fix: Make autodiff deterministic in graph shape

[samestep]

Description

This PR fixes the global count hack leftover by #907, replacing it with an ordering on nodes according to breadth-first search and the ordering on edge labels already given by the children function.

Implementation strategy and design decisions

Since this PR follows #939, I used the following commands to update diagrams/ (adapted from .github/workflows/build.yml):

cd packages/automator/
yarn start batch registry.json ../../diagrams/ --src-prefix=../examples/src/

In order to make this work correctly (without --folders), I made a small tweak to packages/automator/index.tsx. I'll update our Registry wiki page after this PR is merged.

Checklist

• I have commented my code, particularly in hard-to-understand areas
• My changes generate no new ESLint warnings
• I have reviewed any generated changes to the diagrams/ folder

[codecov]

Codecov Report

Merging #945 (3405b84) into main (c042fe5) will decrease coverage by 0.00%.
The diff coverage is 78.12%.

@@            Coverage Diff             @@
##             main     #945      +/-   ##
==========================================
- Coverage   63.19%   63.19%   -0.01%     
==========================================
  Files          62       62              
  Lines        7920     7930      +10     
  Branches     1817     1827      +10     
==========================================
+ Hits         5005     5011       +6     
- Misses       2791     2795       +4     
  Partials      124      124              

Impacted Files	Coverage Δ
packages/core/src/types/ad.ts	100.00% <ø> (ø)
packages/core/src/engine/Autodiff.ts	79.78% <76.66%> (-0.39%)	⬇️
packages/core/src/engine/AutodiffFunctions.ts	100.00% <100.00%> (ø)

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View logs

[wodeni]

Looks great! Glad that the index hack is gone now. Had a small question about idToIndex below. I obviously don't have the context for this. If it's needed, please feel free to just merge this.

[samestep]

I updated the Registry wiki page.