set terminal png small color
set output 'newer_costs.png'
set xlabel "Index tuples"
set ylabel "Added cost"
set logscale x
set logscale y
fo = 256.0
h(x) = (x <= fo) ? 0 : (x <= fo*fo) ? 1 : (x <= fo*fo*fo) ? 2 : (x <= fo*fo*fo*fo) ? 3 : (x <= fo*fo*fo*fo*fo) ? 4 : 5
head(x) = 4*log(1 + (x/fo)/10000) + 0.25
historical(x) = 4 * (x/fo)/100000 + 0.25
ninepoint2(x) = 4 * (x/fo)/10000 + 0.25
plot [10:1e9][0.1:10] 0.0025*(ceil(log(x)/log(2))) + 0.125*(h(x)+1), head(x), historical(x), ninepoint2(x)