With fast native code its more than practical to search the entire space of floating point numbers and guarantee that you find the optimal magic number:
As already mentioned in another comment it has been taken further by Řrřola who has optimised a version with the newton step including the constants involved in that.
http://jheriko-rtw.blogspot.co.uk/2009/04/understanding-and-...
As already mentioned in another comment it has been taken further by Řrřola who has optimised a version with the newton step including the constants involved in that.
http://rrrola.wz.cz/inv_sqrt.html