logarithm and exponent computation performance Using glibc on a x86 processor, which takes more CPU time? $a\ log\ b$ or $b^a$?  For which values of $a$ is one faster than the other?  Optional: Does the base used matter?
See also: What algorithm is used by computers to calculate logarithms?
Because I know someone will mention it, I know that $a\ log\ b$ does not equal $b^a$.

I just ran a test in Python 2.7 (with optimization turned off) in Ubuntu 12 on a VM running on a 64 bit Xeon.  It appears that for $|a|=\{0,1,2\}$ computing the exponent is slightly faster if not the same.  For all other values of $a$, computing the log is faster.  The value of b doesn't seem to matter.  
This is only for the scenario I mentioned above.  Feel free to run this same test on other platforms/architectures and post your results here.
import math
from datetime import datetime

a, b = 2, 33

then = datetime.now()
for _ in xrange(10000000):
    y = a * math.log(b)
print datetime.now() - then

then = datetime.now()
for _ in xrange(10000000):
    y = math.pow(b, a)
print datetime.now() - then

