Calculating Fatigue Factor of Safety in Workbench

How is the fatigue factor of safety (FS) calculated in the workbench when using either the Goodman or Gerber analysis type and maximum principal stress? Since there are several different ways of doing this, depending on what assumptions you make about increasing load, I would like the actual equations used.

If using Goodman theory with constant amplitude loading, then FS can be calculated with a linear equation where FS = 1/((Salt/Se) + Smean/Sult), where Salt and Smean are the alternating and mean uniaxial equivalent stresses, after accounting for loading ratio and multiaxial stress (i.e. in this case, maximum principal stress is being used).

If using Gerber, then the equation is quadratic, since the mean stress term is squared, so you get, 1 = (Salt/Se)*FS + (Smean*FS/Sult)^2.

If the loading is non-constant amplitude, then iterative methods are required. (A load factor is applied internally until a life of 1 is found for the given loading. That load factor is then the FS). In any case, the user can perform a sanity check on his FS by taking the FS, using that value as the scale factor on another tool and he should get a life equal to the design life on his FS result. (Some exceptions exist where static failure is the limiting case).