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here is the silly question of mine,

if mathematica takes 3 seconds to evaluate the function f[3] then I plug the this value f[3] into a new function g[f[3],f[3]], Let's ignore the evaluation time for the new function g, how long does it take for g[f[3],f[3]], 3 seconds or 6 seconds?

if it is 6 seconds, how can I make mathematica temporarily to remember the value of f[3]


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up vote 8 down vote accepted

Use With to define temporary constants.

With[{a=f[3]}, g[a,a]]

Memoization is also worth mentioning but keep in mind that once a value is remembered, it won't be forgotten (until to explcitly clear it). I.e. when you use memoization, Mathematica will remember permanently (not temporarily).

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With keeps the code clear for longer cases but sometimes I'd do:

g[#,#] & @ f[3]
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$RecursionLimit = Infinity;
fibonacci[1] = 1; fibonacci[2] = 1;
fibonacci[i_] := fibonacci[i] = fibonacci[i - 1] + fibonacci[i - 2];
fibonacci[20000]; // AbsoluteTiming
fibonacci[20000]; // AbsoluteTiming
(*{0.135008, Null}*)
(*{0., Null}*)
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