Average Error: 19.2 → 8.1
Time: 18.7s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -3.243383502461250735927636408958304994176 \cdot 10^{273}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le -1.35321217516395200911005703941410336597 \cdot 10^{-184}:\\ \;\;\;\;\sqrt{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \left(\sqrt{\frac{1}{\left({\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(V \cdot \ell\right)\right) \cdot \left(-\sqrt[3]{\frac{-1}{A}}\right)}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 1.589556908299396665332730600726135753089 \cdot 10^{-317}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le 2.147616532337955576797605026006365807503 \cdot 10^{304}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{{A}^{\frac{2}{3}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{\sqrt[3]{V}}}\right) \cdot c0\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -3.243383502461250735927636408958304994176 \cdot 10^{273}:\\
\;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\

\mathbf{elif}\;V \cdot \ell \le -1.35321217516395200911005703941410336597 \cdot 10^{-184}:\\
\;\;\;\;\sqrt{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \left(\sqrt{\frac{1}{\left({\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(V \cdot \ell\right)\right) \cdot \left(-\sqrt[3]{\frac{-1}{A}}\right)}} \cdot c0\right)\\

\mathbf{elif}\;V \cdot \ell \le 1.589556908299396665332730600726135753089 \cdot 10^{-317}:\\
\;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\

\mathbf{elif}\;V \cdot \ell \le 2.147616532337955576797605026006365807503 \cdot 10^{304}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt{\frac{{A}^{\frac{2}{3}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{\sqrt[3]{V}}}\right) \cdot c0\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r181297 = c0;
        double r181298 = A;
        double r181299 = V;
        double r181300 = l;
        double r181301 = r181299 * r181300;
        double r181302 = r181298 / r181301;
        double r181303 = sqrt(r181302);
        double r181304 = r181297 * r181303;
        return r181304;
}
↓
double f(double c0, double A, double V, double l) {
        double r181305 = V;
        double r181306 = l;
        double r181307 = r181305 * r181306;
        double r181308 = -3.2433835024612507e+273;
        bool r181309 = r181307 <= r181308;
        double r181310 = c0;
        double r181311 = A;
        double r181312 = r181305 / r181311;
        double r181313 = r181306 * r181312;
        double r181314 = sqrt(r181313);
        double r181315 = r181310 / r181314;
        double r181316 = -1.353212175163952e-184;
        bool r181317 = r181307 <= r181316;
        double r181318 = cbrt(r181311);
        double r181319 = r181318 * r181318;
        double r181320 = sqrt(r181319);
        double r181321 = 1.0;
        double r181322 = -1.0;
        double r181323 = cbrt(r181322);
        double r181324 = 2.0;
        double r181325 = pow(r181323, r181324);
        double r181326 = r181325 * r181307;
        double r181327 = r181322 / r181311;
        double r181328 = cbrt(r181327);
        double r181329 = -r181328;
        double r181330 = r181326 * r181329;
        double r181331 = r181321 / r181330;
        double r181332 = sqrt(r181331);
        double r181333 = r181332 * r181310;
        double r181334 = r181320 * r181333;
        double r181335 = 1.5895569082994e-317;
        bool r181336 = r181307 <= r181335;
        double r181337 = 2.1476165323379556e+304;
        bool r181338 = r181307 <= r181337;
        double r181339 = sqrt(r181311);
        double r181340 = sqrt(r181307);
        double r181341 = r181339 / r181340;
        double r181342 = r181310 * r181341;
        double r181343 = 0.6666666666666666;
        double r181344 = pow(r181311, r181343);
        double r181345 = cbrt(r181305);
        double r181346 = r181345 * r181345;
        double r181347 = r181344 / r181346;
        double r181348 = sqrt(r181347);
        double r181349 = r181318 / r181306;
        double r181350 = r181349 / r181345;
        double r181351 = sqrt(r181350);
        double r181352 = r181348 * r181351;
        double r181353 = r181352 * r181310;
        double r181354 = r181338 ? r181342 : r181353;
        double r181355 = r181336 ? r181315 : r181354;
        double r181356 = r181317 ? r181334 : r181355;
        double r181357 = r181309 ? r181315 : r181356;
        return r181357;
}

