Average Error: 19.0 → 7.8
Time: 6.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.8700420056280899 \cdot 10^{68}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le -3.66804977381144 \cdot 10^{-167}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\left(\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}{\left|\sqrt[3]{V}\right|}\\ \mathbf{elif}\;V \cdot \ell \le 2.01505104436057934 \cdot 10^{305}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \frac{\sqrt[3]{A}}{\ell}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.8700420056280899 \cdot 10^{68}:\\
\;\;\;\;c0 \cdot \left(\left|\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \frac{\sqrt[3]{A}}{\ell}}\right)\\

\mathbf{elif}\;V \cdot \ell \le -3.66804977381144 \cdot 10^{-167}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;c0 \cdot \frac{\sqrt{\left(\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}{\left|\sqrt[3]{V}\right|}\\

\mathbf{elif}\;V \cdot \ell \le 2.01505104436057934 \cdot 10^{305}:\\
\;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r238592 = c0;
        double r238593 = A;
        double r238594 = V;
        double r238595 = l;
        double r238596 = r238594 * r238595;
        double r238597 = r238593 / r238596;
        double r238598 = sqrt(r238597);
        double r238599 = r238592 * r238598;
        return r238599;
}
↓
double f(double c0, double A, double V, double l) {
        double r238600 = V;
        double r238601 = l;
        double r238602 = r238600 * r238601;
        double r238603 = -1.87004200562809e+68;
        bool r238604 = r238602 <= r238603;
        double r238605 = c0;
        double r238606 = A;
        double r238607 = cbrt(r238606);
        double r238608 = r238607 * r238607;
        double r238609 = r238608 / r238600;
        double r238610 = cbrt(r238609);
        double r238611 = fabs(r238610);
        double r238612 = r238607 / r238601;
        double r238613 = r238610 * r238612;
        double r238614 = sqrt(r238613);
        double r238615 = r238611 * r238614;
        double r238616 = r238605 * r238615;
        double r238617 = -3.66804977381144e-167;
        bool r238618 = r238602 <= r238617;
        double r238619 = 1.0;
        double r238620 = r238602 / r238606;
        double r238621 = r238619 / r238620;
        double r238622 = sqrt(r238621);
        double r238623 = r238605 * r238622;
        double r238624 = 0.0;
        bool r238625 = r238602 <= r238624;
        double r238626 = cbrt(r238608);
        double r238627 = r238626 * r238610;
        double r238628 = r238626 * r238612;
        double r238629 = r238627 * r238628;
        double r238630 = sqrt(r238629);
        double r238631 = cbrt(r238600);
        double r238632 = fabs(r238631);
        double r238633 = r238630 / r238632;
        double r238634 = r238605 * r238633;
        double r238635 = 2.0150510443605793e+305;
        bool r238636 = r238602 <= r238635;
        double r238637 = sqrt(r238606);
        double r238638 = r238619 / r238602;
        double r238639 = sqrt(r238638);
        double r238640 = r238637 * r238639;
        double r238641 = r238605 * r238640;
        double r238642 = r238636 ? r238641 : r238616;
        double r238643 = r238625 ? r238634 : r238642;
        double r238644 = r238618 ? r238623 : r238643;
        double r238645 = r238604 ? r238616 : r238644;
        return r238645;
}

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 (* V l) < -1.87004200562809e+68 or 2.0150510443605793e+305 < (* V l)

    1. Initial program 25.7

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

    3. Applied add-cube-cbrt25.9

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

    4. Applied times-frac17.9

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

    6. Applied add-cube-cbrt18.0

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

    7. Applied associate-*l*18.0

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

    9. Applied sqrt-prod11.7

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

    10. Simplified11.7

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

    if -1.87004200562809e+68 < (* V l) < -3.66804977381144e-167

    1. Initial program 5.0

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

    3. Applied clear-num5.1

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

    if -3.66804977381144e-167 < (* V l) < 0.0

    1. Initial program 43.9

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

    3. Applied add-cube-cbrt44.1

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

    4. Applied times-frac30.2

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

    6. Applied add-cube-cbrt30.4

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

    7. Applied associate-*l*30.4

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

    9. Applied cbrt-div30.3

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

    10. Applied associate-*l/30.4

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

    11. Applied cbrt-div30.4

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

    12. Applied associate-*r/30.4

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

    13. Applied frac-times30.5

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

    14. Applied sqrt-div19.9

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

    15. Simplified19.9

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

    16. Simplified19.9

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

    if 0.0 < (* V l) < 2.0150510443605793e+305

    1. Initial program 10.2

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

    3. Applied div-inv10.6

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

    4. Applied sqrt-prod1.4

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification7.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.8700420056280899 \cdot 10^{68}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le -3.66804977381144 \cdot 10^{-167}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\left(\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \frac{\sqrt[3]{A}}{\ell}\right)}}{\left|\sqrt[3]{V}\right|}\\ \mathbf{elif}\;V \cdot \ell \le 2.01505104436057934 \cdot 10^{305}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \frac{\sqrt[3]{A}}{\ell}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))