Optimize src/ad.jl

[amontoison]

@tmigot

• It seems that you forgot to divide by 2 in the definition of f for NLS (line 122);
• We should maybe add a get_f because we redefine it in many cases;
• ℓ(x) is not defined anymore with a if ... else ... end, I think that it could help Symbolics if we remove this kind of "branch".

[github-actions[bot]]

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
DerivativeFreeSolvers.jl
JSOSolvers.jl
NLPModelsIpopt.jl
OptimizationProblems.jl
Percival.jl
QuadraticModels.jl
SolverBenchmark.jl
SolverTools.jl

[codecov[bot]]

Codecov Report

Patch coverage: 94.11% and project coverage change: -0.19 :warning:

Comparison is base (d122c8e) 98.44% compared to head (6fe3cce) 98.25%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #110 +/- ## ========================================== - Coverage 98.44% 98.25% -0.19% ========================================== Files 8 8 Lines 964 976 +12 ========================================== + Hits 949 959 +10 - Misses 15 17 +2 ``` | [Impacted Files](https://codecov.io/gh/JuliaSmoothOptimizers/ADNLPModels.jl/pull/110?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers) | Coverage Δ | | |---|---|---| | [src/ad.jl](https://codecov.io/gh/JuliaSmoothOptimizers/ADNLPModels.jl/pull/110?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers#diff-c3JjL2FkLmps) | `95.60% <94.11%> (-1.87%)` | :arrow_down: | Help us with your feedback. Take ten seconds to tell us [how you rate us](https://about.codecov.io/nps?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers). Have a feature suggestion? [Share it here.](https://app.codecov.io/gh/feedback/?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers)

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