# set terminal png transparent nocrop enhanced font arial 8 size 420,320 
# set output 'bivariat.6.png'
set key 4, -3, 0 Right noreverse noinvert enhanced box linetype -2 linewidth 1.000 samplen 4 spacing 1 width 0 height 0 autotitles
set title "Min(x,y) and Max(x,y)" 0.000000,0.000000  font ""
set xrange [ -5.00000 : 5.00000 ] noreverse nowriteback
set yrange [ -10.0000 : 10.0000 ] noreverse nowriteback
f(x)=sin(x-1)-.75*sin(2*x-1)+(x**2)/8-5
integral_f(x) = (x>0)?integral1a(x):-integral1b(x)
integral1a(x) = (x<=0)?0:(integral1a(x-delta)+delta*f(x))
integral1b(x) = (x>=0)?0:(integral1b(x+delta)+delta*f(x))
integral2_f(x,y) = (x<y)?integral2(x,y):-integral2(y,x)
integral2(x,y) = (x>y)?0:(integral2(x+delta,y)+delta*f(x))
ack(m,n) = (m == 0) ? n + 1 : (n == 0) ? ack(m-1,1) : ack(m-1,ack(m,n-1))
min(x,y) = (x < y) ? x : y
max(x,y) = (x > y) ? x : y
delta = 0.2
plot sin(x), x**2, x**3, max(sin(x), min(x**2, x**3))+0.5