Hi Debasis

I think you are calculating vertical deflection only for external force while comparing with beam formulae Deflection = PL3/(192 EI)

By subtracting deflection from Caesar (W+P1+F1) & (W+P1) you will get deflection only for external force.

I cross check with 10" dia, sch 30 length 8000 mm error coming 3%.
When I increase the length % error is decreasing.
As Anindya-da mention earlier restraint stiffness (1.0E12 N/cm),truncation and round off errors could be possible factor for small error.

When I increase the length even error come down below 1%.

Regards

Habib