$ vacuumdb test --verbose --analyze  &> vacuumdb.test.$(date +'%Y%m%d').log
$ ls -l vacuumdb.test.20171226.log
-rw-r--r-- 1 postgres postgres 84161 Dec 26 11:34 vacuumdb.test.20171226.log

$ man bash
...
   Redirecting Standard Output and Standard Error
       This construct allows both the standard output (file descriptor 1) and the standard error output (file descriptor 2) to be redirected to the file whose name is the expansion of word.

       There are two formats for redirecting standard output and standard error:

              &>word
       and
              >&word

       Of the two forms, the first is preferred.  This is semantically equivalent to

              >word 2>&1

       When using the second form, word may not expand to a number or -.  If it does, other redirection operators apply (see Duplicating File Descriptors below) for compatibility reasons.