matlab - Poor fit with nlinfit -

i'm having fitting issues nlinfit. can't seem figure out how improve fit. decreasing tolx or tolfun has not changed value in coeffs.

 model = @(a,x) 1./(1 + a*x.^2);   model0 = [1e13];    opts = statset('tolx', 1e-25, 'tolfun', 1e-25);   coeffs = nlinfit(freqdata, noisedata, model, model0, opts); 

here's fit. http://i.imgur.com/v1dkd4x.png

it seems dealing small numbers there might floating point precision issue. why won't transform expression different from, fit, inverse transform? example:

take 1/model transformation, have simple polynomial fitting,

model_new=(x,a)=1+a*x.^2 

where can use polyfit , polyval, take 1/result ...