from FuncDesigner import *
x = oovar()
f = sin(x + 5000000)/(x+5000000)
S = 10000000
cons = [x>=0, x<=S]
startPoint = {x:0.1}
S = oosystem()
r = S.minimize(f, startPoint, solver='interalg', fTol = 0.000000001, constraints = cons, iprint = -1)
print('value %e  at point %e' %(r.ff, r(x)))
# obvious upper bound:
# sin(x+ 5000000)<=1, x+5000000 >= 5000000, thus sin(x + 5000000)/(x+5000000) <= 1.0/5000000
# in the same way sin(x + 5000000)/(x+5000000) >= -1.0/5000000
print(1.0/5000000 - abs(r.ff))

# maximization:
#value 1.994124e-07  at point 7.317041e+03
#[  5.87598607e-10]
# minimization:
#value -1.991849e-07  at point 1.143669e+03
#[  8.15073300e-10]
# distances to analitically calculated guaranteed bounds less than 1e-9,
# and distance to exact optimum is even less