◆ advanced25 mindraft

Buying an order for free

Richardson extrapolation cancels the leading error term algebraically. Complex-step differentiation removes the subtraction entirely, and with it the whole roundoff branch.

assumes you already have

Differentiating a function you can only sample

Planned outline

Richardson: combine D(h) and D(h/2) so the leading h^p term cancels.
Building a Romberg-style tableau, and where it stops helping.
Complex-step: expand along the imaginary axis, take the imaginary part, never subtract.
Why complex step needs f to be analytic and generically implemented.
How both relate to automatic differentiation, which supersedes them for instrumented code.

Interactives planned

Each numbered point above gets at least one thing you can manipulate, not a figure. See AGENTS.md for the widget vocabulary and the rule that every lesson ships at least one graded interaction and one recall card.