### find_root does not fulfill tolerance

In Sage 7.3 the result of:

```
find_root((4*x^4-x^2).function(x),-0.25,0.4,xtol=1e-13,rtol=1e-13)
```

is

```
1.6619679287440101e-10
```

One would expect that the error with the exact solution (x=0) would be lower than 1e-13. I imagine that the multiplicity of the root produces this effect. Does somebody know the numerical algorithm behind find_root?

Thanks in advance.