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 r129818 = c0;
        double r129819 = A;
        double r129820 = V;
        double r129821 = l;
        double r129822 = r129820 * r129821;
        double r129823 = r129819 / r129822;
        double r129824 = sqrt(r129823);
        double r129825 = r129818 * r129824;
        return r129825;
}
↓
double f(double c0, double A, double V, double l) {
        double r129826 = V;
        double r129827 = l;
        double r129828 = r129826 * r129827;
        double r129829 = -1.87004200562809e+68;
        bool r129830 = r129828 <= r129829;
        double r129831 = c0;
        double r129832 = A;
        double r129833 = cbrt(r129832);
        double r129834 = r129833 * r129833;
        double r129835 = r129834 / r129826;
        double r129836 = cbrt(r129835);
        double r129837 = fabs(r129836);
        double r129838 = r129833 / r129827;
        double r129839 = r129836 * r129838;
        double r129840 = sqrt(r129839);
        double r129841 = r129837 * r129840;
        double r129842 = r129831 * r129841;
        double r129843 = -3.66804977381144e-167;
        bool r129844 = r129828 <= r129843;
        double r129845 = 1.0;
        double r129846 = r129828 / r129832;
        double r129847 = r129845 / r129846;
        double r129848 = sqrt(r129847);
        double r129849 = r129831 * r129848;
        double r129850 = 0.0;
        bool r129851 = r129828 <= r129850;
        double r129852 = cbrt(r129834);
        double r129853 = r129852 * r129836;
        double r129854 = r129852 * r129838;
        double r129855 = r129853 * r129854;
        double r129856 = sqrt(r129855);
        double r129857 = cbrt(r129826);
        double r129858 = fabs(r129857);
        double r129859 = r129856 / r129858;
        double r129860 = r129831 * r129859;
        double r129861 = 2.0150510443605793e+305;
        bool r129862 = r129828 <= r129861;
        double r129863 = sqrt(r129832);
        double r129864 = r129845 / r129828;
        double r129865 = sqrt(r129864);
        double r129866 = r129863 * r129865;
        double r129867 = r129831 * r129866;
        double r129868 = r129862 ? r129867 : r129842;
        double r129869 = r129851 ? r129860 : r129868;
        double r129870 = r129844 ? r129849 : r129869;
        double r129871 = r129830 ? r129842 : r129870;
        return r129871;
}

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)))))