I now have this in my nginx.conf is this what you meant ? Does this log to the same error_log ?

log_format main '$remote_addr - $remote_user [$time_local] $request ' '"$status" $body_bytes_sent "$http_referer" ' '"$http_user_agent" "$http_x_forwarded_for"';

log_format timing '$remote_addr - $remote_user [$time_local] $request ' 'upstream_response_time $upstream_response_time ' 'msec $msec request_time $request_time';