The manual/hand/analytical calculation of pipe span length, pipe sagging deflection and/or dead weight stress is typically performed using simply supported beam or fully anchored beam formulas.

There are some adjusted formulas considering the intermediate situation.

However, the real piping layout corresponds rather to continuously supported beam situation. Moreover, the actual pipe span length may not be uniformly distributed. In addition, you might have direction changes (elbows), branched pipe connections, inserted loops, valves etc.
This is the reason why Caesar II stress model quantifies realistic sagging deflections that may not match the simply hand-calculated values.

As long as you develop the piping system model correctly, including all the relevant piping components weights and following the actual layout and support arrangement, you should not be worried about results accuracy.

The analytical/hand-calculation span formulas are simplified tools, which were extensively used in the past, when piping flexibility programs were not available or hardly accessible.

Regards,