The Vincenty distance is now deprecated since GeoPy version 1.13 - you should use geopy.distance.distance() instead!

Some previous answers were based on the haversine formula, which assumes the earth is a sphere, which results in errors of up to about 0.5% (according to help(geopy.distance)). The Vincenty distance uses more accurate ellipsoidal models, such as WGS-84, and is implemented in geopy. For example,

import geopy.distance

coords_1 = (52.2296756, 21.0122287)
coords_2 = (52.406374, 16.9251681)

print(geopy.distance.geodesic(coords_1, coords_2).km)

will print the distance of 279.352901604 kilometers using the default ellipsoid WGS-84. (You can also choose .miles or one of several other distance units.)

Ensure that your latitude and longitude values are in the correct units (degrees for the second formula or radians for the first one) for the expression you are using, and the procedure should work as expected.

Can you provide sample data that does not work?

The answers to Haversine Formula in Python (Bearing and Distance between two GPS points) provide Python implementations that answer your question.

Using the implementation below I performed 100,000 iterations in less than 1 second on an older laptop. I think for your purposes this should be sufficient. However, you should profile anything before you optimize for performance.

from math import radians, cos, sin, asin, sqrt
def haversine(lon1, lat1, lon2, lat2):
    """
    Calculate the great circle distance between two points 
    on the earth (specified in decimal degrees)
    """
    # convert decimal degrees to radians 
    lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])
    # haversine formula 
    dlon = lon2 - lon1 
    dlat = lat2 - lat1 
    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
    c = 2 * asin(sqrt(a)) 
    # Radius of earth in kilometers is 6371
    km = 6371* c
    return km

To underestimate haversine(lat1, long1, lat2, long2) * 0.90 or whatever factor you want. I don't see how introducing error to your underestimation is useful.