Oracle Performance Tuning – Improvement After Table Analyze

The second form of your query will work if you make your mark your function as deterministic, meaning that for a given set of input values, it will always return the same result.
With that set, Oracle will only run the conversion once for each parameters in the where clause rather than for every row.

With this:

CREATE OR REPLACE FUNCTION TO_MINUTE_D (DATE_IN IN DATE)
RETURN NUMBER DETERMINISTIC AS
BEGIN
  /* Minute 0 = 12/30/1899 12:00am */
  RETURN
    (TRUNC(DATE_IN, 'DD') - TO_DATE('12/30/1899', 'MM/DD/YYYY')) * 1440 +
    TO_NUMBER(TO_CHAR(DATE_IN, 'HH24'))  * 60 +
    TO_NUMBER(TO_CHAR(DATE_IN, 'MI'));
END TO_MINUTE_D;
/

On a table filled with a large bunch of dummy rows (increasing ints), I get the following timings consistently:

SQL> SELECT * FROM MY_TABLE
WHERE START_MINUTE < TO_MINUTE(TO_DATE('2013-01-31', 'YYYY-MM-DD'))
AND STOP_MINUTE > TO_MINUTE(TO_DATE('2013-01-01', 'YYYY-MM-DD'));

no rows selected

Elapsed: 00:00:12.69

versus deterministic-annotated function:

SQL> SELECT * FROM MY_TABLE
     WHERE START_MINUTE < TO_MINUTE_D(TO_DATE('2013-01-31', 'YYYY-MM-DD'))
     AND STOP_MINUTE > TO_MINUTE_D(TO_DATE('2013-01-01', 'YYYY-MM-DD')); 

no rows selected

Elapsed: 00:00:00.07

You should get very close to what you have with the values plugged in directly, and indexes on those columns can be used as if you'd plugged in literals.

(Putting the conversion function on the start|stop_minute columns isn't a good idea in general as you've discovered, unless you have a function-based index on those that matches exactly.)

I think the article Raj quoted (https://www.pythian.com/blog/analyze-index-validate-structure-dark-side/) describes this pretty well. "clustering factor" was also my first guess while reading the description of your problem. I also prefer to use RMAN to check for corruption.

RMAN> backup check logical validate database;

Afterwards you can query V$DATABASE_BLOCK_CORRUPTION for details on any corrupt block.

Normally there is a reason for huge clustering. You can check the following details:

• How many rows does the index have?
• How many blocks does it consume?

This may help you to determine if the clustering_factor is high. You can also query dba_extents to determine the clustering_factor.

• What type of management does the tablespace use? I guess it's not ASSM since the database is pretty old and was upgraded several times.

Why is clustering bad for performance? When Oracle reads data from disk or cache it always reads in block. If the block is half empty you loose 50% of your reading performance. In case you do a full table or full index scan Oracle scans all blocks belonging to the segment (index or table). It does not check if a block is empty or not. Oracle reads from the first block to the last (HWM). If your index has 10mil blocks but it only needs 1mil blocks Oracle reads 9mil trash blocks.

ASSM (Automatic Segment Space Management) helps a lot to reduce/prevent clustering. If possible you should migrate Manual Segment Space Managed Tbs to ASSM Tbs.

Why checking for corruption? I always start analyzing a database by gathering ASM or statspack reports from the production database (not a test/dev db). This does not hurt anyone and will give you a lot of details on the database and it's little secrets. Corruption does usually not affect performance since the database does not try to repair it -- it just crashes the current query.