Rationalization and subtractive cancellation
Measure loss of precision in sqrt(x+1)-sqrt(x) at x=10^16 and compare an algebraically rationalized expression with a high-precision reference.
Proposed original example. Source release and any execution are separate steps.
How much error is removed by changing the expression while preserving its exact-arithmetic meaning?
Use 80-digit Decimal square roots for the exact integer input and retain both float errors.
What you could produce
- A scoped observations JSON record and a comparison with the stated reference.
Before you use it
- Python 3.13 standard library
Limits to keep in view
- No research code was executed by the preparation tool.
- Author output cannot issue an independent scientific-verification result.
Source and permission context
Original local preparation by the Executable Science seed collection; upstream API references remain separately attributed.
Catalog listing reviewed. This review covers the description and source links displayed here.
Local draft title, collective byline, original summary, and proposed split terms reviewed.
Reviewed 2026-09-14. Copying or adapting source files remains subject to their own terms.
Before copying source material
- Proposed local-draft licenses: original code MIT, explanations CC-BY-4.0, synthetic numeric data CC0-1.0; publication/disclosure approval remains separate.
Put this resource to work.
Find a numerical failure before trusting an experiment
Does an apparently sensible floating-point answer survive a separately formulated reference calculation?
Prepare controls for an interpretability claim
Does a proposed attribution or activation-based conclusion survive its stated baseline, precision and intervention controls?