41 Cistern Program

[Gerson W. Barbosa]

(08-19-2016 01:13 PM)Gerson W. Barbosa Wrote:  

Code:


%%HP: T(3)A(D)F(.);
\<< \-> L D a h
  \<< 'SQ(D)/4.*L*IM(ACOSH(1.-2.*h/D))+\pi*a*SQ(h)*(1.-2.*h/(3.*D))+L*\v/(h*(D-h))*(h-D/2.)' EVAL
  \>>
\>>

Or, stack-only, 122.5 bytes:

Code:


%%HP: T(3)A(D)F(.);
\<< SWAP PICK3 PICK3 DUP + SWAP 3. * 1. UNROT / - * \pi * OVER SQ * 4. ROLLD DUP + OVER / NEG 1. + DUP ACOSH IM SWAP 1. OVER SQ - \v/ * - SWAP SQ * * 4. / +
\>>

This of course can be optimized even further, either for size or speed. Size optimization left out as an exercise for the interested reader :-)



L     D    a    h   -->       Volume

2     1 0.25 0.5  -->  0.916297857295

0     4    2    4   --> 33.5103216382 (32*π/3)

0     4    2    2   --> 16.7551608191 (16*π/3)