Increase accuracy of fsolve

I am trying to increase the accuracy of the solution obtained from fsolve by changing the options of fsolve as follows:

options = optimset('Display','iter');

options.MaxIter = 5000 ;

options.MaxFunEvals = 5000000 ;

options.FunctionTolerance = 1e-16;

options.OptimalityTolerance = 1e-16;

options.StepTolerance = 1e-16;

solution = fsolve(@ComputeFunction,solution,options);

However, nothing seems to change even after including the three lines on changing the tolerance. The total number of iterations performed remains the same. Information on the last two iterations is included below for your reference.

                                         Norm of      First-order 
 Iteration  Func-count     f(x)          step          optimality
  2132      855333     3.66897e-09    0.000570497          0.544      
  2133      855734     3.66897e-09    8.73214e-15          0.145

Any idea on how I can actually raise the accuracy especially by lowering the value of f(x) even more? Thanks!

[Walter Roberson]

My reading of that is that the last step was by just slightly more than 1E-16 and that the next step would have been less than 1E-16

The documentation recommends against using a tolerance that low https://www.mathworks.com/help/optim/ug/tolerances-and-stopping-criteria.html says using a step tolerance less than eps can lead to inaccuracies; eps is about 2E-16, twice as large as what you are asking for.