[don't merge] test hvp and derivative

[yebai]

Split DI tests to verify whether DI crash encountered in #878 is caused by OOM error -- the idea is that smaller number of tests reduce memory requirement.

EDIT: Mooncake likely run into one of opaque closure bug on Julia 1.11. The issue got fixed when transitioning to Julia 1.12.

[github-actions]

Mooncake.jl documentation for PR #915 is available at:
https://chalk-lab.github.io/Mooncake.jl/previews/PR915/

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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[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 │   Primal │ Mooncake │ MooncakeFwd │  Zygote │ ReverseDiff │ Enzyme │
│                     String │   String │   String │      String │  String │      String │ String │
├────────────────────────────┼──────────┼──────────┼─────────────┼─────────┼─────────────┼────────┤
│                   sum_1000 │ 110.0 ns │     1.91 │        1.92 │    1.28 │        5.28 │   10.1 │
│                  _sum_1000 │ 952.0 ns │     6.75 │        1.01 │  1650.0 │        32.7 │   1.08 │
│               sum_sin_1000 │  6.64 μs │     2.56 │        1.36 │    1.73 │        10.4 │   1.89 │
│              _sum_sin_1000 │  5.08 μs │     3.22 │        2.27 │   298.0 │        14.7 │   2.57 │
│                   kron_sum │ 386.0 μs │     7.31 │        2.86 │     4.7 │       180.0 │   6.67 │
│              kron_view_sum │ 381.0 μs │     8.87 │        4.39 │    9.69 │       195.0 │   5.82 │
│      naive_map_sin_cos_exp │  2.18 μs │     2.52 │        1.44 │ missing │        7.14 │   2.32 │
│            map_sin_cos_exp │  2.18 μs │     2.83 │        1.49 │    1.61 │        6.01 │   2.91 │
│      broadcast_sin_cos_exp │  2.31 μs │     2.45 │        1.43 │    3.89 │        1.46 │    2.2 │
│                 simple_mlp │ 442.0 μs │     4.77 │        2.91 │    1.62 │        6.66 │   3.19 │
│                     gp_lml │ 200.0 μs │     10.1 │        2.37 │    4.16 │     missing │   7.12 │
│ turing_broadcast_benchmark │  1.93 ms │     4.22 │        3.18 │ missing │        25.2 │   2.09 │
│         large_single_block │ 391.0 ns │     4.43 │         2.0 │  4500.0 │        31.7 │    2.2 │
└────────────────────────────┴──────────┴──────────┴─────────────┴─────────┴─────────────┴────────┘