def test_SumApprox_monotone_terms():
x, y, z = symbols('x y z')
expr1 = exp(z) * (x**2 + y**2 + 1)
bnds1 = {x: (0, 1e-3), y: (100, 1000)}
sum_approx_m2 = SumApprox(bounds=bnds1, reltol=1e-2)
sum_approx_m5 = SumApprox(bounds=bnds1, reltol=1e-5)
sum_approx_m11 = SumApprox(bounds=bnds1, reltol=1e-11)
assert (optimize(expr1, [sum_approx_m2]) / exp(z) - (y**2)).simplify() == 0
assert (optimize(expr1, [sum_approx_m5]) / exp(z) -
(y**2 + 1)).simplify() == 0
assert (optimize(expr1, [sum_approx_m11]) / exp(z) -
(y**2 + 1 + x**2)).simplify() == 0
def test_SumApprox_trivial():
x = symbols('x')
expr1 = 1 + x
sum_approx = SumApprox(bounds={x: (-1e-20, 1e-20)}, reltol=1e-16)
apx1 = optimize(expr1, [sum_approx])
assert apx1 - 1 == 0