# Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning

arXiv: https://arxiv.org/abs/2306.02408 · HTML: https://mlsanity.com/paper/2306.02408/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 57 references that are in the map.
- First posted on arXiv 4 Jun 2023.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [StructGPT: A General Framework for Large Language Model to Reason over Structured Data](https://mlsanity.com/paper/2305.09645/) (2023)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [TALM: Tool Augmented Language Models](https://mlsanity.com/paper/2205.12255/) (2022)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [Limitations of Language Models in Arithmetic and Symbolic Induction](https://mlsanity.com/paper/2208.05051/) (2022)
- [ChatCoT: Tool-Augmented Chain-of-Thought Reasoning on Chat-based Large Language Models](https://mlsanity.com/paper/2305.14323/) (2023)
- [JiuZhang: A Chinese Pre-trained Language Model for Mathematical Problem Understanding](https://mlsanity.com/paper/2206.06315/) (2022)

## Built on by (most cited first, 30 of 49)

- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Tool Learning with Large Language Models: A Survey](https://mlsanity.com/paper/2405.17935/) (2024)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [Building Math Agents with Multi-Turn Iterative Preference Learning](https://mlsanity.com/paper/2409.02392/) (2024)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [ChatGLM-Math: Improving Math Problem-Solving in Large Language Models with a Self-Critique Pipeline](https://mlsanity.com/paper/2404.02893/) (2024)
- [From Exploration to Mastery: Enabling LLMs to Master Tools via Self-Driven Interactions](https://mlsanity.com/paper/2410.08197/) (2024)
- [JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models](https://mlsanity.com/paper/2405.14365/) (2024)
- [Evaluating Mathematical Reasoning of Large Language Models: A Focus on Error Identification and Correction](https://mlsanity.com/paper/2406.00755/) (2024)
- [Improving Large Language Models via Fine-grained Reinforcement Learning with Minimum Editing Constraint](https://mlsanity.com/paper/2401.06081/) (2024)
- [CapRL: Stimulating Dense Image Caption Capabilities via Reinforcement Learning](https://mlsanity.com/paper/2509.22647/) (2025)
- [Leveraging Online Olympiad-Level Math Problems for LLMs Training and Contamination-Resistant Evaluation](https://mlsanity.com/paper/2501.14275/) (2025)
- [FFT: Towards Harmlessness Evaluation and Analysis for LLMs with Factuality, Fairness, Toxicity](https://mlsanity.com/paper/2311.18580/) (2023)
- [Causal Evaluation of Language Models](https://mlsanity.com/paper/2405.00622/) (2024)
- [UrbanKGent: A Unified Large Language Model Agent Framework for Urban Knowledge Graph Construction](https://mlsanity.com/paper/2402.06861/) (2024)
- [CATP-LLM: Empowering Large Language Models for Cost-Aware Tool Planning](https://mlsanity.com/paper/2411.16313/) (2024)
- [Adapting Large Language Models for Education: Foundational Capabilities, Potentials, and Challenges](https://mlsanity.com/paper/2401.08664/) (2023)
- [Differential Transformer](https://mlsanity.com/paper/2410.05258/) (2024)
- [DnA-Eval: Enhancing Large Language Model Evaluation through Decomposition and Aggregation](https://mlsanity.com/paper/2405.15329/) (2024)
- [RealCritic: Towards Effectiveness-Driven Evaluation of Language Model Critiques](https://mlsanity.com/paper/2501.14492/) (2025)
- [Accurate and Regret-aware Numerical Problem Solver for Tabular Question Answering](https://mlsanity.com/paper/2410.12846/) (2024)
- [Beyond the Safety Bundle: Auditing the Helpful and Harmless Dataset](https://mlsanity.com/paper/2411.08243/) (2024)
- [Efficient numeracy in language models through single-token number embeddings](https://mlsanity.com/paper/2510.06824/) (2025)
- [PDE-Agent: A toolchain-augmented multi-agent framework for PDE solving](https://mlsanity.com/paper/2512.16214/) (2025)
- [Multimodal Multi-Hop Question Answering Through a Conversation Between Tools and Efficiently Finetuned Large Language Models](https://mlsanity.com/paper/2309.08922/) (2023)

## Abstract (arXiv)

Chain-of-thought prompting~(CoT) and tool augmentation have been validated in recent work as effective practices for improving large language models~(LLMs) to perform step-by-step reasoning on complex math-related tasks. However, most existing math reasoning datasets may be not able to fully evaluate and analyze the ability of LLMs in manipulating tools and performing reasoning, as they may only require very few invocations of tools or miss annotations for evaluating intermediate reasoning steps. To address the issue, we construct CARP, a new Chinese dataset consisting of 4,886 computation-intensive algebra problems with formulated annotations on intermediate steps. In CARP, we test four LLMs with CoT prompting, and find that they are all prone to make mistakes at the early steps of the solution, leading to wrong answers. Based on this finding, we propose a new approach that can deliberate the reasoning steps with tool interfaces, namely DELI. In DELI, we first initialize a step-by-step solution based on retrieved exemplars, then iterate two deliberation procedures that check and refine the intermediate steps of the generated solution, from the perspectives of tool manipulation and natural language reasoning, until obtaining converged solutions or reaching the maximum turn. Experimental results on CARP and six other datasets show that the proposed DELI mostly outperforms competitive baselines, and can further boost the performance of existing CoT methods. Our data and code are available in urlhttps://github.com/RUCAIBox/CARP.