Average Error: 19.4 → 12.2
Time: 5.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le 2.96439387504747926505941275720932823419 \cdot 10^{-323}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{V} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 1.666028060170161707591813005969240947671 \cdot 10^{121}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt[3]{A}}}{\sqrt{V \cdot \sqrt[3]{\ell}}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le 2.96439387504747926505941275720932823419 \cdot 10^{-323}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{V} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}\\

\mathbf{elif}\;V \cdot \ell \le 1.666028060170161707591813005969240947671 \cdot 10^{121}:\\
\;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt[3]{A}}}{\sqrt{V \cdot \sqrt[3]{\ell}}}\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r175358 = c0;
        double r175359 = A;
        double r175360 = V;
        double r175361 = l;
        double r175362 = r175360 * r175361;
        double r175363 = r175359 / r175362;
        double r175364 = sqrt(r175363);
        double r175365 = r175358 * r175364;
        return r175365;
}
↓
double f(double c0, double A, double V, double l) {
        double r175366 = V;
        double r175367 = l;
        double r175368 = r175366 * r175367;
        double r175369 = 2.9643938750475e-323;
        bool r175370 = r175368 <= r175369;
        double r175371 = c0;
        double r175372 = A;
        double r175373 = cbrt(r175372);
        double r175374 = r175373 * r175373;
        double r175375 = cbrt(r175367);
        double r175376 = r175375 * r175375;
        double r175377 = r175374 / r175376;
        double r175378 = r175377 / r175366;
        double r175379 = r175373 / r175375;
        double r175380 = r175378 * r175379;
        double r175381 = sqrt(r175380);
        double r175382 = r175371 * r175381;
        double r175383 = 1.6660280601701617e+121;
        bool r175384 = r175368 <= r175383;
        double r175385 = sqrt(r175372);
        double r175386 = r175371 * r175385;
        double r175387 = sqrt(r175368);
        double r175388 = r175386 / r175387;
        double r175389 = r175377 * r175373;
        double r175390 = sqrt(r175389);
        double r175391 = r175366 * r175375;
        double r175392 = sqrt(r175391);
        double r175393 = r175390 / r175392;
        double r175394 = r175371 * r175393;
        double r175395 = r175384 ? r175388 : r175394;
        double r175396 = r175370 ? r175382 : r175395;
        return r175396;
}

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 3 regimes

  2. if (* V l) < 2.9643938750475e-323

    1. Initial program 23.8

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

    3. Applied *-un-lft-identity23.8

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

    4. Applied times-frac21.4

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt21.7

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

    7. Applied add-cube-cbrt21.8

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

    8. Applied times-frac21.8

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

    9. Applied associate-*r*18.1

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

    10. Simplified18.1

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

    if 2.9643938750475e-323 < (* V l) < 1.6660280601701617e+121

    1. Initial program 9.0

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

    3. Applied sqrt-div0.8

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

    4. Applied associate-*r/2.8

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

    if 1.6660280601701617e+121 < (* V l)

    1. Initial program 23.2

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

    3. Applied *-un-lft-identity23.2

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

    4. Applied times-frac19.1

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt19.3

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

    7. Applied add-cube-cbrt19.4

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

    8. Applied times-frac19.4

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

    9. Applied associate-*r*17.4

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

    10. Simplified17.4

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

    12. Applied frac-times19.0

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

    13. Applied sqrt-div9.9

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

  4. Final simplification12.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le 2.96439387504747926505941275720932823419 \cdot 10^{-323}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{V} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 1.666028060170161707591813005969240947671 \cdot 10^{121}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt[3]{A}}}{\sqrt{V \cdot \sqrt[3]{\ell}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))