python3 <<'PY'
import math
a=0.25; b=1.0/12
def Aub(y1,y2):
    al=2*a+2*b-y1-y2
    return math.sqrt(al)*(a+b+math.sqrt(max(0,b*(b-y1)))+math.sqrt(max(0,a*(a-y2))))
def BC(y1,y2):
    best=-1; by=None
    for j in range(201):
      y3=a*j/200
      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(51):
  y1=b*i/50
  for j in range(51):
    y2=a*j/50
    u=Aub(y1,y2)
    bc,by=BC(y1,y2)
    t=u+bc
    if t>best: best=t; arg=(y1,y2,u,bc,by)
print("bestUB",best,arg,"cost",1-best)
PY