Remove LogDensityProblemsAD Extension

[willtebbutt]

Now that LogDensityProblemsAD support ADTypes, Mooncake does not need to directly implement the LogDensityProblemsAD interface.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

[github-actions]

Performance Ratio:
Ratio of time to compute gradient and time to compute function.
Warning: results are very approximate! See here for more context.

┌────────────────────────────┬──────────┬─────────┬─────────────┬─────────┐
│                      Label │ Mooncake │  Zygote │ ReverseDiff │  Enzyme │
│                     String │   String │  String │      String │  String │
├────────────────────────────┼──────────┼─────────┼─────────────┼─────────┤
│                   sum_1000 │     69.2 │     1.0 │         5.5 │ missing │
│                  _sum_1000 │      6.6 │  1320.0 │        34.0 │ missing │
│               sum_sin_1000 │     2.29 │    1.69 │        10.6 │ missing │
│              _sum_sin_1000 │     2.77 │   284.0 │        13.7 │ missing │
│                   kron_sum │     74.1 │    3.89 │       240.0 │ missing │
│              kron_view_sum │     55.6 │    8.86 │       224.0 │ missing │
│      naive_map_sin_cos_exp │     2.52 │ missing │        7.18 │ missing │
│            map_sin_cos_exp │     2.68 │    1.44 │        6.03 │ missing │
│      broadcast_sin_cos_exp │      2.6 │    3.16 │        1.46 │ missing │
│                 simple_mlp │     4.16 │    2.03 │         8.2 │ missing │
│                     gp_lml │     9.43 │    3.72 │     missing │ missing │
│ turing_broadcast_benchmark │     3.19 │ missing │        27.0 │ missing │
│         large_single_block │     4.01 │  4120.0 │        31.2 │ missing │
└────────────────────────────┴──────────┴─────────┴─────────────┴─────────┘