python3 <<'PY'
import math,random
a=0.25; b=1.0/12
def cval(y1,y2,q,r):
    mu1=a+b-y1
    nu1=a+b
    alpha=2*a+2*b-y1-y2
    den=r*(alpha-q)/q-(mu1-r)
    if abs(den)<1e-13: return None
    c=(a*(alpha-q)-(mu1-r)*nu1)/den
    return c
def Aval(y1,y2,q,r,c):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; nu1=a+b; q2=alpha-q; r2=mu1-r; c2=nu1-c
    t1=math.sqrt(a*r*c)+math.sqrt(b*r*(q-c))+math.sqrt(b*(q-r)*c)+math.sqrt(a*(q-r)*(q-c))
    t2=math.sqrt(a*r2*c2)+math.sqrt(b*r2*(q2-c2))+math.sqrt(b*(q2-r2)*c2)+math.sqrt(a*(q2-r2)*(q2-c2))
    return t1/math.sqrt(q)+t2/math.sqrt(q2)
def G(y1,y2,q,r):
    c=cval(y1,y2,q,r)
    if c is None: return -1
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; nu1=a+b; q2=alpha-q
    if q<=0 or q2<=0 or r<-1e-9 or r>q+1e-9 or r>mu1+1e-9 or (q-r)>(alpha-mu1)+1e-9 or c<-1e-9 or c>q+1e-9 or c>nu1+1e-9 or (nu1-c)>q2+1e-9: return -1
    y3=a
    gam=y1+y2+y3
    C=math.sqrt(gam)*(math.sqrt(b*y1)+math.sqrt(a*y2)+math.sqrt(a*y3))
    B=b**1.5
    return Aval(y1,y2,q,r,c)+B+C
print("noC",G(0,0,0.375,0.125))
print("full",G(b,a,1/3,a))
best=-1; arg=None
for it in range(200000):
  y1=random.random()*b; y2=random.random()*a
  alpha=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=alpha-mu1
  q=random.uniform(1e-4,alpha-1e-4)
  lo=max(0.0,q-mu2); hi=min(q,mu1)
  if hi<lo: continue
  r=random.uniform(lo,hi)
  g=G(y1,y2,q,r)
  if g>best: best=g; arg=(y1,y2,q,r)
print("rand",best,arg,"1-best",1-best)
PY