  A recently published method for solving the neutrino evolution equation with
constant matter density is further refined and used to lay out an exact
algorithm for computing oscillation probabilities, which is moderately faster
than previous methods when looping through neutrinos of different energies. In
particular, the three examples of $\overset{\scriptscriptstyle{(-)}}{\nu}_e$
survival, $\overset{\scriptscriptstyle{(-)}}{\nu}_\mu$ survival and
$\overset{\scriptscriptstyle{(-)}}{\nu}_e$ appearance probabilities are written
in terms of mixing angles, mass differences and matter electron density. A
program based on this new method is found to be roughly twice as fast as, and
in agreement with, the leading GLoBES package. Furthermore, the behaviour of
all relevant effective parameters is sketched out in terms of a range of
neutrino energies, or matter electron densities. For instance, the
$\overset{\scriptscriptstyle{(-)}}{\nu}_e$ survival probability in constant
matter density is found to have no dependence on the mixing angle $\theta_{23}$
or the CP-violating phase $\delta_{13}$.
