# Funsearch

> FunSearch (Program Search) method skill. USE WHEN the user explicitly requests FunSearch / Program Search, or wants search with a programs database that stores and samples from high-scoring programs.

- Skill: `optima-cityu/funsearch` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add optima-cityu/funsearch`
- Raw SKILL.md: https://api.skillmd.com/api/skills/optima-cityu/funsearch/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: optima-cityu (https://skillmd.com/u/optima-cityu)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/optima-cityu/funsearch

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# FunSearch Skill

> **Paper**: Romera-Paredes et al., "Mathematical discoveries from program search with large language models", Nature 625 (2024).

## 1. Method Essence

FunSearch organizes search using a **ProgramsDatabase**: programs are stored and indexed by evaluation score, with sampling prioritizing high-score buckets for mutation. New programs are evaluated and stored by score, forming a "high-score priority, low-score elimination" evolution. It also uses an **islands mechanism** for diversity: multiple independent sub-populations evolve separately, with periodic exchange.

Core components:
- **Database**: Archive of programs + scores, stratified by score (higher score = higher probability of being sampled as parent)
- **Sampler**: Generates mutation prompts from high-score programs (not from empty prompts)
- **Evaluator**: Independent evaluation, results written back to database

## 2. Recommended Parameters

See `params.yaml` in this directory for the recommended parameter configuration.

### What Happens During Evolution

1. Database initialized with seed programs (or random generation)
2. Each generation:
   - Sample parent from high-score bucket
   - Generate N variants via LLM mutation
   - Evaluate variants independently
   - Store scored variants back to database
   - Optionally: eliminate low-score programs
3. Islands evolve independently, periodically exchanging best programs
4. Database naturally stratifies: top programs dominate sampling

### Common Pitfalls

- Database collapses (all programs similar) → increase island count or mutation diversity
- Too aggressive elimination → lose useful building blocks; increase `population_size`
- No improvement → check if sampling always picks the same parent; increase `samples_per_prompt`

## 4. Acceptance Criteria

- Database stratification visible (programs in different score buckets)
- High-score programs repeatedly used as mutation parents (exploitation)
- Periodic sampling from lower buckets (exploration)
- Clear elimination of consistently low-scoring programs
- Final best program in top database bucket