math expressions optimalization

Hello.


I`m going to implement simple alghoritm to
optimalize math expressions in terms of
use of memory cells.
E.g.
I have given out=a*b+c*(a+c+d)
then i divide this expression into parts:
x1=a*b
x2=c+d
c3=a+x2
x4=c*x3
x5=x1+x4


To do this step i just convert my expression
to Polish Notation.


Now I run alghoritm which optimalize expression.


Output is:
x1=a*b
x2=c+d
x2=a+x2
x2=c*x2
x1=x1+x2 <- out


So we`ve used only 2 memory cells - not 5 like above.
I`ve written program which do this but I`m not sure
my program works well - I`d like to compare to another
solution.


I don`t know the name of such alghoritm in English
and can find it on the net.


If somebody would provide me with links to web pages
about my problem...


Thanks.

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