Formula generation was producing empty output for programs containing ROL operations in loops (e.g., A069195). The issue affected any program that generates a self-recursive formula like a(n) = a(n-k).

Root Cause

FormulaSimplify::replaceSimpleRecursiveRefs is designed to eliminate helper functions that are simple shifted references to other recursive functions (e.g., a(n) = b(n+1) where b is recursive). The helper function isSimpleRecursiveReference was incorrectly treating self-recursive definitions as simple references:

// Before: incorrectly matched both cases
a(n) = b(n+1)  // ✓ Simple reference to another function - should match
a(n) = a(n-7)  // ✗ Self-recursive definition - should NOT match

This caused the formula to be erased, resulting in empty output.

Changes

• Added early return in isSimpleRecursiveReference when refFuncName == funcName
• Self-recursive functions now correctly bypass the simplification logic

The fix is a 3-line guard placed immediately after extracting the referenced function name.

• Fixes Empty formula generated for A069195 #630

✨ Let Copilot coding agent set things up for you — coding agent works faster and does higher quality work when set up for your repo.