Multiplications in one product with the 3-dimensional Laplacian, assembled against reshaped

At its defaults it draws multiplications in one product with the 3-dimensional laplacian, assembled against reshaped. Both curves are exact counts rather than estimates. The assembled matrix has n^3 rows, so multiplying by it is n^6 multiplications; applying the 3 one-dimensional factors along their own indices is 3·n^4. The fitted slopes are 6.00 and 4.00 against 6 and 4 exactly. At n = 256 that is 2.81·10¹⁴ against 1.29·10¹⁰, a factor of 2.18·10⁴ — and the ratio is n^2, so it grows with every size rather than settling.

kron-cost is one function in lib/figures/tensor.js — an index that is a tuple — a matrix that is d small ones, and the inverse that is nearly one. 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.

Both curves are exact counts rather than estimates. The assembled matrix has n^3 rows, so multiplying by it is n^6 multiplications; applying the 3 one-dimensional factors along their own indices is 3·n^4. The fitted slopes are 6.00 and 4.00 against 6 and 4 exactly. At n = 256 that is 2.81·10¹⁴ against 1.29·10¹⁰, a factor of 2.18·10⁴ — and the ratio is n^2, so it grows with every size rather than settling.

Both curves are exact counts rather than estimates. The assembled matrix has n^2 rows, so multiplying by it is n^4 multiplications; applying the 2 one-dimensional factors along their own indices is 2·n^3. The fitted slopes are 4.00 and 3.00 against 4 and 3 exactly. At n = 256 that is 4.29·10⁹ against 3.36·10⁷, a factor of 128 — and the ratio is n^1, so it grows with every size rather than settling.

Both curves are exact counts rather than estimates. The assembled matrix has n^3 rows, so multiplying by it is n^6 multiplications; applying the 3 one-dimensional factors along their own indices is 3·n^4. The fitted slopes are 6.00 and 4.00 against 6 and 4 exactly. At n = 256 that is 2.81·10¹⁴ against 1.29·10¹⁰, a factor of 2.18·10⁴ — and the ratio is n^2, so it grows with every size rather than settling.

Both curves are exact counts rather than estimates. The assembled matrix has n^5 rows, so multiplying by it is n^10 multiplications; applying the 5 one-dimensional factors along their own indices is 5·n^6. The fitted slopes are 10.00 and 6.00 against 10 and 6 exactly. At n = 256 that is 1.21·10²⁴ against 1.41·10¹⁵, a factor of 8.59·10⁸ — and the ratio is n^4, so it grows with every size rather than settling.

Both curves are exact counts rather than estimates. The assembled matrix has n^6 rows, so multiplying by it is n^12 multiplications; applying the 6 one-dimensional factors along their own indices is 6·n^7. The fitted slopes are 12.00 and 7.00 against 12 and 7 exactly. At n = 256 that is 7.92·10²⁸ against 4.32·10¹⁷, a factor of 1.83·10¹¹ — and the ratio is n^5, so it grows with every size rather than settling.

Both curves are exact counts rather than estimates. The assembled matrix has n^4 rows, so multiplying by it is n^8 multiplications; applying the 4 one-dimensional factors along their own indices is 4·n^5. The fitted slopes are 8.00 and 5.00 against 8 and 5 exactly. At n = 256 that is 1.84·10¹⁹ against 4.4·10¹², a factor of 4.19·10⁶ — and the ratio is n^3, so it grows with every size rather than settling.

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.

3 distinct claims across 6 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 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.