Javascript math recursive function optimisation

Question

This is what I've got

let base = 10000
let yearly = 31557600
let apy = 0.09

let loop = 0;
let new_base = '0';
function recurse(base){
    new_base = base*(1+apy*1/(yearly));
    if(loop < 3600){
        loop++;
        return recurse(new_base);    
    }
    else {
        return new_base;
    }
}
base = recurse(base);
console.log(base);

if I change 3600 by a very large number I get the error: Maximum call stack size exceeded

This seems normal to me because the recursive operation is executed too many times,

what would be the solution ? Is it possible to transform the recursive function into a linear function for example?

Thanks

This recursive function is a simple for loop in disguise. for(let i = 0; i < 3600; i++){new_base = new_base *(1+apy*1/(yearly));} — Marko Taht
– Marko Taht, Commented Jun 27, 2022 at 11:21
Unclear why you would need recursion for this since there is nothing recursive about this. — epascarello
– epascarello, Commented Jun 27, 2022 at 11:22
In Chrome the maximum call stack size is around 10k. If you want to be doing high-performance functions like this you probably shouldn't be using javascript. — bryce
– bryce, Commented Jun 27, 2022 at 11:23

halfer · Accepted Answer · 2022-09-04 19:42:17Z

2

Well it can be transformed to an equation, but not a linear one.

Here, is the approach:

I will rename the base as b0, and the new base as b1

b1 = b0 * (1 + (apy/yearly)

and after loop is incremented new base will be updated, let's call the new b1 as b2:

b2 = b1 * (1 + (apy/yearly))

b2 = b0 * (1 + (apy/yearly))^2

and so on..

so the final returned value will be:

base * (1 + (apy/yearly))^3600

and the general formula will be

base * (1 + (apy/yearly))^n, where n is 3600 in your case.

Putting the constants plugged in you will get 10,000.102669931423184360664719158

edited Sep 4, 2022 at 19:42

halfer

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answered Jun 27, 2022 at 11:34

amew

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2 Comments

Maxime R Over a year ago

Thanks a lot, do you know how to write base * (1 + (apy/yearly))^n in javascript ?

amew Over a year ago

Yes, thanks to javascript we can use **. So the equation will be written as, base*(1+(apy/yearly))**n. And FYI python also supports ** for exponentiation. And please remember to upvote the answer as solution. Thanks

Lzh · Accepted Answer · 2022-06-27 11:26:09Z

Do you need recursion? No.

function recurse2(base){
    new_base = base*(1+apy*1/(yearly));
    for(loop = 1; loop < 100; loop++){
        new_base = base*(1+apy*1/(yearly));
    }
    return new_base;
}

You don't even tail optimization. This is just a value that is being mutated over and over. You don't need a new stackframe (function call) to mutate said value, just loop over it.

How did I arrive at this function? Just think what happens to the base when you pass it in and how it changes with each "recursion". It just gets multiplied by some expression each time. So we can just do that in a loop.

You can even improve the code snippet that I have here with a do {} while();

The following screenshot shows quick tests that show that function recurse2 that I wrote is identical*.

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