def alt_cosine(x,y):
    return 1 - np.inner(x,y)/np.sqrt(np.dot(x,x)*np.dot(y,y))

from libc.math cimport sqrt
def alt_cosine_2(x,y):
    return 1 - np.inner(x,y)/sqrt(np.dot(x,x)*np.dot(y,y))

>>> cosine() # ... make some timings
5.27526156300155e-05 # mean calculation time for one loop

>>> alt_cosine()
9.913400815003115e-06

>>> alt_cosine_2()
7.0269494536660205e-06

import numpy as np

def f1(x, y):
    return 1 - np.inner(x,y)/np.sqrt(np.dot(x,x)*np.dot(y,y))

from numpy import inner, sqrt, dot

def f2(x, y):
    return 1 - inner(x,y)/sqrt(dot(x,x)*dot(y,y))

x = np.ones(100000)

%timeit f1(x,x)
# 58.1 µs ± 19.1 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

%timeit f2(x,x)
# 36.3 µs ± 3.32 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

def f3(x, y, inner=inner, sqrt=sqrt, dot=dot):
    return 1 - inner(x,y)/sqrt(dot(x,x)*dot(y,y))

%timeit f3(x,x)
# 36.5 µs ± 3.42 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)