[gdalle-bot]

Important

This PR was generated by a coding agent, please disregard it until @gdalle has reviewed it.

Summary

• New operators value_gradient_and_hvp(f, [prep,] backend, x, tx, [contexts...]) -> (y, grad, tg) and value_gradient_and_hvp!, so that every second-order operator with a value also returns the primal value (like value_gradient_and_hessian and value_derivative_and_second_derivative).
• gradient_and_hvp(!) are deprecated and forward to the new operators, with a Base.depwarn.
• Backends which get the value for free return it: reverse-over-forward (inner value_and_gradient), Mooncake (value_and_hvp!!), Symbolics and FastDifferentiation (gradient preparation), GTPSA (value_gradient_and_hessian!), Zygote (forwards to ForwardDiff-over-Zygote), HyperHessians (hvp_gradient_value). Forward-over-anything and reverse-over-reverse use one extra primal call.
• DIT now tests value_gradient_and_hvp(!) instead of the deprecated functions, including the primal value. This keeps DIT's JET tests clear of the deprecation warning, and tests the new operator on every backend.
• DI version bumped to v0.7.22, DIT compat on DI raised accordingly, and CHANGELOG entries added.

This is also a prerequisite for an upcoming revamp of DIT scenarios, where every second-order operator with a value then returns the same orders (y, grad, second-order).

Tests

• New DifferentiationInterface/test/Core/Internals/deprecations.jl: the deprecated functions return the same results as the new ones and are flagged by @test_deprecated.
• DIT Standard group passed locally (Julia 1.13, -O1): 57266 tests.

🤖 Generated with Claude Code

Model used: Claude Opus 5.5

[codecov]

Codecov Report

❌ Patch coverage is 80.00000% with 17 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.18%. Comparing base (1ae85dd) to head (6945b9a).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
...ifferentiationInterfaceMooncakeExt/second_order.jl	0.00%	17 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1086   +/-   ##
=======================================
  Coverage   98.18%   98.18%           
=======================================
  Files         143      144    +1     
  Lines        8246     8265   +19     
=======================================
+ Hits         8096     8115   +19     
  Misses        150      150           

Flag	Coverage Δ
DI	98.07% <77.92%> (+<0.01%)	⬆️
DIT	98.49% <100.00%> (+<0.01%)	⬆️

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