python3 <<'PY'
import math
a=0.25; b=1.0/12
def oneA(t):
    y1=3*t-2/3; al=2*a+2*b-y1-t; mu1=a+b-y1; mu2=b+a-t; nu1=a+b
    r1=mu1/al; r2=mu2/al; s1=nu1/al; s3=1-s1
    return al*(math.sqrt(a*r1*s1)+math.sqrt(b*r1*s3)+math.sqrt(b*r2*s1)+math.sqrt(a*r2*s3))
def Aval(y1,y2,q,r):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; nu1=a+b; q2=alpha-q
    if q<=0 or q2<=0: return -1
    lo=max(0.0,q-(alpha-mu1)); hi=min(q,mu1)
    if r<lo-1e-12 or r>hi+1e-12: 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-10 or c>q+1e-10 or c>nu1+1e-10 or nu1-c>q2+1e-10: return -1
    r2=mu1-r; c2=nu1-c
    return (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)))+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))))
def best2(y1,y2,N=300):
    alpha=2*a+2*b-y1-y2; mu1=a+b-y1; mu2=alpha-mu1
    best=-1
    for iq in range(1,N):
      q=alpha*iq/N
      lo=max(0.0,q-mu2); hi=min(q,mu1)
      for ir in range(N+1):
        r=lo+(hi-lo)*ir/N
        v=Aval(y1,y2,q,r)
        if v>best: best=v
    return best
for t in [0.228,0.229,0.230,0.23045,0.231,0.232,0.233,0.234,0.235,0.24]:
  y1=3*t-2/3; y2=t
  print(t,oneA(t),best2(y1,y2,150),"gap",best2(y1,y2,150)-oneA(t))
PY