Average Error: 18.6 → 4.6
Time: 23.4s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le 8.501538855356609 \cdot 10^{-63}:\\ \;\;\;\;\left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \left(\sqrt{\frac{\frac{1}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}}\right)\right) \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 4.2920313642901636 \cdot 10^{+232}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \left(\sqrt{\frac{\frac{1}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}}\right)\right) \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le 8.501538855356609 \cdot 10^{-63}:\\
\;\;\;\;\left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \left(\sqrt{\frac{\frac{1}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}}\right)\right) \cdot c0\\

\mathbf{elif}\;V \cdot \ell \le 4.2920313642901636 \cdot 10^{+232}:\\
\;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \left(\sqrt{\frac{\frac{1}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}}\right)\right) \cdot c0\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r3191196 = c0;
        double r3191197 = A;
        double r3191198 = V;
        double r3191199 = l;
        double r3191200 = r3191198 * r3191199;
        double r3191201 = r3191197 / r3191200;
        double r3191202 = sqrt(r3191201);
        double r3191203 = r3191196 * r3191202;
        return r3191203;
}
↓
double f(double c0, double A, double V, double l) {
        double r3191204 = V;
        double r3191205 = l;
        double r3191206 = r3191204 * r3191205;
        double r3191207 = 8.501538855356609e-63;
        bool r3191208 = r3191206 <= r3191207;
        double r3191209 = 1.0;
        double r3191210 = cbrt(r3191204);
        double r3191211 = r3191210 * r3191210;
        double r3191212 = r3191209 / r3191211;
        double r3191213 = sqrt(r3191212);
        double r3191214 = cbrt(r3191211);
        double r3191215 = r3191209 / r3191214;
        double r3191216 = cbrt(r3191205);
        double r3191217 = r3191216 * r3191216;
        double r3191218 = r3191215 / r3191217;
        double r3191219 = sqrt(r3191218);
        double r3191220 = A;
        double r3191221 = cbrt(r3191210);
        double r3191222 = r3191220 / r3191221;
        double r3191223 = r3191222 / r3191216;
        double r3191224 = sqrt(r3191223);
        double r3191225 = r3191219 * r3191224;
        double r3191226 = r3191213 * r3191225;
        double r3191227 = c0;
        double r3191228 = r3191226 * r3191227;
        double r3191229 = 4.2920313642901636e+232;
        bool r3191230 = r3191206 <= r3191229;
        double r3191231 = sqrt(r3191220);
        double r3191232 = r3191231 * r3191227;
        double r3191233 = sqrt(r3191206);
        double r3191234 = r3191232 / r3191233;
        double r3191235 = r3191230 ? r3191234 : r3191228;
        double r3191236 = r3191208 ? r3191228 : r3191235;
        return r3191236;
}

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 2 regimes

  2. if (* V l) < 8.501538855356609e-63 or 4.2920313642901636e+232 < (* V l)

    1. Initial program 22.0

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

    3. Applied *-un-lft-identity22.0

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

    4. Applied times-frac20.2

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

    6. Applied add-cube-cbrt20.5

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

    7. Applied *-un-lft-identity20.5

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

    8. Applied times-frac20.5

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

    9. Applied associate-*l*20.5

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

    10. Simplified19.4

      \[\leadsto c0 \cdot \sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \color{blue}{\frac{\frac{A}{\sqrt[3]{V}}}{\ell}}}\]
    11. Using strategy rm

    12. Applied sqrt-prod13.8

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

    14. Applied add-cube-cbrt13.9

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

    15. Applied add-cube-cbrt14.0

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

    16. Applied cbrt-prod14.0

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

    17. Applied *-un-lft-identity14.0

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

    18. Applied times-frac14.0

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

    19. Applied times-frac13.0

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

    20. Applied sqrt-prod5.2

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

    if 8.501538855356609e-63 < (* V l) < 4.2920313642901636e+232

    1. Initial program 6.2

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

    3. Applied sqrt-div0.4

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

    4. Applied associate-*r/2.4

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le 8.501538855356609 \cdot 10^{-63}:\\ \;\;\;\;\left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \left(\sqrt{\frac{\frac{1}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}}\right)\right) \cdot c0\\ \mathbf{elif}\;V \cdot \ell \le 4.2920313642901636 \cdot 10^{+232}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \left(\sqrt{\frac{\frac{1}{\sqrt[3]{\sqrt[3]{V} \cdot \sqrt[3]{V}}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{\sqrt[3]{V}}}}{\sqrt[3]{\ell}}}\right)\right) \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019133 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))