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) < -3.2433835024612507e+273 or -1.353212175163952e-184 < (* V l) < 1.5895569082994e-317

    1. Initial program 42.8

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

    3. Applied clear-num42.8

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

    4. Simplified27.8

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

    6. Applied sqrt-div27.3

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

    7. Applied associate-*r/27.3

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

    8. Simplified27.3

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

    if -3.2433835024612507e+273 < (* V l) < -1.353212175163952e-184

    1. Initial program 8.3

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

    3. Applied clear-num8.7

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

    4. Simplified15.5

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

    6. Applied add-cube-cbrt15.9

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

    7. Applied add-cube-cbrt16.0

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

    8. Applied times-frac16.0

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

    9. Applied associate-*l*10.1

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

    10. Simplified10.1

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

    12. Applied associate-*l/9.3

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

    13. Applied associate-/r/8.9

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

    14. Applied sqrt-prod2.3

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

    15. Applied associate-*r*3.1

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

    16. Simplified2.6

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

    17. Taylor expanded around -inf 5.2

      \[\leadsto \left(c0 \cdot \sqrt{\frac{1}{\color{blue}{-1 \cdot \left({\left(\frac{-1}{A}\right)}^{\frac{1}{3}} \cdot \left({\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(V \cdot \ell\right)\right)\right)}}}\right) \cdot \sqrt{\sqrt[3]{A} \cdot \sqrt[3]{A}}\]

    18. Simplified2.4

      \[\leadsto \left(c0 \cdot \sqrt{\frac{1}{\color{blue}{\left(\left(V \cdot \ell\right) \cdot {\left(\sqrt[3]{-1}\right)}^{2}\right) \cdot \left(-\sqrt[3]{\frac{-1}{A}}\right)}}}\right) \cdot \sqrt{\sqrt[3]{A} \cdot \sqrt[3]{A}}\]

    if 1.5895569082994e-317 < (* V l) < 2.1476165323379556e+304

    1. Initial program 9.9

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

    3. Applied sqrt-div0.5

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

    4. Simplified0.5

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

    if 2.1476165323379556e+304 < (* V l)

    1. Initial program 39.8

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

    3. Applied clear-num39.8

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

    4. Simplified22.4

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

    6. Applied add-cube-cbrt22.6

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

    7. Applied add-cube-cbrt22.6

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

    8. Applied times-frac22.6

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

    9. Applied associate-*l*22.6

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

    10. Simplified26.1

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

    12. Applied add-cube-cbrt26.1

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

    13. Applied times-frac25.6

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

    14. Applied sqrt-prod16.8

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

    15. Simplified18.1

      \[\leadsto c0 \cdot \left(\color{blue}{\sqrt{\frac{{A}^{\frac{2}{3}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}} \cdot \sqrt{\frac{\sqrt[3]{1}}{\frac{\ell \cdot \sqrt[3]{V}}{\sqrt[3]{A}}}}\right)\]

    16. Simplified12.7

      \[\leadsto c0 \cdot \left(\sqrt{\frac{{A}^{\frac{2}{3}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \color{blue}{\sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{\sqrt[3]{V}}}}\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification8.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -3.243383502461250735927636408958304994176 \cdot 10^{273}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le -1.35321217516395200911005703941410336597 \cdot 10^{-184}:\\ \;\;\;\;\sqrt{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \left(\sqrt{\frac{1}{\left({\left(\sqrt[3]{-1}\right)}^{2} \cdot \left(V \cdot \ell\right)\right) \cdot \left(-\sqrt[3]{\frac{-1}{A}}\right)}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 1.589556908299396665332730600726135753089 \cdot 10^{-317}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \le 2.147616532337955576797605026006365807503 \cdot 10^{304}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{{A}^{\frac{2}{3}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\ell}}{\sqrt[3]{V}}}\right) \cdot c0\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))