import sys; sys.path.insert(0,'.')
import engine as E
from engine import A, iv
lo, hi = 1e9, -1e9
N = 200
for i in range(N):
    S = iv(A(i)/(300*N), A(i+1)/(300*N))
    v = E.P1_eval(S) + E.Mcomb_eval(S)
    rz = 2*E.BETA*(1+6*S)/E.GAMMA1
    lo = min(lo, float((v - rz).lower())); hi = max(hi, float((v + rz).upper()))
print("t>=300: analytic part in", lo, hi, "(+ non-analytic < 1e-19)")
S0 = A(0); v0 = E.P1_eval(S0)+E.Mcomb_eval(S0); print("s=0 value:", v0, " c0 =", 8 - E.SQ2*(8+4*E.LOG2+A(3)/4*E.LOG2**2))