Right click on the formula field shown in your field explorer. Create a new formula and call it field2. Click on editor. Use the editor to create your new formula. You can use the functions, report fields and operators to build your new formula or just type it in. When you are finished, click on save and close. If everything is correct, you will return to your report. If not, you will see error messages. Use field2 in your report as needed.
Your syntax would be
If {table.Field1} = "A172" then "dogs"
else
if {table.Field1} = "R175" then "cats"
This would set field2 to either "dogs" or "cats"
Hope this helps. Good luck.