Average Error: 19.4 → 13.6
Time: 24.5s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.193059146023880502697436443480710721354 \cdot 10^{-203}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{A \cdot \frac{1}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 5.374992541585612810021994873950276178792 \cdot 10^{257}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\sqrt{A}}{V} \cdot \frac{\sqrt{A}}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -2.193059146023880502697436443480710721354 \cdot 10^{-203}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{A \cdot \frac{1}{V \cdot \ell}}}\\

\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 5.374992541585612810021994873950276178792 \cdot 10^{257}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r114269 = c0;
        double r114270 = A;
        double r114271 = V;
        double r114272 = l;
        double r114273 = r114271 * r114272;
        double r114274 = r114270 / r114273;
        double r114275 = sqrt(r114274);
        double r114276 = r114269 * r114275;
        return r114276;
}
↓
double f(double c0, double A, double V, double l) {
        double r114277 = V;
        double r114278 = l;
        double r114279 = r114277 * r114278;
        double r114280 = -2.1930591460238805e-203;
        bool r114281 = r114279 <= r114280;
        double r114282 = c0;
        double r114283 = A;
        double r114284 = r114283 / r114279;
        double r114285 = sqrt(r114284);
        double r114286 = sqrt(r114285);
        double r114287 = r114282 * r114286;
        double r114288 = 1.0;
        double r114289 = r114288 / r114279;
        double r114290 = r114283 * r114289;
        double r114291 = sqrt(r114290);
        double r114292 = sqrt(r114291);
        double r114293 = r114287 * r114292;
        double r114294 = -0.0;
        bool r114295 = r114279 <= r114294;
        double r114296 = r114288 / r114277;
        double r114297 = sqrt(r114296);
        double r114298 = r114283 / r114278;
        double r114299 = sqrt(r114298);
        double r114300 = r114297 * r114299;
        double r114301 = r114282 * r114300;
        double r114302 = 5.374992541585613e+257;
        bool r114303 = r114279 <= r114302;
        double r114304 = sqrt(r114283);
        double r114305 = sqrt(r114279);
        double r114306 = r114304 / r114305;
        double r114307 = r114282 * r114306;
        double r114308 = r114304 / r114277;
        double r114309 = r114304 / r114278;
        double r114310 = r114308 * r114309;
        double r114311 = sqrt(r114310);
        double r114312 = r114282 * r114311;
        double r114313 = r114303 ? r114307 : r114312;
        double r114314 = r114295 ? r114301 : r114313;
        double r114315 = r114281 ? r114293 : r114314;
        return r114315;
}

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) < -2.1930591460238805e-203

    1. Initial program 14.3

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

    3. Applied add-sqr-sqrt14.3

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

    4. Applied sqrt-prod14.5

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

    5. Applied associate-*r*14.5

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

    7. Applied div-inv14.4

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

    if -2.1930591460238805e-203 < (* V l) < -0.0

    1. Initial program 40.5

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

    3. Applied *-un-lft-identity40.5

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

    4. Applied times-frac27.4

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

    5. Applied sqrt-prod40.3

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

    if -0.0 < (* V l) < 5.374992541585613e+257

    1. Initial program 15.9

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

    3. Applied sqrt-div6.9

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

    if 5.374992541585613e+257 < (* V l)

    1. Initial program 34.8

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

    3. Applied add-sqr-sqrt34.8

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

    4. Applied times-frac21.9

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

  4. Final simplification13.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.193059146023880502697436443480710721354 \cdot 10^{-203}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{A \cdot \frac{1}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 5.374992541585612810021994873950276178792 \cdot 10^{257}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\sqrt{A}}{V} \cdot \frac{\sqrt{A}}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))