order-spread

At its defaults it draws multiply-adds in three contraction networks, under the cheapest, greedy and dearest evaluation order. Every bar is an exact count and every order returns the same numbers: nothing is approximated anywhere on this picture. The matrix chain's orders run from 15,125 to 512,793,750, a factor of 3.39·10⁴. The inner product of two trains with 5 cores runs from 3,344 to 6.581·10⁹ — a factor of 1.968·10⁶, because its worst order forms the whole tensor the trains represent. The alternating-least-squares step runs from 105,120 to 113,040, a factor of 1.075, which is the counterweight: on that network the search is not worth running, and nothing about the shape of it says so in advance.

order-spread is one function in lib/figures/contract.js — contraction order — one expression, one value, and orders that differ by two million. 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.

Every bar is an exact count and every order returns the same numbers: nothing is approximated anywhere on this picture. The matrix chain's orders run from 15,125 to 512,793,750, a factor of 3.39·10⁴. The inner product of two trains with 5 cores runs from 3,344 to 6.581·10⁹ — a factor of 1.968·10⁶, because its worst order forms the whole tensor the trains represent. The alternating-least-squares step runs from 105,120 to 113,040, a factor of 1.075, which is the counterweight: on that network the search is not worth running, and nothing about the shape of it says so in advance.

Every bar is an exact count and every order returns the same numbers: nothing is approximated anywhere on this picture. The matrix chain's orders run from 15,125 to 512,793,750, a factor of 3.39·10⁴. The inner product of two trains with 5 cores runs from 3,344 to 6.581·10⁹ — a factor of 1.968·10⁶, because its worst order forms the whole tensor the trains represent. The alternating-least-squares step runs from 105,120 to 113,040, a factor of 1.075, which is the counterweight: on that network the search is not worth running, and nothing about the shape of it says so in advance.

Every bar is an exact count and every order returns the same numbers: nothing is approximated anywhere on this picture. The matrix chain's orders run from 15,125 to 512,793,750, a factor of 3.39·10⁴. The inner product of two trains with 4 cores runs from 2,320 to 5.141·10⁷ — a factor of 2.216·10⁴, because its worst order forms the whole tensor the trains represent. The alternating-least-squares step runs from 105,120 to 113,040, a factor of 1.075, which is the counterweight: on that network the search is not worth running, and nothing about the shape of it says so in advance.

Every bar is an exact count and every order returns the same numbers: nothing is approximated anywhere on this picture. The matrix chain's orders run from 15,125 to 512,793,750, a factor of 3.39·10⁴. The inner product of two trains with 3 cores runs from 1,296 to 4.014·10⁵ — a factor of 309.7, because its worst order forms the whole tensor the trains represent. The alternating-least-squares step runs from 105,120 to 113,040, a factor of 1.075, which is the counterweight: on that network the search is not worth running, and nothing about the shape of it says so in advance.

Every bar is an exact count and every order returns the same numbers: nothing is approximated anywhere on this picture. The matrix chain's orders run from 15,125 to 512,793,750, a factor of 3.39·10⁴. The inner product of two trains with 6 cores runs from 4,368 to 8.424·10¹¹ — a factor of 1.928·10⁸, because its worst order forms the whole tensor the trains represent. The alternating-least-squares step runs from 105,120 to 113,040, a factor of 1.075, which is the counterweight: on that network the search is not worth running, and nothing about the shape of it says so in advance.

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.

7 distinct claims across 5 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 146 of 287 generators — 131 print a residual and 15 are exempt with a published reason; 141 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.