Average Error: 19.3 → 12.6
Time: 23.9s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.074815782204149782432519341284458306068 \cdot 10^{-283}:\\ \;\;\;\;\sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 8.274008779449527226174688106162953762312 \cdot 10^{278}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -6.074815782204149782432519341284458306068 \cdot 10^{-283}:\\
\;\;\;\;\sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\

\mathbf{elif}\;V \cdot \ell \le 8.274008779449527226174688106162953762312 \cdot 10^{278}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r139548 = c0;
        double r139549 = A;
        double r139550 = V;
        double r139551 = l;
        double r139552 = r139550 * r139551;
        double r139553 = r139549 / r139552;
        double r139554 = sqrt(r139553);
        double r139555 = r139548 * r139554;
        return r139555;
}
↓
double f(double c0, double A, double V, double l) {
        double r139556 = V;
        double r139557 = l;
        double r139558 = r139556 * r139557;
        double r139559 = -6.07481578220415e-283;
        bool r139560 = r139558 <= r139559;
        double r139561 = A;
        double r139562 = cbrt(r139561);
        double r139563 = r139562 * r139562;
        double r139564 = r139558 / r139562;
        double r139565 = r139563 / r139564;
        double r139566 = sqrt(r139565);
        double r139567 = sqrt(r139566);
        double r139568 = r139561 / r139558;
        double r139569 = sqrt(r139568);
        double r139570 = sqrt(r139569);
        double r139571 = c0;
        double r139572 = r139570 * r139571;
        double r139573 = r139567 * r139572;
        double r139574 = 0.0;
        bool r139575 = r139558 <= r139574;
        double r139576 = 1.0;
        double r139577 = r139576 / r139556;
        double r139578 = sqrt(r139577);
        double r139579 = r139561 / r139557;
        double r139580 = sqrt(r139579);
        double r139581 = r139578 * r139580;
        double r139582 = r139571 * r139581;
        double r139583 = 8.274008779449527e+278;
        bool r139584 = r139558 <= r139583;
        double r139585 = sqrt(r139561);
        double r139586 = sqrt(r139558);
        double r139587 = r139585 / r139586;
        double r139588 = r139587 * r139571;
        double r139589 = r139561 / r139556;
        double r139590 = r139589 / r139557;
        double r139591 = sqrt(r139590);
        double r139592 = r139591 * r139571;
        double r139593 = r139584 ? r139588 : r139592;
        double r139594 = r139575 ? r139582 : r139593;
        double r139595 = r139560 ? r139573 : r139594;
        return r139595;
}

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) < -6.07481578220415e-283

    1. Initial program 14.5

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

    3. Applied *-commutative14.5

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

    5. Applied add-sqr-sqrt14.5

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

    6. Applied sqrt-prod14.7

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

    7. Applied associate-*l*14.7

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

    9. Applied add-cube-cbrt14.7

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

    10. Applied associate-/l*14.7

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

    if -6.07481578220415e-283 < (* V l) < 0.0

    1. Initial program 54.6

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

    3. Applied *-un-lft-identity54.6

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

    4. Applied times-frac34.6

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

    5. Applied sqrt-prod39.5

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

    if 0.0 < (* V l) < 8.274008779449527e+278

    1. Initial program 14.9

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

    3. Applied *-commutative14.9

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

    5. Applied sqrt-div6.4

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

    if 8.274008779449527e+278 < (* V l)

    1. Initial program 39.5

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

    3. Applied *-commutative39.5

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

    5. Applied associate-/r*23.2

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

  4. Final simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -6.074815782204149782432519341284458306068 \cdot 10^{-283}:\\ \;\;\;\;\sqrt{\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 8.274008779449527226174688106162953762312 \cdot 10^{278}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))