If anybody wants to further play around with this, I wrote the following script in python using matplotlib:

  import numpy
  import matplotlib.pyplot as plt
  import struct
  
  def power(x,p):
    i = struct.unpack("i", struct.pack("f", x))[0]
    i = (1-p) * 0x3f7a3bea + (p*i)
    return struct.unpack("f", struct.pack("i", i))[0]
  
  p = -0.5
  xs = numpy.arange(0.1,100,0.1)
  ys1 = map(lambda x: x**p, xs)
  ys2 = map(lambda x: power(x, p), xs)
  
  plt.plot(xs, ys1, label="Real function")
  plt.plot(xs, ys2, label="Approximation")
  
  plt.title("Graph of x^%d"%p)
  plt.legend(loc="upper left")
  plt.savefig("graph.png")

Change p to whatever you want (even values greater than 1) to see different powers.