Mach number: RPN vs. AOS comparison Message #1 Posted by Karl Schneider on 5 Oct 2003, 5:08 a.m.
I evaluated the Machnumber equation given by r.d. baertschiger below:
M= sqrt[ 5 [({ [( 1 + 0.2 [ 350/661.5 ]^2 )^3.5 1 ] [ 1 ( 6.875^1E6 ) 25500 ]^5.2656 } +1 )^0.286 1 ] ]
using a number of diiferent machines.
RESULTS
 RPN (12C, 15C, 17Bii, 28S, 48G, 49G):
I got the correct answer (0.835724536) every time within one minute of work, once I saw how the expressions nested (match the braces "{}" by multiplying two long results.)
 Nonsymbolic AOS with precedence (20S, Casio fx3600p):
I got the correct answer on the first try with somewhat more time, when entering the expression exactly as written, which utilizes precedence. Doing the ()'s slows one down a little.
 Symbolic AOS with precedence (28S, 48G, 49G):
I got the correct answer on the first try, but required more time, due to all the "()". This method gives no intermediate results, however, so the final answer must almost be accepted on faith, unless one scrutinizes the symbolic expressions afterthefact.
 Symbolic AOS without precedence (17Bii):
Serious difficulties getting the correct answer, with repeated failures. Extra ()'s must be inserted at the right time to handle lack of precedence, and if it wasn't done, it's difficult to fix.
 Nonsymbolic AOS without precedence (10B):
Repeated failures required completely starting over, and ()'s were shifted. Horrible!
 Equation writers/editors (48G, 49G, 17Bii):
Very cumbersome; expressions were hard to read. Many failures. 48G equation writer could not keep up with user input.
FINAL VERDICTS
 RPN:
Probably best for correctly solving this type of problem, because you see all intermediate results, and you know what they represent. Error recovery is easy. Of course, a strategy for evaluation must be devised beforehand, but RPN users are good at it.
 Nonsymbolic AOS with precedence:
Also useable, but the intermediate results produced by ")" are less obvious. (How many operations were performed, and what were they?) The user can enter the problem exactly as written, but it must be written according to the rules of precedence. "Fixing" the calculation midstream is nearly impossible.
Instead of entering the experssion lefttoright, a quasiRPN approach can be emulated with liberal use of "=" and storage registers.
 Symbolic AOS and equation writers/editors:
Allows the user to see the complete expression, but not the intermediate results upon evaluation. I wouldn't trust 'em.
 AOS without precedence:
Leave 'em for the business people!
