speed and order of operations with CDF

edit

Why is the absolute value of the exponential of z:

f = fast_callable(exp(z).abs(),domain=CDF,vars='z')

about twice as fast as the exponential of the real part of z:

g = fast_callable(exp(z.real()), domain=CDF, vars='z')

Should I ignore this kind of thing in sage, or is there a good reason in this particular case?

Data:

z = var('z')
f = fast_callable(exp(z).abs(),domain=CDF,vars='z')
g = fast_callable(exp(z.real()), domain=CDF, vars='z') 
timeit('f(4+2*I)')

625 loops, best of 3: 2.94 µs per loop

timeit('g(4+2*I)')

625 loops, best of 3: 5.87 µs per loop

Non-fast_callable times, in case you are interested:

z = var('z')
fs(z) = exp(z).abs()
gs(z) = exp(z.real())
timeit('fs(4+2*I)')

625 loops, best of 3: 1.02 ms per loop

timeit('gs(4+2*I)')

625 loops, best of 3: 988 µs per loop