Im interested in counting the number of operations required to evaluate a given formula. Let me give you an example.
Lets say I have entered the expression $\dfrac{\operatorname{Sqrt}[\operatorname{Sin}[a*x+b*x-c*y]]}{2*a+b}$
Now lets say you have values for those unknows $a,b,c$. Then you would to calculate $a*x+b*x-c*y$ first which requires 3 multiplications, 1 addition and 1 subtraction. Then you take the $\sin(...)$ and then the square root.
Now you might calculate $2*a+b$ which requires 1 multiplication and 1 addition. In the end you take the quotient. This gives a total number of:
$1\times\sin, 1\times\sqrt{\cdot} \ 1 \times$ quotient, $4 \times $ multiplication, $2 \times$ addition and 1 subtraction.
Well you might call one subtraction the result of 1 multiplication and 1 addition. But that doesnt matter to me.
Since I have most of my formulas stored in Mathematica it would be great to have such a function. That would save a lot of time counting by hand.