Question: Completely different results

I'm not really an expert in maple. I'm stuck with a problem that could be related to the precision of the computational engine...

I defined a function which is relatively complicated as follows:

m := proc (x, l, T) options operator, arrow; (exp(l*(x-T)/(1-exp(-l*T)))*exp(l*T/(1-exp(-l*T)))*(1-exp(-l*T))+(2-exp(-l*T)-exp(l*T))*exp(l*(x-T)/(1-exp(-l*T))))/(exp(l*T)-1)-(l*(x-T)*exp(l*(x-T)/(1-exp(-l*T)))-2*exp(-l*T)+4-2*exp(l*T))/(exp(l*T)-1) end proc

whenever i simplify the equation or factor some of the terms, I get completely different results.

As an example, you can define this function as follows

m := proc (x, l, T) options operator, arrow; (exp(x*l/(1-exp(-l*T)))*(1-exp(-l*T))+(2-exp(-l*T)-exp(l*T))*exp(l*(x-T)/(1-exp(-l*T))))/(exp(l*T)-1)-(l*(x-T)*exp(l*(x-T)/(1-exp(-l*T)))-2*exp(-l*T)+4-2*exp(l*T))/(exp(l*T)-1) end proc


By drawing the function, you can see how things get messy.

plot(m(450, (1/250)*x, 250), x = 0 .. 100)


I know the problem occurs as a results of computation round-off. How could I ameliorate that? I have already increase the precision in the option menu, but that didn't help. By the way, how can I be sure that the anwers maple gives me is correct, except using my intuition?


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