Numerical Calculation

Newton's method takes a guess and finds a better guess
- The number of correct bits in the guess tends to double on each iteration
- If the initial guess is good, the new guess is superb
- If there were no correct bits to begin with, it wanders around aimlessly
The initial guess in the original code was terrible:

         my $guess   = Math::BigFloat->new( $num / $root );

For Root(500000, 555) this guesses that the root is 900.9009009
- The root is actually 1.02392563097332211627
At x = 900.9, the curve y = x⁵⁵⁵ - 500000 is extremely steep
- The tangent line is almost vertical (it has a slope of about 3.4e1639)
- So the 'improved' guess is almost the same as the original guess
- But twice as long!