Speeding up code by avoiding repeated evaluation of a function

Question

I want to speed up my code and I have two ideas, but I don't know how I can implement them. Here is a little part of my code, which I want to improve:

   R[FK_, f_] := 
      FixedPoint[
          Integrate[PDF[f, x]*x , {x, 0, id[Q[FK, #], #]}]
          *If[CDF[f, id[Q[FK, #], #]] == 0., 0.1, CDF[f,id[Q[FK, #], #]]]
          *id[Q[FK, #], #] &
     , seedR] ;

1) You can see that the function is evaluated id[Q[FK, #], #] 3 times. That is unecassary. Normaly I would use a Module structure, define a new variable idd = id[Q[FK, #], #], like

    R2[FK_, f_] := 
      Module[{iddd}, 
      FixedPoint[ 
        iddd = id[Q[FK, #], #] &; 
        Integrate[PDF[f, x]*x , {x, 0, iddd}]
        *If[CDF[f, iddd] == 0., 0.1, CDF[f, iddd]]
        *iddd &
      ,seedR]];

but this does not work. Do you have any idea?

2) Probably a easy one:

    If[CDF[f, id[Q[FK, #], #]] == 0., 0.1, CDF[f, id[Q[FK, #], #]]]

This involves the funtion CDF[f, id[Q[FK, #], #]] two times. One time should be enough. How can I do this?

Thanks

Peter

Answer 1

Multiple evaluations can often be avoided by using With. You might try something like

f = With[{q = Q[FK, ....]}, If[CDF[f, id[is, q, #]] == 0., 0.1, CDF[f,id[is, q, #]]]]&