Add compat entries for benchmarks

[penelopeysm]

Closes #941

Closes #942

Closes #943

[github-actions]

Benchmark Report for Commit 37fc083

Computer Information

Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

Benchmark Results

|                 Model | Dimension |  AD Backend |      VarInfo Type | Linked | Eval Time / Ref Time | AD Time / Eval Time |
|-----------------------|-----------|-------------|-------------------|--------|----------------------|---------------------|
| Simple assume observe |         1 | forwarddiff |             typed |  false |                  9.5 |                 1.6 |
|           Smorgasbord |       201 | forwarddiff |             typed |  false |                729.3 |                36.9 |
|           Smorgasbord |       201 | forwarddiff | simple_namedtuple |   true |                414.1 |                48.8 |
|           Smorgasbord |       201 | forwarddiff |           untyped |   true |               1216.4 |                28.2 |
|           Smorgasbord |       201 | forwarddiff |       simple_dict |   true |               3291.7 |                24.2 |
|           Smorgasbord |       201 | reversediff |             typed |   true |               1448.2 |                29.5 |
|           Smorgasbord |       201 |    mooncake |             typed |   true |                943.9 |                 5.2 |
|    Loop univariate 1k |      1000 |    mooncake |             typed |   true |               5674.3 |                 3.9 |
|       Multivariate 1k |      1000 |    mooncake |             typed |   true |               1017.8 |                 8.8 |
|   Loop univariate 10k |     10000 |    mooncake |             typed |   true |              62705.7 |                 3.6 |
|      Multivariate 10k |     10000 |    mooncake |             typed |   true |               9063.6 |                 9.6 |
|               Dynamic |        10 |    mooncake |             typed |   true |                126.8 |                13.4 |
|              Submodel |         1 |    mooncake |             typed |   true |                 13.5 |                 6.2 |
|                   LDA |        12 | reversediff |             typed |   true |                443.2 |                 5.9 |

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 82.92%. Comparing base (e49853c) to head (37fc083).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #945   +/-   ##
=======================================
  Coverage   82.92%   82.92%           
=======================================
  Files          36       36           
  Lines        3964     3964           
=======================================
  Hits         3287     3287           
  Misses        677      677           

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