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set terminal png small color
set output 'new_costs.png'
set xlabel "Index tuples"
set ylabel "Added cost"
set logscale x
set logscale y
h(x) = (x <= 256.0) ? 0 : (x <= 256.0*256) ? 1 : (x <= 256.0*256*256) ? 2 : (x <= 256.0*256*256*256) ? 3 : (x <= 256.0*256*256*256*256) ? 4 : 5
head(x) = 4*log(1 + x/10000) + 0.25
historical(x) = 4 * x/100000 + 0.25
ninepoint2(x) = 4 * x/10000 + 0.25
plot [10:1e9][0.1:10] 0.0025*log(x)/log(2) + 0.125*(h(x)+2), head(x), historical(x), ninepoint2(x)