import sympy, math
sympy.init_printing()

def secmin(f, g0, g1, g2):
    g = [g0, g1, g2]
    fs = [f(g0), f(g1), f(g2)]
    s = [None]
    while True:
        while len(s) < len(g):
            n = len(s)
            s.append((fs[n] - fs[n-1])/(g[n] - g[n-1]))
            
        if s[-1] == s[-2]:
            return
        
        gn = (g[-1] + g[-2] - s[-1] * (g[-1] - g[-3])/(s[-1] - s[-2]))/2
        if gn == g[-1]:
            return
        
        g.append(gn)
        fs.append(f(gn))
        yield g[-1], fs[-1]

for a in [3, -3, 5]:
    for b in [3, -1, -2, 6]:
        print("##", a, b)
        for gn, fn in secmin(lambda x: (x-a)*(x-b), 1, 2, 15):
            print(gn, fn)

k = lambda x: (x+1)*x*(x-1)
for gn, fn in secmin(k, .7, .8, .9):
    print(gn, fn)

.57735**2

x = sympy.symbols('x')
ks = k(x)
ks

ks.diff().simplify()

for gn, fn in secmin(k, .7, -.8, -.9):
    print(gn, fn)

gn+(1/3)**(1/2)

for i, (gn, fn) in enumerate(secmin(lambda x: (x+1)**3, 1, 2, 3)):
    print(i, gn, fn)

for gn, fn in secmin(lambda x: math.sin(2*math.sin(x*5)), 1, 2, 3):
    print(gn, fn)

math.sin(2*math.sin(2.3326063009*5))