python3 - <<'PY'
import math
ln2=math.log(2)
def f(x): return 0.0 if x<=0 else -x*math.log(x)/ln2
def H(x): return f(x)+f(1-x)
def obj(v):
    u,al,be,ga,de,s=v
    if min(u,al,be,ga,de,s)<0 or max(al,be,ga,de,s)>1: return 1e9
    den=ga*de
    if den<1e-12: return 1e9
    w=(3-u*al*be)/den
    if w<-1e-9: return 1e9
    w=max(w,0)
    b12=u*al*(1-be)+w*ga*(1-de);b21=u*(1-al)*be+w*(1-ga)*de;b22=u*(1-al)*(1-be)+w*(1-ga)*(1-de)
    if b12>3+1e-9 or b21>1+1e-9 or b22>1+1e-9: return 1e9
    A1=3-b12;C1=1-b21;R=1-b22;A2=s*R;C2=(1-s)*R
    pA=9+A1+A2;pC=3+C1+C2
    HX=(pA/20)*(f(9/pA)+f(A1/pA)+f(A2/pA))+(u/20)*H(al)+(w/20)*H(ga)
    HY=(u/20)*H(be)+(w/20)*H(de)+(pC/20)*(f(3/pC)+f(C1/pC)+f(C2/pC))
    return 2.1822287-HX-HY
def golden(fun,a,b,tol=1e-12):
    g=(math.sqrt(5)-1)/2;c=b-g*(b-a);d=a+g*(b-a);fc=fun(c);fd=fun(d)
    while b-a>tol:
        if fc<fd: b,d,fd=d,c,fc;c=b-g*(b-a);fc=fun(c)
        else: a,c,fc=c,d,fd;d=a+g*(b-a);fd=fun(d)
    return (a+b)/2
r=0.7700601662472418;b=0.765705560601773;c=3.603953227159927
pB=3/r+b;al=(3/r)/pB;be=r;a=5-b-c;R=1-b*(1-r);s=a/R
v=[pB,al,be,0.7,0.7,s]
print('start',obj(v),v)
for it in range(25):
    for j in range(6):
        st=[0.5,0.05,0.05,0.2,0.2,0.1][j]
        lo=max(0.0001,v[j]-st);hi=min(0.9999,v[j]+st)
        def g(x,j=j): vv=v.copy();vv[j]=x;return obj(vv)
        v[j]=golden(g,lo,hi)
print('end',obj(v),v)
PY