python3 -c "from math import exp
M=[[0,-1,1,-2],[0,2,1,0],[0,0,2,-1],[-2,-1,2,-1]]
N=[[0,2,-1,-2],[-1,-2,-2,-2],[1,2,-2,2],[1,1,0,-1]]
def sm(z):
 e=[exp(x) for x in z]
 d=sum(e)
 return [x/d for x in e]
cs=[0.25,0.0625,-11/256,-175/3072,-109/8192,20891/491520,1791037/47185920,-3663851/264241152]
for t in [0.01,0.02,0.05,0.1]:
 u=[0.25]*4
 v=[0.25]*4
 for it in range(200):
  u=sm([t*sum(M[i][j]*v[j] for j in range(4)) for i in range(4)])
  v=sm([t*sum(u[i]*N[i][j] for i in range(4)) for j in range(4)])
 pred=sum(cs[k]*t**k for k in range(8))
 print(t,u[2],pred,u[2]-pred)"