"""Finds the distances between two frequency profiles, expressed as dictionaries.
Assumes every key in frequencies1 is also in frequencies2
- >>> cosine_distance({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
+ >>> cosine_similarity({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
1.0000000000...
- >>> cosine_distance({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
+ >>> cosine_similarity({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
1.0000000000...
- >>> cosine_distance({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
+ >>> cosine_similarity({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
0.5773502691...
- >>> cosine_distance({'a':0, 'b':1}, {'a':1, 'b':1}) # doctest: +ELLIPSIS
+ >>> cosine_similarity({'a':0, 'b':1}, {'a':1, 'b':1}) # doctest: +ELLIPSIS
0.7071067811...
"""
numerator = 0