Average Error: 19.3 → 9.8
Time: 31.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\ell \cdot V = -\infty:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{elif}\;\ell \cdot V \le -5.601891409264343123426103753339848933114 \cdot 10^{-287}:\\ \;\;\;\;\sqrt{\sqrt[3]{\frac{1}{\ell \cdot V}} \cdot \sqrt[3]{A}} \cdot \left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{\ell \cdot V}\right|}\right)\\ \mathbf{elif}\;\ell \cdot V \le 2.442774188137666401114116722762846155888 \cdot 10^{-317}:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\ell \cdot V = -\infty:\\
\;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\

\mathbf{elif}\;\ell \cdot V \le -5.601891409264343123426103753339848933114 \cdot 10^{-287}:\\
\;\;\;\;\sqrt{\sqrt[3]{\frac{1}{\ell \cdot V}} \cdot \sqrt[3]{A}} \cdot \left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{\ell \cdot V}\right|}\right)\\

\mathbf{elif}\;\ell \cdot V \le 2.442774188137666401114116722762846155888 \cdot 10^{-317}:\\
\;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r5706413 = c0;
        double r5706414 = A;
        double r5706415 = V;
        double r5706416 = l;
        double r5706417 = r5706415 * r5706416;
        double r5706418 = r5706414 / r5706417;
        double r5706419 = sqrt(r5706418);
        double r5706420 = r5706413 * r5706419;
        return r5706420;
}
↓
double f(double c0, double A, double V, double l) {
        double r5706421 = l;
        double r5706422 = V;
        double r5706423 = r5706421 * r5706422;
        double r5706424 = -inf.0;
        bool r5706425 = r5706423 <= r5706424;
        double r5706426 = A;
        double r5706427 = r5706426 / r5706421;
        double r5706428 = sqrt(r5706427);
        double r5706429 = 1.0;
        double r5706430 = r5706429 / r5706422;
        double r5706431 = sqrt(r5706430);
        double r5706432 = r5706428 * r5706431;
        double r5706433 = c0;
        double r5706434 = r5706432 * r5706433;
        double r5706435 = -5.601891409264343e-287;
        bool r5706436 = r5706423 <= r5706435;
        double r5706437 = r5706429 / r5706423;
        double r5706438 = cbrt(r5706437);
        double r5706439 = cbrt(r5706426);
        double r5706440 = r5706438 * r5706439;
        double r5706441 = sqrt(r5706440);
        double r5706442 = fabs(r5706439);
        double r5706443 = cbrt(r5706423);
        double r5706444 = fabs(r5706443);
        double r5706445 = r5706442 / r5706444;
        double r5706446 = r5706433 * r5706445;
        double r5706447 = r5706441 * r5706446;
        double r5706448 = 2.4427741881377e-317;
        bool r5706449 = r5706423 <= r5706448;
        double r5706450 = sqrt(r5706426);
        double r5706451 = sqrt(r5706423);
        double r5706452 = r5706450 / r5706451;
        double r5706453 = r5706433 * r5706452;
        double r5706454 = r5706449 ? r5706434 : r5706453;
        double r5706455 = r5706436 ? r5706447 : r5706454;
        double r5706456 = r5706425 ? r5706434 : r5706455;
        return r5706456;
}

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 (* V l) < -inf.0 or -5.601891409264343e-287 < (* V l) < 2.4427741881377e-317

    1. Initial program 53.0

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

    3. Applied *-un-lft-identity53.0

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

    4. Applied times-frac30.9

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

    5. Applied sqrt-prod38.2

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

    if -inf.0 < (* V l) < -5.601891409264343e-287

    1. Initial program 9.7

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

    3. Applied add-cube-cbrt10.2

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

    4. Applied sqrt-prod10.2

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

    5. Applied associate-*r*10.2

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

    7. Applied div-inv10.2

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

    8. Applied cbrt-prod10.1

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

    10. Applied cbrt-div10.1

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

    11. Applied cbrt-div2.6

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

    12. Applied frac-times2.6

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

    13. Applied sqrt-div1.0

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

    14. Simplified1.0

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

    15. Simplified1.0

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

    if 2.4427741881377e-317 < (* V l)

    1. Initial program 14.9

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

    3. Applied sqrt-div6.6

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

  4. Final simplification9.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V = -\infty:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{elif}\;\ell \cdot V \le -5.601891409264343123426103753339848933114 \cdot 10^{-287}:\\ \;\;\;\;\sqrt{\sqrt[3]{\frac{1}{\ell \cdot V}} \cdot \sqrt[3]{A}} \cdot \left(c0 \cdot \frac{\left|\sqrt[3]{A}\right|}{\left|\sqrt[3]{\ell \cdot V}\right|}\right)\\ \mathbf{elif}\;\ell \cdot V \le 2.442774188137666401114116722762846155888 \cdot 10^{-317}:\\ \;\;\;\;\left(\sqrt{\frac{A}{\ell}} \cdot \sqrt{\frac{1}{V}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))