Under what circumstance, mex-version of lsqcurvefit run slower than m-code of lsqcurvefit？

I converted a function to mex using Coder, which contains lsqcurvefit() to get some speedup. But this mex-version is slower than m-code.

function fit_param_mcode()
param = lsqcurvefit(@obj_fun)
end

% This take 1.6s and 1.5s was spent on objective evaluation
function fit_param_partial_mex()
    param = lsqcurvefit(@obj_fun_mex) % only the obj_fun is mex
end

% This full mex version is converted from fit_param_mcode().
% This take 2.6s and 1.5 was spent on objective evaluation, meaning the
% rest 1.1s is spent on mex-version of lsqcurvefit().
function fit_param_full_mex()
...                                   % both lsqcurvefit and obj_fun are mex
end

So, in my own case, the two versions take the same time to evaluate obj_fun, but self-time of m-code of lsqcurvefit() is much smaller.

I tried to reproduce the above result using other objective functions, such as exponential decay, sin(), cos(). But none of them reproduce the result, meaning the full-mex version is faster in these cases.

It seems this is related to my obj_fun, because my obj_fun does not have an analytical formula and it is based on simulation. Maybe mex-version of lsqcurvefit() take much time to do sanity checks and these checks are slow in mex.

Do you have any ideas?

[Xingwang Yong]

Does anyone know how to add "Tags" and "Products" after I post this question. I submited it by accident, without choosing related products. The "Edit" button does not help.