python3 <<'PY'
import math
a=0.25; b=1.0/12
def F(x,y):
    return math.sqrt(a)*(math.sqrt(x*y)+math.sqrt((1-x)*(1-y)))+math.sqrt(b)*(math.sqrt(x*(1-y))+math.sqrt((1-x)*y))
def BC(y1,y2):
    best=-1; by=None
    for j in range(1001):
      y3=a*j/1000
      beta=a+b-y3
      B=math.sqrt(beta)*(b+math.sqrt(max(0,a*(a-y3))))
      gam=y1+y2+y3
      C=math.sqrt(gam)*(math.sqrt(max(0,b*y1))+math.sqrt(max(0,a*y2))+math.sqrt(max(0,a*y3)))
      if B+C>best: best=B+C; by=y3
    return best,by
best=-1; arg=None
for i in range(101):
  y1=b*i/100
  for j in range(101):
    y2=a*j/100
    al=2*a+2*b-y1-y2
    x=(a+b-y1)/al; y=(a+b)/al
    Aub=al*F(x,y)
    bc,by=BC(y1,y2)
    u=Aub+bc
    if u>best: best=u; arg=(y1,y2,x,y,Aub,bc,by)
print("bestUB",best,arg,"cost",1-best)
PY