Has anyone an idea, why calculating a product from small numbers in the new Mathematica 12.1 does not give the same results as Mathematica 11.2?
For the complete example, which is a part of a likelihood computation, see the attached notebook.
Calculation in Mathematica 12.1
In[1]=
$MachinePrecision
Times @@ {0.0016214960604198744`, 0.001620019767161015`, ..., *[many numbers]*, ... ,
0.0016116789355172978`}
Out[1]= 15.9546
During evaluation of In[1]:= General::munfl: 2.0705*10^-191 8.36448*10^-186 is too small to represent as a normalized machine number; precision may be lost.
During evaluation of In[1]:= General::munfl: 3.24301*10^-189 1.03749*10^-186 is too small to represent as a normalized machine number; precision may be lost.
Out[2]= 0.
Exactly the same calculation in Mathematica 11.2
$MachinePrecision
Times @@ {0.0016214960604198744`, 0.001620019767161015`, ..., *[many numbers]*, ... , 0.0016116789355172978`}
Out[1]= 15.9546
Out[2]= 5.82698961568687*10^-751
P.S. Likelihood calculation is not the problem. Its just the surprising difference between two Mathematica versions.
Times_Test.nb (22.5 KB)