Average Error: 19.3 → 8.0
Time: 19.6s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \le 2.651697625647502861435154931547367013462 \cdot 10^{-311}:\\ \;\;\;\;\left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \frac{\sqrt{\frac{\sqrt[3]{A}}{\ell}}}{\sqrt{V}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \le 2.651697625647502861435154931547367013462 \cdot 10^{-311}:\\
\;\;\;\;\left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right) \cdot c0\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r149606 = c0;
        double r149607 = A;
        double r149608 = V;
        double r149609 = l;
        double r149610 = r149608 * r149609;
        double r149611 = r149607 / r149610;
        double r149612 = sqrt(r149611);
        double r149613 = r149606 * r149612;
        return r149613;
}
↓
double f(double c0, double A, double V, double l) {
        double r149614 = V;
        double r149615 = 2.6516976256475e-311;
        bool r149616 = r149614 <= r149615;
        double r149617 = A;
        double r149618 = cbrt(r149617);
        double r149619 = fabs(r149618);
        double r149620 = 1.0;
        double r149621 = l;
        double r149622 = cbrt(r149621);
        double r149623 = r149622 * r149622;
        double r149624 = r149620 / r149623;
        double r149625 = cbrt(r149614);
        double r149626 = r149625 * r149625;
        double r149627 = r149624 / r149626;
        double r149628 = r149625 * r149622;
        double r149629 = r149618 / r149628;
        double r149630 = r149627 * r149629;
        double r149631 = sqrt(r149630);
        double r149632 = r149619 * r149631;
        double r149633 = c0;
        double r149634 = r149632 * r149633;
        double r149635 = r149618 / r149621;
        double r149636 = sqrt(r149635);
        double r149637 = sqrt(r149614);
        double r149638 = r149636 / r149637;
        double r149639 = r149619 * r149638;
        double r149640 = r149633 * r149639;
        double r149641 = r149616 ? r149634 : r149640;
        return r149641;
}

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 < 2.6516976256475e-311

    1. Initial program 19.0

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

    3. Applied add-cube-cbrt19.3

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

    4. Applied associate-/l*19.3

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

    5. Simplified18.3

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

    7. Applied div-inv18.5

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

    8. Applied sqrt-prod13.7

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

    9. Simplified13.7

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

    10. Simplified13.5

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

    12. Applied add-cube-cbrt13.6

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

    13. Applied add-cube-cbrt13.7

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

    14. Applied add-cube-cbrt13.7

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

    15. Applied times-frac13.7

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

    16. Applied times-frac13.7

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

    17. Applied associate-*l*11.6

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

    18. Simplified11.6

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

    if 2.6516976256475e-311 < V

    1. Initial program 19.7

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

    3. Applied add-cube-cbrt20.0

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

    4. Applied associate-/l*20.0

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

    5. Simplified18.5

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

    7. Applied div-inv18.6

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

    8. Applied sqrt-prod14.0

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

    9. Simplified14.0

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

    10. Simplified14.4

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

    12. Applied associate-*l/13.8

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

    13. Applied sqrt-div4.5

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

    14. Simplified4.5

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

  4. Final simplification8.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \le 2.651697625647502861435154931547367013462 \cdot 10^{-311}:\\ \;\;\;\;\left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right) \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \frac{\sqrt{\frac{\sqrt[3]{A}}{\ell}}}{\sqrt{V}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))