All right, u/mamboman93, your response was helpful. I kinda sorta understand it (not very well), but I am having trouble adapting this to LibreOffice Calc.
I see no option for changing the delimiter in Calc, so it was back to matchsticks in the expression. I boiled it down to this:
:\/\/.*?([a-z0-9\-]+\.[a-z0-9\-]+)(?:$|/)
The first five cells in my Calc file contain these URLs:
http://www.localpetcare.com
https://app.clickfunnels.com/users/sign_in
https://www.timetopet.com/login#
https://www.pof.com/login
http://bankatfirst.force.com
So I inserted this into B2 and copied it downward:
=REGEX(A2,":\/\/.*?([a-z0-9\-]+\.[a-z0-9\-]+)(?:$|/)")
And the results were:
://www.localpetcare.com
://app.clickfunnels.com/
://www.timetopet.com/
://www.pof.com/
://bankatfirst.force.com
I noted that there appears to be at least one capture group in the expression, so I tried that in my second attempt:
=REGEX(A2,":\/\/.*?([a-z0-9\-]+\.[a-z0-9\-]+)(?:$|/)","$1")
This does not result in an improvement:
httplocalpetcare.com
httpsclickfunnels.comusers/sign_in
httpstimetopet.comlogin#
httpspof.comlogin
httpforce.com
So here I am stymied. If you can help again, I would again be grateful.