vim, 274 bytes

Result

AC

Duration

550ms

Code [DL]

:let l=[]
:for i in range(4)
let l+=map(split(getline(i+1),'\_s'),'str2nr(v:val)')
call setline(i+1,'')
endfor
:for i in range(9)
let l[i+3]-=l[i%3]
endfor
:call setline(1, (l[3]*l[7]*l[11]+l[6]*l[10]*l[5]+l[9]*l[4]*l[8]-l[5]*l[7]*l[9]-l[8]*l[10]*l[3]-l[11]*l[4]*l[6])/6)
ZZ

Disassembly

:let l=[]<NL>:for i in range(4)<NL>let l+=map(split(getline(i+1),'\_s'),'str2nr(v:val)')<NL>call setline(i+1,'')<NL>endfor<NL>:for i in range(9)<NL>let l[i+3]-=l[i%3]<NL>endfor<NL>:call setline(1, (l[3]*l[7]*l[11]+l[6]*l[10]*l[5]+l[9]*l[4]*l[8]-l[5]*l[7]*l[9]-l[8]*l[10]*l[3]-l[11]*l[4]*l[6])/6)<NL>ZZ

stdin

89 18 16
44 08 94
08 86 94
25 22 14

stdout

64314

stderr

strace