Multiply-adds in three contraction networks, under the cheapest, greedy and dearest evaluation order
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.
At its defaults
Drawn even though every essay passes arguments — which on this site is every essay, at 100% of placements since the standard pass. A default nothing exercises is a trap for the next essay to call this with none, and this is the page where a default that has drifted from the figures around it becomes visible.
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.
d: 5
The arguments are the ones The order the products are taken in passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
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.
d: 6
The arguments are the ones The order the products are taken in passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
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.
What it checked while drawing
Every figure above checked its own claims on the way to being drawn, and a claim that failed
would have stopped the picture rather than shipped a wrong one. Those checks 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 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.
a train the network is built for
and the matrix chain's cheapest order is the textbook 15,125
and the worst order is not cheaper
nothing beats the exhaustive order on als-step
nothing beats the exhaustive order on chain
nothing beats the exhaustive order on train-inner
the train's inner product spans at least two orders of magnitude
Against the rule
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 217
of 397 generators —
199 print a residual and
18 are exempt with a published reason;
180 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.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.