GATE question doubt

Question

What does the following algorithm approximate? (Assume m>1,ϵ>0m>1,ϵ>0).

x = m;
y = 1;
While (x-y > ϵ)
{
    x = (x+y)/2;
    y = m/x;
}
print(x);

1. logm
2. m²
3. m^1/2
4. m^1/3

Can i get a reason of why it cannot be log m ?

when finding by substituting values

Comments

put m = 6, 9, 5....

you will get values nearer to root or exact root. but far away from logm.

don't only check for 4.

check for 9.

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@ashwin

but log₂6 and root(6) both gives 3(lower bound) only right ?

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Upper bounds will give 6 but there is no floor ir ceil is given and at perfect squares it calculates exact roots hence we should go with that option!

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@ashwin

lets assume m=6

after the program is executed the value print(x) gives 3 as output

now how will we determine whether to choose logm or root(m) ?