only recompute what is affected by the state change at some
position. Complexity is still quadratic from having to sample from all
positions, but the constant is about 300 times better than last commit.

> df <- data.frame(n = c(10000,13000,20000,23000,30000), t = c(5.03,7.53,16.84,21.58,36.12)) ; fit <- lm(t ~ I(n ^ 2), data = df) ; summary(fit)

Call:
lm(formula = t ~ I(n^2), data = df)

Residuals:
       1        2        3        4        5
 0.05330 -0.13314  0.18311 -0.09938 -0.00389

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.083e+00  1.161e-01   9.335   0.0026 **
I(n^2)      3.893e-08  2.286e-10 170.301 4.46e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.146 on 3 degrees of freedom
Multiple R-squared:  0.9999,	Adjusted R-squared:  0.9999
F-statistic: 2.9e+04 on 1 and 3 DF,  p-value: 4.464e-07