def f(x):
    return (x-1.)*(x-2.)*(x-3.)*(x-4.)*(x-5.)

a, b, c = 2.4, 2.5, 3.4
fa, fb, fc = f(a), f(b), f(c)

for step in range(50):

    R, S, T  = fb/fc, fb/fa, fa/fc
    P  = S*(T*(R-T)*(c-b)-(1.-R)*(b-a))
    Q  = (T-1.)*(R-1.)*(S-1.)

    d  = b + P/Q
    fd = f(d)

    if (d-a)*(d-c)>0. or abs(fd)>abs(fb):
        if fa*fb>0.: d = (b+c)*0.5
        else:        d = (a+b)*0.5
        fd = f(d)

    print('Step: %2d, root = %.16f, diff = %.16f' % (step,d,abs(d-3.)))

    if abs(b-d)<1E-14: break

    if fa*fb>0.:
        a, fa = b, fb
        b, fb = d, fd
    else:
        c, fc = b, fb
        b, fb = d, fd