Different results for two equal functions

I am comparing these two functions:

f = sqrt(x.^2+1.0)-1.0

g = x.^2./(sqrt(x.^2+1.0)+1.0)

x = [8^-6 8^-7, 8^-8]

Even though f = g, I get slightly different values e.g. for x = 8^-7 I get f(x) = 1.136868377216 160 e-13 and g(x) = 1.136868377216 096 e-13.

I'm guessing this has something to do with the reduction of significant digits, however I don't know which results are more reliable. My guess is that function f = sqrt(x.^2+1.0)-1.0 is more precise because we only have one x in it but I am not sure...

Answer 1

[Walter Roberson]

The two functions you show algebraically yield identical values only for x = 0.

[Beaya]

Well this is my exact code and I get same values....

 x= [8^-1 8^-4 8^-5 8^-6 8^-7 8^-8 8^-9]

y = x.^2./(sqrt(x.^2+1.0)+1.0)
f = sqrt(x.^2+1.0)-1.0

[Walter Roberson]

Apologies, I had a typo when I did the calculations. The two do come out the same.

To more precision the 8^(-7) answer is

1.136868377216095673908443130184740364*10^(-13)

so your g(x) formula is more precise.

[Beaya]

Thank you but do you know what might be the reason to that? I mean why g(x) is more precise?