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.
Rights need review. Review the scope and upstream conditions before reuse.
Still unresolved
- Proposed local-draft licenses: original code MIT, explanations CC-BY-4.0, synthetic numeric data CC0-1.0; publication/disclosure approval remains separate.
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