Hi Shrivallabha ,
The length , construction etc., of the formula are all immaterial ; what matters is whether it does the following :
For all valid inputs , it should give the correct results
For any invalid input , it should not give a valid result , correct or incorrect.
Just as in a program , what is written is always with a view to whether it is general in nature ( more general code is always preferred to very specific code , unless making it more general makes it much longer or much more difficult to understand or is not really necessary according to the specifications ) , extensible , modular , maintainable .... there are many principles of good programming practice , which not many follow all the time , but which very few will argue against.
The formula which has been posted fails on many counts , not least of which is that is does not give the correct results ; discussions about its length , cleverness , speed are all , in my opinion , irrelevant.
Narayan