing ⚠️
...DifferentiationInterfacePolyesterForwardDiffExt.jl	66.66%	1 Missing ⚠️
... and 5 more

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #709      +/-   ##
==========================================
- Coverage   97.96%   96.80%   -1.17%     
==========================================
  Files         119      105      -14     
  Lines        6297     6194     -103     
==========================================
- Hits         6169     5996     -173     
- Misses        128      198      +70     

Flag	Coverage Δ
DI	97.34% <82.35%> (-1.58%)	⬇️
DIT	95.66% <66.66%> (-0.25%)	⬇️

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[gdalle]

Superseded by #743