import numpy as np
from sawtooth import history
rng=np.random.default_rng(131)
cp=(0,0,1); p=3
for rule in ("Rule 150","Rule 30"):
    ok=tot=0
    for _ in range(300):
        w=int(rng.integers(3,12)); s=rng.integers(0,2,size=w).astype(np.uint8); s[-1]=1
        T=1100
        if rule=="Rule 30":
            H=history(cp,s,T+p,depth=T+w+p+4); e=H[:,0]
        else:
            L=w+T+p+6; x=np.zeros(L,dtype=np.uint8); x[:w]=s; e=[]
            for t in range(T+p):
                e.append(int(x[0])); near=np.concatenate([[cp[t%p]],x[:-1]]); far=np.concatenate([x[1:],[0]]); x=far^x^near
            e=np.array(e)
        D=e[:T]^e[p:T+p]
        for m in (6,7,8,9):
            for r in range(0,(1<<m)-2*w-8):
                if r+(1<<m)<T: tot+=1; ok+=int(D[r]==D[r+(1<<m)])
    print(f"{rule}: Delta_1(r + 2^m) = Delta_1(r) in {100*ok/tot:.1f}% of cases")