Average Error: 18.9 → 12.1
Time: 4.2s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.6220125092199022 \cdot 10^{-97}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 3.80431 \cdot 10^{-322}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.93687473196227216 \cdot 10^{296}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -2.6220125092199022 \cdot 10^{-97}:\\
\;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\

\mathbf{elif}\;V \cdot \ell \le 3.80431 \cdot 10^{-322}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le 1.93687473196227216 \cdot 10^{296}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

\mathbf{else}:\\
\;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r141138 = c0;
        double r141139 = A;
        double r141140 = V;
        double r141141 = l;
        double r141142 = r141140 * r141141;
        double r141143 = r141139 / r141142;
        double r141144 = sqrt(r141143);
        double r141145 = r141138 * r141144;
        return r141145;
}
↓
double f(double c0, double A, double V, double l) {
        double r141146 = V;
        double r141147 = l;
        double r141148 = r141146 * r141147;
        double r141149 = -2.622012509219902e-97;
        bool r141150 = r141148 <= r141149;
        double r141151 = A;
        double r141152 = r141151 / r141148;
        double r141153 = sqrt(r141152);
        double r141154 = sqrt(r141153);
        double r141155 = c0;
        double r141156 = r141154 * r141155;
        double r141157 = r141154 * r141156;
        double r141158 = 3.8043054729776e-322;
        bool r141159 = r141148 <= r141158;
        double r141160 = r141151 / r141146;
        double r141161 = r141160 / r141147;
        double r141162 = sqrt(r141161);
        double r141163 = r141155 * r141162;
        double r141164 = 1.936874731962272e+296;
        bool r141165 = r141148 <= r141164;
        double r141166 = sqrt(r141151);
        double r141167 = sqrt(r141148);
        double r141168 = r141166 / r141167;
        double r141169 = r141168 * r141155;
        double r141170 = 1.0;
        double r141171 = r141170 / r141146;
        double r141172 = r141151 / r141147;
        double r141173 = r141171 * r141172;
        double r141174 = sqrt(r141173);
        double r141175 = r141174 * r141155;
        double r141176 = r141165 ? r141169 : r141175;
        double r141177 = r141159 ? r141163 : r141176;
        double r141178 = r141150 ? r141157 : r141177;
        return r141178;
}

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) < -2.622012509219902e-97

    1. Initial program 13.7

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

    3. Applied *-commutative13.7

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

    5. Applied add-sqr-sqrt13.7

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

    6. Applied sqrt-prod13.9

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

    7. Applied associate-*l*13.9

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

    if -2.622012509219902e-97 < (* V l) < 3.8043054729776e-322

    1. Initial program 35.7

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

    3. Applied associate-/r*26.4

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

    if 3.8043054729776e-322 < (* V l) < 1.936874731962272e+296

    1. Initial program 10.7

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

    3. Applied *-commutative10.7

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

    5. Applied sqrt-div0.7

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

    if 1.936874731962272e+296 < (* V l)

    1. Initial program 39.7

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

    3. Applied *-commutative39.7

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

    5. Applied *-un-lft-identity39.7

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

    6. Applied times-frac23.5

      \[\leadsto \sqrt{\color{blue}{\frac{1}{V} \cdot \frac{A}{\ell}}} \cdot c0\]
  3. Recombined 4 regimes into one program.

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.6220125092199022 \cdot 10^{-97}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 3.80431 \cdot 10^{-322}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.93687473196227216 \cdot 10^{296}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{V} \cdot \frac{A}{\ell}} \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))