Question

Does R have a known problem with uniroot and handling floating points?

>str(uniroot(function(x) x*(x^2-1) + .5, lower = -2, upper = 2,
+                  tol = 0.0001))

List of 4
$ root      : num -1.19
$ f.root    : num -2.55e-07
$ iter      : int 7
$ estim.prec: num 5e-05
> -1.19 * ( 1.19 ^ 2 - 1 ) + 0.5 
[1] 0.004841

Clearly the value of f.root is not equal to the value of the function calculated by hand.

Answer 1

Your value of root is shown to only 2 s.f., but it estimates the precision at 5e-5. That suggests it “knows” other digits in the answer that you are not looking at. Try to print out root-1.19 and you will see what I mean.

In particular, str is intended as a quick way to view the structure of an R object, so it intentionally prints a limited number of digits: the default value of digits.d is 3 (see ?str). Just printing the results (as in uniroot(...) or u1 <- uniroot(...); u1 would have shown you more digits and perhaps have avoided the confusion.