Does anyone know a better way to evaluate dimension of the formula in python?

Question

Now, I have a formula with some symbols. These symbols have units. Does anyone know a python library to evaluate the dimension of the formula.

I checked sympy and pint. Sympy seems to be based on the unit system of physics, but what I want to deal with is general units like USD or KG. Sympy doesn't seem to define these. pint can define units by using UnitRegistry.define, but it doesn't work unless every element in the expression has a unit.

from pint import UnitRegistry

ureg = UnitRegistry(filename=None)
ureg.define("KG = []")
ureg.define("MT = 1000 * KG")
ureg.define("USD = []")
ureg.define("JPY = []")
X = 1 * ureg.USD / ureg.MT
Y = 1 * ureg.JPY / ureg.USD
formula = (X + 50) / 1000 * Y
formula.u
=> JPY/USD

The result I want to get is JPY/KG or USD/MT. This undesirable result is because X + 50 will be dimensionless. If I manually define the units for the numbers, I will get an accurate answer. But then there is no need for dimensional analysis.

I am not obsessed with pint, sympy. Is there any good way to do a dimensional analysis?

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P.S.

Thanks to @wsdookadr, I would like to show examples. What I want to do is to evaluate the dimension of a formula (maybe expressed by string).

Let me have two formulas.

F1 = (X + 50) / 1000 * Y
F2 = (X + 1000) * 0.5

The unit of this X and Y are the same as the previous example. If I could perform dimension analysis, the results would be as follows.

F1 = ([USD/MT] + 50) / 1000 * [JPY/USD]
   = 10^-3 [USD/MT] * [JPY/USD]
   = 10^-3 [JPY/MT]
   = [JPY/KG]
F2 = ([USD / MT] + 1000) * 0.5
   = [USD/MT]