replacement-repair

At its defaults it draws what residual replacement costs and what it buys, at three periods. Each row is the same conjugate gradient run with the recomputed residual assigned back into the recurrence every k steps. Without it, the reported residual reaches 6.92·10⁻²¹ and the answer's stalls at 5.07·10⁻¹⁰. Replacing every 5 steps costs 30 extra matrix–vector products on top of 150 — 20 per cent — and brings the answer's residual to 8.31·10⁻¹⁷, with the two residuals then agreeing to a factor of 2.8.

replacement-repair is one function in lib/figures/resgap.js — residual gap — the number a method reports against the residual of its answer. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Each row is the same conjugate gradient run with the recomputed residual assigned back into the recurrence every k steps. Without it, the reported residual reaches 6.92·10⁻²¹ and the answer's stalls at 5.07·10⁻¹⁰. Replacing every 5 steps costs 30 extra matrix–vector products on top of 150 — 20 per cent — and brings the answer's residual to 8.31·10⁻¹⁷, with the two residuals then agreeing to a factor of 2.8.

Each row is the same conjugate gradient run with the recomputed residual assigned back into the recurrence every k steps. Without it, the reported residual reaches 6.92·10⁻²¹ and the answer's stalls at 5.07·10⁻¹⁰. Replacing every 5 steps costs 30 extra matrix–vector products on top of 150 — 20 per cent — and brings the answer's residual to 8.31·10⁻¹⁷, with the two residuals then agreeing to a factor of 2.8.

Each row is the same conjugate gradient run with the recomputed residual assigned back into the recurrence every k steps. Without it, the reported residual reaches 7.91·10⁻²¹ and the answer's stalls at 5.9·10⁻¹³. Replacing every 5 steps costs 30 extra matrix–vector products on top of 150 — 20 per cent — and brings the answer's residual to 9.15·10⁻¹⁷, with the two residuals then agreeing to a factor of 1.5.

Every figure above asserted its own claims on the way to being drawn, and a claim that failed would have failed the build rather than drawn a wrong picture. Those assertions used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

6 distinct claims across 3 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.

Across the library: the rule bites on 113 of 238 generators — 98 print a residual and 15 are exempt with a published reason; 125 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.