41 Cistern Program

[Gerson W. Barbosa]

(08-16-2016 07:08 PM)Gerson W. Barbosa Wrote:  Or, regardless the angle mode, but at the cost of 2.5 bytes and a few milliseconds more:

« OVER / 1 SWAP - DUP
ACOSH IM SWAP DUP
ACOS SIN * - SWAP SQ * *
»

A faster 55-byte solution:

Code:


  « OVER / 1. SWAP - 
    DUP ACOS SIN DUP2 R→C 
    ARG UNROT * - SWAP SQ 
    * *
  »

3 2 1 → 7.37021819169 (0.0497 s, 50g)

An even faster 60-byte solution:

Code:


  « OVER / 1. SWAP - 1.
    OVER SQ - √ DUP2 R→C 
    ARG UNROT * - SWAP SQ 
    * *
  »

3 2 1 → 7.37021819169 (0.0352 s, 50g)

These require RADIANS mode, however. Also, 2.5 more bytes on the HP-48 (ROT ROT instead of UNROT).

------------------------------------------------------------------------------------

\(V=L\cdot R^{2}\cdot \left \{ Arg\left [ \left ( 1-\frac{H}{R} \right ),\sqrt{1-\left ( 1-\frac{H}{R} \right )^{2}} \right ] - \left ( 1-\frac{H}{R} \right )\cdot \sqrt{1-\left ( 1-\frac{H}{R} \right )^{2}} \right \}\)

where

\(Arg(a,b) = \tan^{-1}\left ( \frac{b}{a} \right )\)

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