Why the both results are different

I compute the little program in matlab

clear; clf;
syms a b 
f1 = 96*pi - 16*pi * (log(a)-log(b)+1)
f1_ = subs(f1,[a b],[12 2])
f1_ = vpa(f1_)
f2 = 96*pi - 16*pi*(log(12)-log(2)+1)
with the output
f1 = 
   
f1_ = 
   
f1_ = 
   
f2 = 161.2638

Why the results are different?

[Walter Roberson]

Ah, sorry, somehow when I formatted your code, the special characters disappeared!! If you could repost that part, that would be good.

[Walter Roberson]

When I test, I get

f1_ =
161.26375811875458240605931894947
f2 =
          161.263758118755

The first of those has been computed to higher precision.

The first has also been computed in a mode that recognized pi as being the indefinitely precise transcendental number, whereas the second one that was calculated purely numeric was calculated with the 16-digit numeric approximation of pi.

Answer 1

[Christian Muth]

With the newest Update R2020a Update 2 the problem is solved. The new output is ok

f1 =

f1_ =

f1_ =

161.26375811875458240605931894947

f2 = 161.2638

[Walter Roberson]

.. and I do happen to be using Update 2.

Which release was the problem observed with?

[Christian Muth]

The answer must be modified. I found the problem is come, if I give the commend digits(2) sometimes in matlab,see:

clear; clf;
syms a b 

digits(2)
f1 = 96*pi - 16*pi * (log(a)-log(b)+1)
f1_ = subs(f1,[a b],[12 2])
f1_ = vpa(f1_)
f2 = 96*pi - 16*pi*(log(12)-log(2)+1)
f3 = 96*sym(pi) - 16*sym(pi)*(log(sym(6)) + 1)
f3 = vpa(f3)

digits(32)
f1 = 96*pi - 16*pi * (log(a)-log(b)+1)
f1_ = subs(f1,[a b],[12 2])
f1_ = vpa(f1_)
f2 = 96*pi - 16*pi*(log(12)-log(2)+1)
f3 = 96*sym(pi) - 16*sym(pi)*(log(sym(6)) + 1)
f3 = vpa(f3)

gives the output

f1 =

f1_ =

f1_ =

160.0

f2 = 161.2638

f3 =

f3 =

160.0

f1 =

f1_ =

f1_ =

161.26375811875458240605931894947

f2 = 161.2638

f3 =

f3 =

161.26375811875458240605931894947

[madhan ravi]

You didn't reply to sir Walter's comment though.

Answer 2

[Christian Muth]

why should I give an answer if digit(2) is problem?