python3 <<'PY'
import math,random
a=0.25; b=1.0/12
def G(y1,y2,q,r):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=b+a-y2; nu1=a+b
    q2=alpha-q
    if y1<-1e-9 or y1>b+1e-9 or y2<-1e-9 or y2>a+1e-9 or q<=1e-12 or q2<=1e-12: return -1
    lo=max(0.0,q-mu2); hi=min(q,mu1)
    if r<lo-1e-9 or r>hi+1e-9: return -1
    den=r*q2/q-(mu1-r)
    if abs(den)<1e-14: return -1
    c=(a*q2-(mu1-r)*nu1)/den
    if c<-1e-8 or c>q+1e-8 or c>nu1+1e-8 or nu1-c>q2+1e-8: return -1
    r2=mu1-r; c2=nu1-c
    t1=math.sqrt(max(0,a*r*c))+math.sqrt(max(0,b*r*(q-c)))+math.sqrt(max(0,b*(q-r)*c))+math.sqrt(max(0,a*(q-r)*(q-c)))
    t2=math.sqrt(max(0,a*r2*c2))+math.sqrt(max(0,b*r2*(q2-c2)))+math.sqrt(max(0,b*(q2-r2)*c2))+math.sqrt(max(0,a*(q2-r2)*(q2-c2)))
    C=math.sqrt(y1+y2+a)*(math.sqrt(b*y1)+math.sqrt(a*y2)+a)
    return t1+t2+b**1.5+C
t0=0.23045484476568612; y3=0.22112258331133355
y1c=3*t0-2/3
G0=G(y1c,t0,2*a+2*b-y1c-t0,(a+b-y1c))
print("G0",G0)
eps=1e-6
bestder=-1e9; bestdir=None
for _ in range(20000):
  a1=random.uniform(-20,20); a2=random.uniform(-20,20)
  d=random.random(); e=random.random()
  y1=y1c+a1*eps; y2=t0+a2*eps
  al=2*a+2*b-y1-y2; mu1=a+b-y1
  q=al-eps
  r=mu1-d*eps
  g=G(y1,y2,q,r)
  if g<0: continue
  der=(g-G0)/eps
  if der>bestder: bestder=der; bestdir=(a1,a2,d,e,g)
print("bestder",bestder,bestdir)
PY