time command > timelog doesn’t work, because time outputs to stderr
time command 2> timelog doesn’t work either, because time actually is a bash keyword, and it’s always run in a subshell
Redirecting the output of time can be achieved by executing the whole command in a block, then redirecting its output:
{ time command; } 2> timelog
Note: Linux also provides a time binary (/usr/bin/time), but with a different output (and might be less efficient ?)