np.exp much slower than np.e?

Question

In [49]: timeit.timeit("np.exp(100)", setup="import numpy as np")
Out[49]: 1.700455904006958

In [50]: timeit.timeit("np.e**100", setup="import numpy as np")
Out[50]: 0.16629505157470703

Is there any reason that using the CPython implementation of np.e**100 is that much slower than using the numpy version? Shouldn't the numpy version be faster as it is pushed down to C code?

Answer 1

One obvious reason is that np.exp is set up to handle arrays, and there's probably a bit of overhead involved there in terms of figuring out the type/dimensions of the input. Try out cases like these, and you might see the difference reduce or vanish:

timeit.timeit("np.exp(x)", 
              setup="import numpy as np; x = np.array([99, 100, 101])")
# This actually seems to be faster than just calculating
#   it for a single value
Out[7]: 1.0747020244598389

timeit.timeit("[np.e**n for n in x]", 
              setup="import numpy as np; x = [99, 100, 101]")
Out[8]: 0.7991611957550049