TypeError when combining auto_reduce_dimensions=True and non_int_type=Decimal

[jonemo]

To reproduce run:

import pint
from decimal import Decimal

reg = pint.UnitRegistry(
    auto_reduce_dimensions=True,
    non_int_type=Decimal,
)
reg("km / h * m")

Resulting output is:

Traceback (most recent call last):
  File "/path/to/my/pintrepro.py", line 10, in <module>
    print(reg("km / h * m"))
          ^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/registry.py", line 1313, in parse_expression
    return build_eval_tree(gen).evaluate(_define_op)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/pint_eval.py", line 146, in evaluate
    return bin_op[op_text](
           ^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/quantity.py", line 998, in __mul__
    return self._mul_div(other, operator.mul)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/quantity.py", line 100, in wrapped
    return f(self, *args, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/quantity.py", line 83, in wrapped
    result.ito_reduced_units()
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/qto.py", line 61, in ito_reduced_units
    return quantity.ito(new_units)
           ^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/quantity.py", line 492, in ito
    self._magnitude = self._convert_magnitude(other, *contexts, **ctx_kwargs)
                      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/quantity.py", line 469, in _convert_magnitude
    return self._REGISTRY.convert(
           ^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/registry.py", line 965, in convert
    return self._convert(value, src, dst, inplace)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/context/registry.py", line 403, in _convert
    return super()._convert(value, src, dst, inplace)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/nonmultiplicative/registry.py", line 254, in _convert
    return super()._convert(value, src, dst, inplace)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/registry.py", line 999, in _convert
    dst_dim = self._get_dimensionality(dst)
              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/registry.py", line 690, in _get_dimensionality
    self._get_dimensionality_recurse(input_units, 1, accumulator)
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/registry.py", line 720, in _get_dimensionality_recurse
    self._get_dimensionality_recurse(reg.reference, exp2, accumulator)
  File "/path/to/my/venv/lib/python3.11/site-packages/pint/facets/plain/registry.py", line 708, in _get_dimensionality_recurse
    exp2 = exp * ref[key]
           ~~~~^~~~~~~~~~
TypeError: unsupported operand type(s) for *: 'float' and 'decimal.Decimal'

Observed with the latest version of pint (0.22).

This doesn't get triggered by every formula, and I have not figured out the minimal necessary conditions to trigger the error. These examples result in the error:

km / h * m
kW / min * W

... but these do not:

m / h * m
km / s * m
m / h * m