Hi!
Unfortunately this is just the leftover test error log, as you can see the dates are from march 2014, so It’s something else.
Can you please check that the {dbPrefix}_ajaxsearchpro and the {dbPrefix}_ajaxsearchpro_statistics tables exist in the wordpress database? (http://i.imgur.com/DWPwPZX.png)
I’m suspecting that maybe those tables were not created when the plugin was activated.