Derivation

Split input into 2 regimes
if l < -2.98475593889235e-310
1. Initial program 18.4
  \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
2. Initial simplification18.4
  \[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\]
3. Using strategy rm
4. Applied add-sqr-sqrt18.5
  \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right)}\]
5. Applied associate-*r*18.5
  \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right) \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}}\]
if -2.98475593889235e-310 < l
1. Initial program 18.6
  \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
2. Initial simplification18.5
  \[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\]
3. Using strategy rm
4. Applied sqrt-div11.0
  \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}}\]
5. Applied associate-*r/13.0
  \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}}\]
Recombined 2 regimes into one program.
Final simplification15.8
\[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -2.98475593889235 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}} \cdot c0}{\sqrt{\ell}}\\ \end{array}\]

Runtime

herbie shell --seed 2018248 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))

In
Out