bound-tightness

At its defaults it draws the proved bound against the error it bounds, at 24 significand bits. Two curves against the Hilbert size on a logarithmic vertical axis: the error the computation actually made, which is known because the exact answer is the integers by construction, and the bound proved for it in interval arithmetic. The bound is above the error at every size, by 9.949 to 23.12 times. Past n = 5 the method refuses to return a bound at all.

bound-tightness is one function in lib/figures/interval.js — intervals — a bound that is proved rather than measured, and what proving it costs. 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.

Two curves against the Hilbert size on a logarithmic vertical axis: the error the computation actually made, which is known because the exact answer is the integers by construction, and the bound proved for it in interval arithmetic. The bound is above the error at every size, by 9.949 to 23.12 times. Past n = 5 the method refuses to return a bound at all.

Two curves against the Hilbert size on a logarithmic vertical axis: the error the computation actually made, which is known because the exact answer is the integers by construction, and the bound proved for it in interval arithmetic. The bound is above the error at every size, by 9.949 to 23.12 times. Past n = 5 the method refuses to return a bound at all.

Two curves against the Hilbert size on a logarithmic vertical axis: the error the computation actually made, which is known because the exact answer is the integers by construction, and the bound proved for it in interval arithmetic. The bound is above the error at every size, by 8.174 to 2822 times. Past n = 7 the method refuses to return a bound at all.

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.

10 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 52 of 99 generators — 37 print a residual and 15 are exempt with a published reason; 47 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.