Average Error: 19.4 → 13.6
Time: 20.6s
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 r103144 = c0;
        double r103145 = A;
        double r103146 = V;
        double r103147 = l;
        double r103148 = r103146 * r103147;
        double r103149 = r103145 / r103148;
        double r103150 = sqrt(r103149);
        double r103151 = r103144 * r103150;
        return r103151;
}
↓
double f(double c0, double A, double V, double l) {
        double r103152 = V;
        double r103153 = l;
        double r103154 = r103152 * r103153;
        double r103155 = -2.1930591460238805e-203;
        bool r103156 = r103154 <= r103155;
        double r103157 = c0;
        double r103158 = A;
        double r103159 = r103158 / r103154;
        double r103160 = sqrt(r103159);
        double r103161 = sqrt(r103160);
        double r103162 = r103157 * r103161;
        double r103163 = 1.0;
        double r103164 = r103163 / r103154;
        double r103165 = r103158 * r103164;
        double r103166 = sqrt(r103165);
        double r103167 = sqrt(r103166);
        double r103168 = r103162 * r103167;
        double r103169 = -0.0;
        bool r103170 = r103154 <= r103169;
        double r103171 = r103163 / r103152;
        double r103172 = sqrt(r103171);
        double r103173 = r103158 / r103153;
        double r103174 = sqrt(r103173);
        double r103175 = r103172 * r103174;
        double r103176 = r103157 * r103175;
        double r103177 = 5.374992541585613e+257;
        bool r103178 = r103154 <= r103177;
        double r103179 = sqrt(r103158);
        double r103180 = sqrt(r103154);
        double r103181 = r103179 / r103180;
        double r103182 = r103157 * r103181;
        double r103183 = r103179 / r103152;
        double r103184 = r103179 / r103153;
        double r103185 = r103183 * r103184;
        double r103186 = sqrt(r103185);
        double r103187 = r103157 * r103186;
        double r103188 = r103178 ? r103182 : r103187;
        double r103189 = r103170 ? r103176 : r103188;
        double r103190 = r103156 ? r103168 : r103189;
        return r103190;
}

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