Average Error: 19.6 → 9.4
Time: 6.0s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.389317920587127450867004748459224000174 \cdot 10^{293} \lor \neg \left(V \cdot \ell \le -1.324477534068431985346733984721304917892 \cdot 10^{-308} \lor \neg \left(V \cdot \ell \le -0.0\right)\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.389317920587127450867004748459224000174 \cdot 10^{293} \lor \neg \left(V \cdot \ell \le -1.324477534068431985346733984721304917892 \cdot 10^{-308} \lor \neg \left(V \cdot \ell \le -0.0\right)\right):\\
\;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\

\mathbf{else}:\\
\;\;\;\;\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}}\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r262085 = c0;
        double r262086 = A;
        double r262087 = V;
        double r262088 = l;
        double r262089 = r262087 * r262088;
        double r262090 = r262086 / r262089;
        double r262091 = sqrt(r262090);
        double r262092 = r262085 * r262091;
        return r262092;
}
↓
double f(double c0, double A, double V, double l) {
        double r262093 = V;
        double r262094 = l;
        double r262095 = r262093 * r262094;
        double r262096 = -1.3893179205871275e+293;
        bool r262097 = r262095 <= r262096;
        double r262098 = -1.324477534068432e-308;
        bool r262099 = r262095 <= r262098;
        double r262100 = -0.0;
        bool r262101 = r262095 <= r262100;
        double r262102 = !r262101;
        bool r262103 = r262099 || r262102;
        double r262104 = !r262103;
        bool r262105 = r262097 || r262104;
        double r262106 = c0;
        double r262107 = 1.0;
        double r262108 = r262107 / r262093;
        double r262109 = A;
        double r262110 = r262109 / r262094;
        double r262111 = r262108 * r262110;
        double r262112 = sqrt(r262111);
        double r262113 = r262106 * r262112;
        double r262114 = cbrt(r262109);
        double r262115 = cbrt(r262095);
        double r262116 = r262114 / r262115;
        double r262117 = fabs(r262116);
        double r262118 = r262117 * r262106;
        double r262119 = sqrt(r262116);
        double r262120 = r262118 * r262119;
        double r262121 = r262105 ? r262113 : r262120;
        return r262121;
}

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 2 regimes

  2. if (* V l) < -1.3893179205871275e+293 or -1.324477534068432e-308 < (* V l) < -0.0

    1. Initial program 48.7

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity48.7

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

    4. Applied times-frac31.0

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

    if -1.3893179205871275e+293 < (* V l) < -1.324477534068432e-308 or -0.0 < (* V l)

    1. Initial program 15.5

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt15.9

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

    4. Applied sqrt-prod15.9

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

    5. Applied associate-*r*15.9

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

    6. Simplified15.9

      \[\leadsto \color{blue}{\left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right)} \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\]
    7. Using strategy rm

    8. Applied cbrt-div15.8

      \[\leadsto \left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}}}\]
    9. Using strategy rm

    10. Applied add-sqr-sqrt15.8

      \[\leadsto \left(\left|\sqrt[3]{\color{blue}{\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{\frac{A}{V \cdot \ell}}}}\right| \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}}\]
    11. Using strategy rm

    12. Applied sqrt-div38.5

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

    13. Applied sqrt-div38.5

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

    14. Applied frac-times38.5

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

    15. Applied cbrt-div34.5

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

    16. Simplified34.5

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

    17. Simplified7.5

      \[\leadsto \left(\left|\frac{\sqrt[3]{A}}{\color{blue}{\sqrt[3]{V \cdot \ell}}}\right| \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification9.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.389317920587127450867004748459224000174 \cdot 10^{293} \lor \neg \left(V \cdot \ell \le -1.324477534068431985346733984721304917892 \cdot 10^{-308} \lor \neg \left(V \cdot \ell \le -0.0\right)\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019318 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))