Add rewrite for softplus(log(x)) -> log1p(x)

[lciti]

Description

This PR adds the simple rewrite softplus(log(x)) -> log1p(x).

I could also extend it to cover the case softplus(-log(x)) -> log1p(1/x). However I have noticed that even the simple exp(-log(x)) -> 1/x is missing, so I wonder if there is an underlying reason to avoid such simplifications, that I am not aware of.

Also, it would be helpful to get feedback from the community before proceeding further with the PR to ensure that the proposed simplification(s) align with the library's design principles and don't introduce any unintended consequences.
Likewise, I would like to know if the approach and location (within the file and test) of the change is appropriate. I am not sufficiently familiar with the code to understand whether the approach I have used is better/worse than a PatternNodeRewriter.

Related Issue

• Closes Missing rewrite softplus(log(x)) -> log1p(x) #1451
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

---

📚 Documentation preview 📚: https://pytensor--1452.org.readthedocs.build/en/1452/

[ricardoV94]

Nitpick I prefer to refer to it by log1pexp, which we have as an alias to softplus:

pytensor/pytensor/tensor/math.py

Line 2474 in ff98ab8

log1pexp = softplus

Also we can add a similar case for log1mexp?

[ricardoV94]

However I have noticed that even the simple exp(-log(x)) -> 1/x is missing, so I wonder if there is an underlying reason to avoid such simplifications, that I am not aware of.

Hmm I don't know if that introduces numerical precision issues...

However the somewhat converse log(1/x) -> -log(x) seems stable and something we may want to do?

[ricardoV94]

if you want you can check against the expected graph directly, something like

assert equal_computations(f.maker.fgraph.outputs, [pt.switch(x > 0, pt.log1p(x), np.asarray([[np.nan]], dtype="float32")])

Or something like that. This is not a request!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 82.12%. Comparing base (ff98ab8) to head (10bcb41).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1452   +/-   ##
=======================================
  Coverage   82.12%   82.12%           
=======================================
  Files         211      211           
  Lines       49757    49762    +5     
  Branches     8819     8820    +1     
=======================================
+ Hits        40862    40867    +5     
  Misses       6715     6715           
  Partials     2180     2180           

Files with missing lines	Coverage Δ
pytensor/tensor/rewriting/math.py	89.28% <100.00%> (+0.03%)	⬆️

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