redirecting std error

Hi,
I use the following command

make all > output-`date +%F-%H-%M-%S`.txt 2>&1

to invoke a MAKE process that takes some weeks to complete. The ouput is redirected to a text file. Now I prefix the above command with time to get time needed for completion of the MAKE process

time make all > output-`date +%F-%H-%M-%S`.txt 2>&1

I would like the output of time to be written in the same file as the output of MAKE instead of the std error.
I have tried a couple of combinations without success.
Please help
Thanks GA

mydate=`date +%F-%H-%M-%S` && echo $mydate > output-$mydate.txt && time make all &>> output-$mydate.txt

>cat a.sh
echo Hello, this is a.sh running
echo Here is a.sh writing to stderr >&2

>a.sh
Hello, this is a.sh running
Here is a.sh writing to stderr

>a.sh 2>err
Hello, this is a.sh running

>a.sh >out
Here is a.sh writing to stderr

>(time a.sh) 2>err
Hello, this is a.sh running

>cat err
Here is a.sh writing to stderr

real 0m0.021s
user 0m0.000s
sys 0m0.000s