If you want to store all stdout while runing an interactive bash:
Install
curl -Lo /usr/local/bin/cybash https://gist.githubusercontent.com/lalyos/94cef8ca8bb3087387312f7f3e775e3b/raw/cybash
chmod +x /usr/local/bin/cybash
Usage
> cybash
... start bashing as usual
all stdout is saved into timestamped terminal-XXX.log
files
One-liner
actually you don't even need 2 lines
bash --rcfile <( echo 'PS1="RECORD> "') > >(tee /tmp/terminal-$(date +%m%d-%H%M).log)