Try adding this at the beginning of the file:
# set the trace prompt to include seconds, nanoseconds, script name and line number
# This is GNU date syntax; by default Macs ship with the BSD date program, which isn't compatible
PS4='+$(date "+%s:%N") %N:%i> '
# save file stderr to file descriptor 3 and redirect stderr (including trace
# output) to a file with the script's PID as an extension
exec 3>&2 2>/tmp/startlog.$$
# set options to turn on tracing and expansion of commands contained in the prompt
setopt xtrace prompt_subst
and this at the end:
# turn off tracing
unsetopt xtrace
# restore stderr to the value saved in FD 3
exec 2>&3 3>&-
And you should get a detailed log showing the epoch_second.nanosecond time of the execution of each line. Note that GNU date (and OS support) is required to have nanosecond output.
Edit:
added comments
Edit 2:
If you have zsh 4.3.12 or later, you should be able to set PS4 like this instead of using the date command:
zmodload zsh/datetime
setopt promptsubst
PS4='+$EPOCHREALTIME %N:%i> '
which should work on both Linux and OS X to give you nanosecond precision.