Original examples

Finite-difference step-size sensitivity

Sweep sixteen step sizes for forward and central differentiation of exp(x) at zero, exposing truncation and rounding behavior against the analytical derivative.

Proposed original example. Source release and any execution are separate steps.

A QUESTION TO TAKE FURTHER

How does derivative error change across a fixed grid of shrinking step sizes?

Compare all estimates with the analytical value one; retain the full prespecified sweep rather than reporting only the best step.

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.

Put this resource to work.

RESEARCH BRIEF · 7 SOURCES

Separate a solver's stopping signal from solution accuracy

When does a tiny residual or smaller step fail to imply a more accurate scientific result?

Open the brief