Does IMMUTABLE property propagate?

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Given f1(x) as IMMUTABLE and f2(x) as IMMUTABLE, and f3(f1,f2) as
IMMUTABLE, does the query planner cache the result of f3 and reuse it
or if you want to get a little more speed you better explicitly define
yourself f3 as IMMUTABLE?

I had an aggregate query like:

select id,
sum(p1*f1(a)/f2(b) as r1,
sum(p2*f1(a)/f2(b) as r2,
...
sum(pn*f1(a)/f2(b) as rn

...
group by id;

Where f1(x) and f2(x) were defined as IMMUTABLE.

By the experiments I ran looks like after defining a new function
f3(a,b):= f1(a)/f2(b) and rewriting the query as:

select id,
sum(p1*f3(a,b) as r1,
sum(p2*f3(a,b) as r2,
...
sum(pn*f3(a,b) as rn

...
group by id;

*Looks like* I got a little (5%) improvement in performance of the
query. Is there a way to find out if the function is re-evaluated each
time?
Is this the recommended way to proceed?

Thank you!

Petru Ghita
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