Average Error: 19.4 → 8.3
Time: 10.2s
Precision: binary64
\[[V, l] = \mathsf{sort}([V, l]) \\]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -1.5714420946376377 \cdot 10^{+207}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -1.5645807136330107 \cdot 10^{-87}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq 8.488026387056449 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\
\mathbf{if}\;V \cdot \ell \leq -1.5714420946376377 \cdot 10^{+207}:\\
\;\;\;\;t_0\\

\mathbf{elif}\;V \cdot \ell \leq -1.5645807136330107 \cdot 10^{-87}:\\
\;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\

\mathbf{elif}\;V \cdot \ell \leq 0:\\
\;\;\;\;t_0\\

\mathbf{elif}\;V \cdot \ell \leq 8.488026387056449 \cdot 10^{+293}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\


\end{array}

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (/ (sqrt (/ A V)) (sqrt l)))))
   (if (<= (* V l) -1.5714420946376377e+207)
     t_0
     (if (<= (* V l) -1.5645807136330107e-87)
       (* c0 (sqrt (* A (/ 1.0 (* V l)))))
       (if (<= (* V l) 0.0)
         t_0
         (if (<= (* V l) 8.488026387056449e+293)
           (* c0 (/ (sqrt A) (sqrt (* V l))))
           (* c0 (sqrt (/ (/ A l) V)))))))))
double code(double c0, double A, double V, double l) {
	return c0 * sqrt(A / (V * l));
}
↓
double code(double c0, double A, double V, double l) {
	double t_0 = c0 * (sqrt(A / V) / sqrt(l));
	double tmp;
	if ((V * l) <= -1.5714420946376377e+207) {
		tmp = t_0;
	} else if ((V * l) <= -1.5645807136330107e-87) {
		tmp = c0 * sqrt(A * (1.0 / (V * l)));
	} else if ((V * l) <= 0.0) {
		tmp = t_0;
	} else if ((V * l) <= 8.488026387056449e+293) {
		tmp = c0 * (sqrt(A) / sqrt(V * l));
	} else {
		tmp = c0 * sqrt((A / l) / V);
	}
	return tmp;
}

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if (*.f64 V l) < -1.57144209463763766e207 or -1.56458071363301071e-87 < (*.f64 V l) < -0.0

    1. Initial program 35.1

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied add-cube-cbrt_binary6435.3

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{V \cdot \ell}} \]

    3. Applied times-frac_binary6425.0

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}} \]

    4. Applied associate-*r/_binary6425.5

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \sqrt[3]{A}}{\ell}}} \]

    5. Applied sqrt-div_binary6416.1

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \sqrt[3]{A}}}{\sqrt{\ell}}} \]

    6. Simplified15.8

      \[\leadsto c0 \cdot \frac{\color{blue}{\sqrt{\frac{A}{V}}}}{\sqrt{\ell}} \]

    if -1.57144209463763766e207 < (*.f64 V l) < -1.56458071363301071e-87

    1. Initial program 5.4

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied div-inv_binary645.4

      \[\leadsto c0 \cdot \sqrt{\color{blue}{A \cdot \frac{1}{V \cdot \ell}}} \]

    if -0.0 < (*.f64 V l) < 8.48802638705644869e293

    1. Initial program 9.9

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied sqrt-div_binary640.7

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}} \]

    if 8.48802638705644869e293 < (*.f64 V l)

    1. Initial program 40.4

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied add-cube-cbrt_binary6440.4

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{V \cdot \ell}} \]

    3. Applied times-frac_binary6423.0

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}} \]

    4. Applied associate-*l/_binary6423.0

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \frac{\sqrt[3]{A}}{\ell}}{V}}} \]

    5. Simplified22.9

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\frac{A}{\ell}}}{V}} \]
  3. Recombined 4 regimes into one program.

  4. Final simplification8.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1.5714420946376377 \cdot 10^{+207}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1.5645807136330107 \cdot 10^{-87}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 8.488026387056449 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022094 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))