Date added to CiviCRM DB error when using with a smart group that has a custom field type
This line: 


  Warning: fopen(/var/www/html/example/docroot/sites/default/files/civicrm/ConfigAndLog/CiviCRM.c496aa562571a7869b7d0ea6d810ea10.log): failed to open stream: Permission denied in Log_file


indicates a permissions error. Check that your webserver user can write to the directory:

/var/www/html/example/docroot/sites/default/files/civicrm/ConfigAndLog


and to this file if it exists:

/var/www/html/example/docroot/sites/default/files/civicrm/ConfigAndLog/CiviCRM.c496aa562571a7869b7d0ea6d810ea10.log


That may not fix the search problem you describe, but you should then get more information in the log file.