Average Error: 19.2 → 19.4
Time: 18.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \le -9.678217132402725572671911550579244480911 \cdot 10^{-129}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\ \mathbf{elif}\;\ell \le -1.404945491901074724427885644744025668452 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{\frac{\sqrt[3]{A}}{\ell}} \cdot \left(\sqrt{\frac{\sqrt[3]{A}}{\frac{V}{\sqrt[3]{A}}}} \cdot c0\right)\\ \mathbf{elif}\;\ell \le -1.189107474010094506541488408199064447205 \cdot 10^{-257} \lor \neg \left(\ell \le 3.505014405888156119976021688504012599447 \cdot 10^{138}\right):\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\ell \le -9.678217132402725572671911550579244480911 \cdot 10^{-129}:\\
\;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\

\mathbf{elif}\;\ell \le -1.404945491901074724427885644744025668452 \cdot 10^{-142}:\\
\;\;\;\;\sqrt{\frac{\sqrt[3]{A}}{\ell}} \cdot \left(\sqrt{\frac{\sqrt[3]{A}}{\frac{V}{\sqrt[3]{A}}}} \cdot c0\right)\\

\mathbf{elif}\;\ell \le -1.189107474010094506541488408199064447205 \cdot 10^{-257} \lor \neg \left(\ell \le 3.505014405888156119976021688504012599447 \cdot 10^{138}\right):\\
\;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r123554 = c0;
        double r123555 = A;
        double r123556 = V;
        double r123557 = l;
        double r123558 = r123556 * r123557;
        double r123559 = r123555 / r123558;
        double r123560 = sqrt(r123559);
        double r123561 = r123554 * r123560;
        return r123561;
}
↓
double f(double c0, double A, double V, double l) {
        double r123562 = l;
        double r123563 = -9.678217132402726e-129;
        bool r123564 = r123562 <= r123563;
        double r123565 = A;
        double r123566 = V;
        double r123567 = r123566 * r123562;
        double r123568 = r123565 / r123567;
        double r123569 = sqrt(r123568);
        double r123570 = sqrt(r123569);
        double r123571 = c0;
        double r123572 = r123571 * r123570;
        double r123573 = r123570 * r123572;
        double r123574 = -1.4049454919010747e-142;
        bool r123575 = r123562 <= r123574;
        double r123576 = cbrt(r123565);
        double r123577 = r123576 / r123562;
        double r123578 = sqrt(r123577);
        double r123579 = r123566 / r123576;
        double r123580 = r123576 / r123579;
        double r123581 = sqrt(r123580);
        double r123582 = r123581 * r123571;
        double r123583 = r123578 * r123582;
        double r123584 = -1.1891074740100945e-257;
        bool r123585 = r123562 <= r123584;
        double r123586 = 3.505014405888156e+138;
        bool r123587 = r123562 <= r123586;
        double r123588 = !r123587;
        bool r123589 = r123585 || r123588;
        double r123590 = r123565 / r123566;
        double r123591 = r123590 / r123562;
        double r123592 = sqrt(r123591);
        double r123593 = r123571 * r123592;
        double r123594 = r123589 ? r123573 : r123593;
        double r123595 = r123575 ? r123583 : r123594;
        double r123596 = r123564 ? r123573 : r123595;
        return r123596;
}

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 l < -9.678217132402726e-129 or -1.4049454919010747e-142 < l < -1.1891074740100945e-257 or 3.505014405888156e+138 < l

    1. Initial program 18.8

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

    3. Applied add-sqr-sqrt18.8

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

    4. Applied sqrt-prod19.0

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

    5. Applied associate-*r*19.0

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

    6. Simplified19.0

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

    if -9.678217132402726e-129 < l < -1.4049454919010747e-142

    1. Initial program 21.6

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

    3. Applied add-cube-cbrt22.0

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

    4. Applied times-frac17.7

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

    5. Applied sqrt-prod38.1

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

    6. Applied associate-*r*38.1

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

    7. Simplified38.2

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

    if -1.1891074740100945e-257 < l < 3.505014405888156e+138

    1. Initial program 19.7

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

    3. Applied associate-/r*19.5

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

  4. Final simplification19.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \le -9.678217132402725572671911550579244480911 \cdot 10^{-129}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\ \mathbf{elif}\;\ell \le -1.404945491901074724427885644744025668452 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{\frac{\sqrt[3]{A}}{\ell}} \cdot \left(\sqrt{\frac{\sqrt[3]{A}}{\frac{V}{\sqrt[3]{A}}}} \cdot c0\right)\\ \mathbf{elif}\;\ell \le -1.189107474010094506541488408199064447205 \cdot 10^{-257} \lor \neg \left(\ell \le 3.505014405888156119976021688504012599447 \cdot 10^{138}\right):\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))