# Towards a Deterministic Math Solver for Clinical Language Models

arXiv: https://arxiv.org/abs/2609.10728 · HTML: https://mlsanity.com/paper/2609.10728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Executable Code Actions Elicit Better LLM Agents](https://mlsanity.com/paper/2402.01030/) (2024)
- [Know Your Limits: A Survey of Abstention in Large Language Models](https://mlsanity.com/paper/2407.18418/) (2024)
- [MedCalc-Bench: Evaluating Large Language Models for Medical Calculations](https://mlsanity.com/paper/2406.12036/) (2024)
- [AgentMD: Empowering Language Agents for Risk Prediction with Large-Scale Clinical Tool Learning](https://mlsanity.com/paper/2402.13225/) (2024)
- [From Scores to Steps: Diagnosing and Improving LLM Performance in Evidence-Based Medical Calculations](https://mlsanity.com/paper/2509.16584/) (2025)
- [MeNTi: Bridging Medical Calculator and LLM Agent with Nested Tool Calling](https://mlsanity.com/paper/2410.13610/) (2024)
- [MedCalc-R1: Knowledge-Guided Reward Framework for Medical Mathematical Reasoning](https://mlsanity.com/paper/2608.08623/) (2026)
- [Humans and Large Language Models in Clinical Decision Support: A Study with Medical Calculators](https://mlsanity.com/paper/2411.05897/) (2024)

## Abstract (arXiv)

Large language models are unreliable at arithmetic, which is a problem for clinical calculators where a single numerical error changes the recommendation. The standard response is to hardcode each calculator as a validated function, one at a time. We test an alternative: the model does not calculate. Instead, it writes case-specific Python that a restricted local executor runs as a deterministic solver, and the model's task reduces to deciding how to use it. We evaluate this Program-Solve interface on MedCalc-Bench Verified (1,100 cases, 55 calculators) against direct model arithmetic and a hand-written 22-calculator library, using Qwen2.5-7B and Qwen2.5-32B-AWQ, after auditing the benchmark's formulas against current clinical guidelines and flagging 16 of 55 with version, use or coefficient concerns. With formulas and gold variables supplied and both routes reading the whole note, handing off to the solver is not a reliable advantage at 7B (75.31% against 72.02%, a paired +3.29 points with a 95% calculator-cluster interval of [-3.49, 10.38]) but is one at 32B (90.53% against 83.47%, +7.05 [0.47, 14.60], clear of zero). The hand-written library is exact on its 440 supported cases but abstains elsewhere (40.0% overall). Adding an executor thus helps some open-weight models more than others even under matched formula, variable and note access, and is not a substitute for verified formulas or reliable variable extraction either way.