Yes, I understand that explicitly defining variables results in a performance enhancement. Perhaps I misused the term "math intensive". What I meant was, there is a lot of math code, but there are no intensive computations.
I "grew up" on early versions of BASIC. I was an early adoptor of the IBM PC. It was a Model 1 which was only produced for 6 months. I had to write my own database software as there was none available. I did many, many benchmarks with declared/undeclared variables and on that slow processor it made a huge difference. Huge, but not enough as I had to resort to writing most computational routines in assember in order to attain adequate speed. But as the PC evolved, it got faster and faster. Today, my cell phone is a zillion times faster than my first PC.
It just doesn't take that long to compute a gamma function - with or without explicitly declared variables. My time savings comes on the developmental end, not on the processing end. I could do a turing test between my program without declared variables, and one with declarations, and I doubt one could tell the difference. Sure, some programs will show a noticible improvement and if I ever need the speed I'll certainly take the time to declare everything. In the meantime, I live by an old graduate school addage - A difference that doesn't make a difference is not a difference.
Klaus, Andrew: I really appreciate your advice and all the great help you both have provided over the last few years. May you live long and prosper!