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I have two questions.

So, I have a function g defined in terms of another function, f:

g[z_] := Product[f[z][[i]], { i, 1, Length [f[z] ] }];

My problem is that f[z_] takes a while to compute.

Question 1: When I call g, does it compute f twice?

Question 2: If so, is there a way to make it not do that?

Note: I simplified my code a little bit. g is actually defined in terms of two parameters, so I cannot generate a table of f and have it call the parts of the table.

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    $\begingroup$ g[z_]:=Times@@f[z] $\endgroup$ – ciao Aug 12 at 22:13
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    $\begingroup$ You cannot have a pattern object (e.g., z_) on the RHS of a function definition except in a rule. To avoid multiple evaluations use a Module, eg., g[z_] := Module[{ft = f[z]}, ...] $\endgroup$ – Bob Hanlon Aug 12 at 23:17
  • $\begingroup$ @BobHanlon sorry, that was a typo. $\endgroup$ – Descartes Before the Horse Aug 12 at 23:32
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    $\begingroup$ ciao gives a good example of how one can more simply write what you have shown in your answer, and it is thus likely more efficient—however, it all comes down to your f[z] definition. Are you using SetDelayed ( i.e., := ) or Set ( i.e., = )? In either case, you can use memoization to remember the values you have calculated for some f[z]. This looks something like: ...=f[z]=... where, before the ...=, you have either Set or SetDelayed and f[z_]. $\endgroup$ – CA Trevillian Aug 13 at 1:27
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BobHanlon gives a good answer for 2. For question 1, Here's an easy way to test. Define f[z_] using Echo and have it return a known result. Then evaluate g[z].

In[1]:= f[z_]:=(Echo@"f[z] was called";{1,2,3});
In[2]:= g[z_]:=Product[f[z][[i]],{i,1,Length[f[z]]}];
In[3]:= g[1]
>>f[z] was called
>>f[z] was called
>>f[z] was called
f[z] was called
Out[3]= 6
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  • $\begingroup$ This is a neat way to profile, but couldn’t one also just use Trace? $\endgroup$ – CA Trevillian Aug 13 at 1:22
  • $\begingroup$ Sure, but Trace is not always easy to follow. Echo is simple. $\endgroup$ – Mat Aug 13 at 1:27
  • $\begingroup$ valid point. I don’t know my way around Echo & Trace is easy to apply after function definition occurs, rather than needing to insert it into the definition. Wood screw versus a machine screw maybe ;) $\endgroup$ – CA Trevillian Aug 13 at 1:30

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