Average Error: 19.2 → 12.3
Time: 58.1s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.756886674182593 \cdot 10^{+248}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{elif}\;V \cdot \ell \le -5.737663690670792 \cdot 10^{-214}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.976262583365 \cdot 10^{-323}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 1.231583818494 \cdot 10^{-316}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}} \cdot \left(\sqrt{\sqrt{\sqrt[3]{\frac{A}{\ell}} \cdot \left(\left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right) \cdot \frac{1}{V}\right)}} \cdot c0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -7.756886674182593 \cdot 10^{+248}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\

\mathbf{elif}\;V \cdot \ell \le -5.737663690670792 \cdot 10^{-214}:\\
\;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le -1.976262583365 \cdot 10^{-323}:\\
\;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 1.231583818494 \cdot 10^{-316}:\\
\;\;\;\;\sqrt{\sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}} \cdot \left(\sqrt{\sqrt{\sqrt[3]{\frac{A}{\ell}} \cdot \left(\left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right) \cdot \frac{1}{V}\right)}} \cdot c0\right)\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r46583634 = c0;
        double r46583635 = A;
        double r46583636 = V;
        double r46583637 = l;
        double r46583638 = r46583636 * r46583637;
        double r46583639 = r46583635 / r46583638;
        double r46583640 = sqrt(r46583639);
        double r46583641 = r46583634 * r46583640;
        return r46583641;
}
↓
double f(double c0, double A, double V, double l) {
        double r46583642 = V;
        double r46583643 = l;
        double r46583644 = r46583642 * r46583643;
        double r46583645 = -7.756886674182593e+248;
        bool r46583646 = r46583644 <= r46583645;
        double r46583647 = c0;
        double r46583648 = 1.0;
        double r46583649 = r46583648 / r46583643;
        double r46583650 = A;
        double r46583651 = r46583650 / r46583642;
        double r46583652 = r46583649 * r46583651;
        double r46583653 = sqrt(r46583652);
        double r46583654 = r46583647 * r46583653;
        double r46583655 = -5.737663690670792e-214;
        bool r46583656 = r46583644 <= r46583655;
        double r46583657 = r46583650 / r46583644;
        double r46583658 = sqrt(r46583657);
        double r46583659 = r46583658 * r46583647;
        double r46583660 = -1.976262583365e-323;
        bool r46583661 = r46583644 <= r46583660;
        double r46583662 = sqrt(r46583651);
        double r46583663 = sqrt(r46583643);
        double r46583664 = r46583662 / r46583663;
        double r46583665 = r46583664 * r46583647;
        double r46583666 = 1.231583818494e-316;
        bool r46583667 = r46583644 <= r46583666;
        double r46583668 = r46583650 / r46583643;
        double r46583669 = r46583648 / r46583642;
        double r46583670 = r46583668 * r46583669;
        double r46583671 = sqrt(r46583670);
        double r46583672 = sqrt(r46583671);
        double r46583673 = cbrt(r46583668);
        double r46583674 = r46583673 * r46583673;
        double r46583675 = r46583674 * r46583669;
        double r46583676 = r46583673 * r46583675;
        double r46583677 = sqrt(r46583676);
        double r46583678 = sqrt(r46583677);
        double r46583679 = r46583678 * r46583647;
        double r46583680 = r46583672 * r46583679;
        double r46583681 = sqrt(r46583650);
        double r46583682 = sqrt(r46583644);
        double r46583683 = r46583681 / r46583682;
        double r46583684 = r46583683 * r46583647;
        double r46583685 = r46583667 ? r46583680 : r46583684;
        double r46583686 = r46583661 ? r46583665 : r46583685;
        double r46583687 = r46583656 ? r46583659 : r46583686;
        double r46583688 = r46583646 ? r46583654 : r46583687;
        return r46583688;
}

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 5 regimes

  2. if (* V l) < -7.756886674182593e+248

    1. Initial program 35.5

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

    3. Applied *-un-lft-identity35.5

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

    4. Applied times-frac22.1

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

    6. Applied div-inv22.1

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

    7. Applied associate-*r*22.3

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

    8. Simplified22.3

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

    if -7.756886674182593e+248 < (* V l) < -5.737663690670792e-214

    1. Initial program 7.9

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

    if -5.737663690670792e-214 < (* V l) < -1.976262583365e-323

    1. Initial program 24.5

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

    3. Applied *-un-lft-identity24.5

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

    4. Applied times-frac24.0

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

    6. Applied associate-*r/23.7

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

    7. Applied sqrt-div34.0

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

    8. Simplified34.0

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

    if -1.976262583365e-323 < (* V l) < 1.231583818494e-316

    1. Initial program 60.7

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

    3. Applied *-un-lft-identity60.7

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

    4. Applied times-frac37.4

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

    6. Applied add-sqr-sqrt37.5

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

    7. Applied associate-*r*37.5

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}}\right) \cdot \sqrt{\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}}}\]
    8. Using strategy rm

    9. Applied add-cube-cbrt37.5

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

    10. Applied associate-*r*37.5

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

    if 1.231583818494e-316 < (* V l)

    1. Initial program 15.0

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

    3. Applied sqrt-div6.4

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification12.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.756886674182593 \cdot 10^{+248}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{elif}\;V \cdot \ell \le -5.737663690670792 \cdot 10^{-214}:\\ \;\;\;\;\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le -1.976262583365 \cdot 10^{-323}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}} \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 1.231583818494 \cdot 10^{-316}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{\ell} \cdot \frac{1}{V}}} \cdot \left(\sqrt{\sqrt{\sqrt[3]{\frac{A}{\ell}} \cdot \left(\left(\sqrt[3]{\frac{A}{\ell}} \cdot \sqrt[3]{\frac{A}{\ell}}\right) \cdot \frac{1}{V}\right)}} \cdot c0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))