def MullerSolve(fx,x0,x1,x2,err1,err2,N):
    count = 0
    f0 = fx(x0)
    f1 = fx(x1)
    f2 = fx(x2)
    q = (x2 - x1) / (x1 - x0)
    p = 0
    a = 0
    b = 0
    c = 0
    while True:
        p = (x2 - x0) / (x1 - x0)

        a = q**2 * f0 - q*p*f1 + q*f2
        b = q**2 *f0 - p**2 *f1 + (p + q)*f2
        c = p*f2
        h1 = 0
        if b < 0:
            h1 = -2 * c / (b - (b**2 - 4*a*c)**0.5)
        else:
            h1 = -2 * c / (b + (b**2 - 4*a*c)**0.5)
        x3 = x2 + h1 * (x2 - x1)
        f3 = fx(x3)

        print(f"k={count}: x{count}={x0:.5}, f(x{count})={f0:.5}; x{count+1}={x1:.5}, f(x{count+1})={f1:.5}; x{count+2}={x2:.5}, f(x{count+2})={f2:.5}; x{count+3}={x3:.5}, f(x{count+3})={f3:.5}")
        print(f"p={p:.5}, q={q:.5}, a={a:.5}, b={b:.5}, c={c:.5}, h={h1:.5}")

        k = err1 + 1
        if abs(f3) < 1:
            k = abs(x3 - x2)
        else:
            k = abs(x3 - x2) / abs(f3)

        if abs(f3) < err2 or k < err1:
            return x3, 1
        count += 1
        if count > N:
            return None, 0
        x0 = x1
        x1 = x2
        x2 = x3
        f0 = f1
        f1 = f2
        f2 = f3
        q = h1


if __name__ == "__main__":
    err1 = 1e-5
    err2 = 1e-5
    N = 100

    x0 = 0.3
    x1 = 0.5
    x2 = 0.4
    fx = lambda x: 8*x**4 - 8*x**2 + 1

    result, status = MullerSolve(fx, x0, x1, x2, err1, err2, N)
    if status == 1:
        print(f"fx收敛 解为: {result}")
    else:
        print("fx不收敛")