Average Error: 19.1 → 13.9
Time: 4.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \le -5.556283518325683243464468114976330835385 \cdot 10^{-309}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\frac{A}{\ell}}{\sqrt[3]{V}}}}\right) \cdot \sqrt{\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}}\\ \mathbf{elif}\;V \le 3.621419097460427185242147570218797506351 \cdot 10^{-142}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \le 2.480087127913832854241189970085787477828 \cdot 10^{154}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \le -5.556283518325683243464468114976330835385 \cdot 10^{-309}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\frac{A}{\ell}}{\sqrt[3]{V}}}}\right) \cdot \sqrt{\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}}\\

\mathbf{elif}\;V \le 3.621419097460427185242147570218797506351 \cdot 10^{-142}:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\

\mathbf{elif}\;V \le 2.480087127913832854241189970085787477828 \cdot 10^{154}:\\
\;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r128405 = c0;
        double r128406 = A;
        double r128407 = V;
        double r128408 = l;
        double r128409 = r128407 * r128408;
        double r128410 = r128406 / r128409;
        double r128411 = sqrt(r128410);
        double r128412 = r128405 * r128411;
        return r128412;
}
↓
double f(double c0, double A, double V, double l) {
        double r128413 = V;
        double r128414 = -5.556283518325683e-309;
        bool r128415 = r128413 <= r128414;
        double r128416 = c0;
        double r128417 = 1.0;
        double r128418 = cbrt(r128417);
        double r128419 = r128418 * r128418;
        double r128420 = cbrt(r128413);
        double r128421 = r128420 * r128420;
        double r128422 = r128419 / r128421;
        double r128423 = A;
        double r128424 = l;
        double r128425 = r128423 / r128424;
        double r128426 = r128425 / r128420;
        double r128427 = r128422 * r128426;
        double r128428 = sqrt(r128427);
        double r128429 = sqrt(r128428);
        double r128430 = r128416 * r128429;
        double r128431 = r128417 / r128413;
        double r128432 = r128431 * r128425;
        double r128433 = sqrt(r128432);
        double r128434 = sqrt(r128433);
        double r128435 = r128430 * r128434;
        double r128436 = 3.621419097460427e-142;
        bool r128437 = r128413 <= r128436;
        double r128438 = sqrt(r128431);
        double r128439 = sqrt(r128425);
        double r128440 = r128438 * r128439;
        double r128441 = r128416 * r128440;
        double r128442 = 2.480087127913833e+154;
        bool r128443 = r128413 <= r128442;
        double r128444 = cbrt(r128423);
        double r128445 = r128444 * r128444;
        double r128446 = r128445 / r128413;
        double r128447 = sqrt(r128446);
        double r128448 = r128444 / r128424;
        double r128449 = sqrt(r128448);
        double r128450 = r128447 * r128449;
        double r128451 = r128416 * r128450;
        double r128452 = r128443 ? r128451 : r128441;
        double r128453 = r128437 ? r128441 : r128452;
        double r128454 = r128415 ? r128435 : r128453;
        return r128454;
}

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 < -5.556283518325683e-309

    1. Initial program 19.6

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

    3. Applied *-un-lft-identity19.6

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

    4. Applied times-frac19.6

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

    6. Applied add-sqr-sqrt19.8

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

    7. Applied associate-*r*19.8

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

    9. Applied add-cube-cbrt19.8

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

    10. Applied add-cube-cbrt19.8

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

    11. Applied times-frac19.8

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

    12. Applied associate-*l*19.8

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

    13. Simplified19.8

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

    if -5.556283518325683e-309 < V < 3.621419097460427e-142 or 2.480087127913833e+154 < V

    1. Initial program 23.6

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

    3. Applied *-un-lft-identity23.6

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

    4. Applied times-frac23.0

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

    5. Applied sqrt-prod11.4

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

    if 3.621419097460427e-142 < V < 2.480087127913833e+154

    1. Initial program 13.3

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

    3. Applied add-cube-cbrt13.7

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

    4. Applied times-frac11.8

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

    5. Applied sqrt-prod4.1

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

  4. Final simplification13.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \le -5.556283518325683243464468114976330835385 \cdot 10^{-309}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\frac{A}{\ell}}{\sqrt[3]{V}}}}\right) \cdot \sqrt{\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}}\\ \mathbf{elif}\;V \le 3.621419097460427185242147570218797506351 \cdot 10^{-142}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \le 2.480087127913832854241189970085787477828 \cdot 10^{154}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))