From: Christophe Mckeon <chromatophore@...>
Date: 2008-12-20T04:51:29+09:00
Subject: Re: about Float

and just in case you need further convincing, this is the scariest 
example i've ever seen. taken from Stefano Taschini's 
http://intervals.rubyforge.org/

Take into consideration the rather innocent looking function

  def f(x,y)
    (333.75-x**2)* y**6 + x**2 * (11* x**2 * y**2-121 * y**4 -2) +
      5.5 * y**8 + x/(2*y)
  end

We can calculate it for some specific x and y,

  f(77617.0,33096.0)          # => 1.17260394005318

There is only one problem: this result is WRONG. The correct result can 
be obtained by calculating separately the numerator and denominator of f 
using integer arithmetic.

  def f_num(x,y)
    ((33375- 100 * x**2)* y**6 +
      100 * x**2 * (11* x**2 * y**2-121 * y**4 -2) +
      550 * y**8) *
    2*y + 100 *x
  end

  def f_den(x,y)
    200*y
  end

  f_num(77617, 33096).to_f / f_den(77617, 33096).to_f
                              # => -0.827396059946821

_c
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