Average Error: 19.0 → 8.4
Time: 7.2s
Precision: binary64
\[[V, l]=\mathsf{sort}([V, l])\]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \leq -2.9852745842571337 \cdot 10^{+192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -2.116845488611897 \cdot 10^{-93}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq 6.09891151415403 \cdot 10^{+266}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]
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 -2.9852745842571337 \cdot 10^{+192}:\\
\;\;\;\;t_0\\

\mathbf{elif}\;V \cdot \ell \leq -2.116845488611897 \cdot 10^{-93}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\

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

\mathbf{elif}\;V \cdot \ell \leq 6.09891151415403 \cdot 10^{+266}:\\
\;\;\;\;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) -2.9852745842571337e+192)
     t_0
     (if (<= (* V l) -2.116845488611897e-93)
       (* c0 (sqrt (/ A (* V l))))
       (if (<= (* V l) 0.0)
         t_0
         (if (<= (* V l) 6.09891151415403e+266)
           (* 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) <= -2.9852745842571337e+192) {
		tmp = t_0;
	} else if ((V * l) <= -2.116845488611897e-93) {
		tmp = c0 * sqrt(A / (V * l));
	} else if ((V * l) <= 0.0) {
		tmp = t_0;
	} else if ((V * l) <= 6.09891151415403e+266) {
		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) < -2.9852745842571337e192 or -2.1168454886118972e-93 < (*.f64 V l) < 0.0

    1. Initial program 33.7

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

    2. Applied add-cube-cbrt_binary6433.9

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

    3. Applied times-frac_binary6424.7

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

    4. Applied associate-*r/_binary6425.4

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

    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 -2.9852745842571337e192 < (*.f64 V l) < -2.1168454886118972e-93

    1. Initial program 5.0

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

    2. Applied add-cube-cbrt_binary645.4

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

    3. Applied times-frac_binary6412.5

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

    4. Applied add-cube-cbrt_binary6412.7

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

    5. Applied pow1_binary6412.7

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \color{blue}{{\left(\frac{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\ell}\right)}^{1}}} \]

    6. Applied pow1_binary6412.7

      \[\leadsto c0 \cdot \sqrt{\color{blue}{{\left(\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}\right)}^{1}} \cdot {\left(\frac{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\ell}\right)}^{1}} \]

    7. Applied pow-prod-down_binary6412.7

      \[\leadsto c0 \cdot \sqrt{\color{blue}{{\left(\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\left(\sqrt[3]{\sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}\right) \cdot \sqrt[3]{\sqrt[3]{A}}}{\ell}\right)}^{1}}} \]

    8. Simplified5.0

      \[\leadsto c0 \cdot \sqrt{{\color{blue}{\left(\frac{A}{V \cdot \ell}\right)}}^{1}} \]

    if 0.0 < (*.f64 V l) < 6.0989115141540304e266

    1. Initial program 10.1

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

    2. Applied sqrt-div_binary640.7

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

    if 6.0989115141540304e266 < (*.f64 V l)

    1. Initial program 37.6

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

    2. Applied add-cube-cbrt_binary6437.7

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

    3. Applied times-frac_binary6423.1

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

    4. Applied associate-*l/_binary6423.1

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

    5. Simplified23.0

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

  4. Final simplification8.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2.9852745842571337 \cdot 10^{+192}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -2.116845488611897 \cdot 10^{-93}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 6.09891151415403 \cdot 10^{+266}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022019 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))