Odyssey: An Interactive Workbench for Expert-Driven Floating-Point Expression Rewriting

Title of the Paper

Odyssey: An Interactive Workbench for Expert-Driven Floating-Point Expression Rewriting

Paper Information

• Domain: Floating-point mathematical expression rewriting and visualization development tools
• Keywords: Floating-point computation, expert programming, debugging, development tools, expression rewriting, dynamic analysis

Research Background and Problem Statement

• Identified Problems or Challenges:

  1. Floating-point computations are widely used in scientific, engineering, and graphical applications, but rounding errors in floating-point numbers can lead to results that significantly deviate from actual values.
  2. Although automated tools (e.g., Herbie) exist to identify and improve rounding errors in floating-point expressions, users often find it challenging to effectively utilize these tools, especially when specifying goals, interpreting results, and conducting independent exploration.
  3. Current tools often neglect multi-source comparisons for expression rewriting, resulting in complex outputs that lack user trust.

• Significance: Rounding errors in floating-point numbers can lead to irreproducible scientific research, deviations in financial market indices, and even severe consequences in military applications. Therefore, accurately diagnosing and correcting such errors is critical for ensuring the reliability of results in these fields.

• Research Motivation and Related Work:

  1. Existing tools (e.g., Herbie) adopt automated methods to rewrite floating-point expressions but still have shortcomings in terms of user experience and accuracy.
  2. Analysis tools related to floating-point computations include error analysis, dynamic analysis, and code optimization. Combining these functionalities with user-interactive tools could provide a more comprehensive solution.

Proposed Solution

• Proposed Solution: Develop a new interactive workbench, Odyssey, enabling users to analyze and optimize floating-point expressions through a three-stage workflow (diagnosing issues, generating solutions, optimizing results).

• Innovations:

  1. Provides interactive error diagnosis tools, including local error heatmaps and range adjustments.
  2. Supports the collection and management of expression rewrites from multiple sources (e.g., automated tools, manual user input, and other references).
  3. Offers real-time error feedback for expressions, helping users optimize and adjust branch conditions to avoid rounding errors.

• Implementation Steps and Key Techniques:

  1. Problem Diagnosis: Use error visualization tools (e.g., local error heatmaps) to highlight problematic expressions and identify specific erroneous operations.
  2. Solution Generation: Integrate with Herbie to allow users to generate rewritten expressions or manually input expressions with immediate error feedback.
  3. Result Optimization: Achieve better performance and error characteristics by adjusting expression branch conditions and specific parameters; supports multi-expression comparison and branch rewriting.

Research Outcomes

• Specific Outcomes:

  1. Developed an integrated workbench that significantly improves the efficiency of floating-point expression analysis through user interaction and convenient tool integration.
  2. In user testing, various floating-point experts using Odyssey successfully solved 5 out of 7 real-world problems and expressed widespread appreciation for the tool's visualization capabilities.

• Advantages Over Existing Solutions:

  1. Odyssey significantly improves the interactivity of expression rewriting, addressing the shortcomings of existing tools in terms of analysis speed and user engagement.
  2. Provides adjustable and real-time feedback mechanisms, allowing experts to focus on creative problem-solving rather than tool limitations.

• Experimental and Evaluation Results:

  1. Expert users demonstrated efficient analysis and improvement of expression issues during experiments, with an average ability to quickly complete multiple tasks.
  2. Survey results showed unanimous agreement among experts that Odyssey effectively aids in identifying problems, generating new solutions, and mixing and optimizing expressions.

• Limitations and Future Directions:

  1. The tool's implementation requires further technical refinement, such as interface layout improvements and more advanced expression editing support.
  2. Future plans include expanding integration with multi-source analysis tools, supporting multi-precision expressions, and advanced features like operation cost analysis.
  3. Exploration of leveraging language models (e.g., GPT) to generate expression rewrites and error explanations to further enhance the tool's intelligence.