Could AccumBounds use maximum/minimum?

[asmeurer]

We have

>>> limit(sin(x) + cos(x), x, oo)
AccumBounds(-2, 2)

But it is actually limited by +/-sqrt(2). The maximum and minimum functions can compute this:

>>> maximum(sin(x) + cos(x), x)
sqrt(2)
>>> minimum(sin(x) + cos(x), x)
-sqrt(2)

Can we use this in the general case?

Also, sin(oo) + cos(oo) has the same problem, but fixing that would be harder, because it's basically AccumBounds(1, 1) + AccumBounds(1, 1).

[oscarbenjamin]

Perhaps related is a recent SO question asking to be able to merge linear combinations of sin and cos having the same frequency but different amplitude and phase. There doesn't seem to be a sympy function for that:
https://stackoverflow.com/questions/64481861/python-sympy-superposition-of-several-waves

[asmeurer]

minimum and maximum just take the derivative and set it equal to 0. But I guess it fails for more complicated examples, like the one in the SO question. So maybe such a function could be used inside of solve to help it there, if it isn't good enough for such cases already. Or maybe there's a more general way to improve solve.