Increase precision of betainc C implementation

[ricardoV94]

Description

Need to use more aggressive constants to match Scipy

Related Issue

• Closes New betainc C implementation less precise than Scipy #906
• 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):

[ricardoV94]

Actually this is fine, we just need to use the same constants Scipy used to use when betainc relied on Cephes

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 81.23%. Comparing base (56c30e0) to head (78bb748).
Report is 9 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #908      +/-   ##
==========================================
- Coverage   81.24%   81.23%   -0.01%     
==========================================
  Files         170      170              
  Lines       46928    46826     -102     
  Branches    11484    11465      -19     
==========================================
- Hits        38126    38041      -85     
+ Misses       6603     6592      -11     
+ Partials     2199     2193       -6     

Files	Coverage Δ
pytensor/scalar/math.py	87.26% <100.00%> (ø)

... and 21 files with indirect coverage changes

[twiecki]

Obviously!

[jessegrabowski]

Isn't there a beta function that doesn't have a C implementation at all? I recall seeing warnings when you do pm.find_constrained_prior on a Beta. It's not related to this is it?

[ricardoV94]

Isn't there a beta function that doesn't have a C implementation at all? I recall seeing warnings when you do pm.find_constrained_prior on a Beta. It's not related to this is it?

We added C code because of those warnings, but I also disabled that sort of warnings because they were counter-productive: #794 (People were sampling with JAX and worrying about the warning)