You can copy search criteria and use it in another search or rule. Once you have created a search, use the action menu in the top right and select "Copy search fields".
Create a new search or rule and then choose "Paste search fields" from the action menu. This will paste the fields that you copied.
If you already have some fields in the new search, the pasted fields will be appended. If the join type (or/and) is different from the new search join type, then a nested search will be created instead of appending the search fields.
You can also paste search fields into a nested search.
If you are happy with more complex features, choose "Copy all search field names" and then build your own search in a text editor. Then copy and paste the new search in a search or rule. This method does require that you follow the copy search format exactly or you will get a warning message.

If you want to try this for yourself, copy the text below and then tap on the action menu in the top of a search/rule screen, then choose "Paste search fields"

or (
  Subject Contains Product
  Subject Contains Service
)