Average Error: 18.9 → 12.4
Time: 20.6s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -8.197618637031193 \cdot 10^{+280}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le -9.120801290541009 \cdot 10^{-265}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \ell} \cdot A}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\sqrt{\frac{A}{\ell}} \cdot \left(c0 \cdot \sqrt{\frac{1}{V}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 1.3703350004941968 \cdot 10^{+298}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -8.197618637031193 \cdot 10^{+280}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le -9.120801290541009 \cdot 10^{-265}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \ell} \cdot A}\\

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

\mathbf{elif}\;V \cdot \ell \le 1.3703350004941968 \cdot 10^{+298}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r4726352 = c0;
        double r4726353 = A;
        double r4726354 = V;
        double r4726355 = l;
        double r4726356 = r4726354 * r4726355;
        double r4726357 = r4726353 / r4726356;
        double r4726358 = sqrt(r4726357);
        double r4726359 = r4726352 * r4726358;
        return r4726359;
}
↓
double f(double c0, double A, double V, double l) {
        double r4726360 = V;
        double r4726361 = l;
        double r4726362 = r4726360 * r4726361;
        double r4726363 = -8.197618637031193e+280;
        bool r4726364 = r4726362 <= r4726363;
        double r4726365 = c0;
        double r4726366 = A;
        double r4726367 = cbrt(r4726366);
        double r4726368 = r4726367 * r4726367;
        double r4726369 = r4726368 / r4726360;
        double r4726370 = sqrt(r4726369);
        double r4726371 = r4726365 * r4726370;
        double r4726372 = r4726367 / r4726361;
        double r4726373 = sqrt(r4726372);
        double r4726374 = r4726371 * r4726373;
        double r4726375 = -9.120801290541009e-265;
        bool r4726376 = r4726362 <= r4726375;
        double r4726377 = 1.0;
        double r4726378 = r4726377 / r4726362;
        double r4726379 = r4726378 * r4726366;
        double r4726380 = sqrt(r4726379);
        double r4726381 = r4726365 * r4726380;
        double r4726382 = -0.0;
        bool r4726383 = r4726362 <= r4726382;
        double r4726384 = r4726366 / r4726361;
        double r4726385 = sqrt(r4726384);
        double r4726386 = r4726377 / r4726360;
        double r4726387 = sqrt(r4726386);
        double r4726388 = r4726365 * r4726387;
        double r4726389 = r4726385 * r4726388;
        double r4726390 = 1.3703350004941968e+298;
        bool r4726391 = r4726362 <= r4726390;
        double r4726392 = sqrt(r4726366);
        double r4726393 = sqrt(r4726362);
        double r4726394 = r4726392 / r4726393;
        double r4726395 = r4726394 * r4726365;
        double r4726396 = r4726384 / r4726360;
        double r4726397 = sqrt(r4726396);
        double r4726398 = r4726365 * r4726397;
        double r4726399 = r4726391 ? r4726395 : r4726398;
        double r4726400 = r4726383 ? r4726389 : r4726399;
        double r4726401 = r4726376 ? r4726381 : r4726400;
        double r4726402 = r4726364 ? r4726374 : r4726401;
        return r4726402;
}

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 5 regimes

  2. if (* V l) < -8.197618637031193e+280

    1. Initial program 38.2

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

    3. Applied add-cube-cbrt38.3

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

    4. Applied times-frac24.0

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}}\]
    5. Using strategy rm

    6. Applied sqrt-prod34.3

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

    7. Applied associate-*r*34.4

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

    if -8.197618637031193e+280 < (* V l) < -9.120801290541009e-265

    1. Initial program 9.2

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

    3. Applied div-inv9.2

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

    if -9.120801290541009e-265 < (* V l) < -0.0

    1. Initial program 53.9

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

    3. Applied *-un-lft-identity53.9

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

    4. Applied times-frac34.2

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

    5. Applied sqrt-prod40.4

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

    6. Applied associate-*r*40.8

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

    if -0.0 < (* V l) < 1.3703350004941968e+298

    1. Initial program 10.0

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

    3. Applied div-inv10.4

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

    5. Applied un-div-inv10.0

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

    6. Applied sqrt-div0.8

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

    if 1.3703350004941968e+298 < (* V l)

    1. Initial program 40.8

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

    3. Applied div-inv40.8

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

    5. Applied *-un-lft-identity40.8

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

    6. Applied associate-*l*40.8

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

    7. Simplified23.7

      \[\leadsto c0 \cdot \sqrt{1 \cdot \color{blue}{\frac{\frac{A}{\ell}}{V}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification12.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -8.197618637031193 \cdot 10^{+280}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le -9.120801290541009 \cdot 10^{-265}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \ell} \cdot A}\\ \mathbf{elif}\;V \cdot \ell \le -0.0:\\ \;\;\;\;\sqrt{\frac{A}{\ell}} \cdot \left(c0 \cdot \sqrt{\frac{1}{V}}\right)\\ \mathbf{elif}\;V \cdot \ell \le 1.3703350004941968 \cdot 10^{+298}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))