Having performance issue for an extract date without time to compare with sysdate,
If you want an index to be used, you should remove the function from the column. You can rewrite the condition (which removes the time part from the two datetimes): 

where trunc(timefield) = trunc(sysdate)


to the equivalent (where the function is applied only to sysdate and not the column):

where (timefield &gt;= trunc(sysdate) and timefield &lt; trunc(sysdate) + 1)


This way, the condition is "sargable" and an index on timefield can be used. With the previous condition, a table scan (or a full index scan) was required.