Average Error: 19.0 → 12.5
Time: 4.8s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -9.06360601863790799 \cdot 10^{284}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le -3.08257491941769578 \cdot 10^{-195}:\\ \;\;\;\;\left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 6.900941 \cdot 10^{-318}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.3470627133444004 \cdot 10^{300}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -9.06360601863790799 \cdot 10^{284}:\\
\;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le -3.08257491941769578 \cdot 10^{-195}:\\
\;\;\;\;\left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\\

\mathbf{elif}\;V \cdot \ell \le 6.900941 \cdot 10^{-318}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le 1.3470627133444004 \cdot 10^{300}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

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

\end{array}
double f(double c0, double A, double V, double l) {
        double r213110 = c0;
        double r213111 = A;
        double r213112 = V;
        double r213113 = l;
        double r213114 = r213112 * r213113;
        double r213115 = r213111 / r213114;
        double r213116 = sqrt(r213115);
        double r213117 = r213110 * r213116;
        return r213117;
}
↓
double f(double c0, double A, double V, double l) {
        double r213118 = V;
        double r213119 = l;
        double r213120 = r213118 * r213119;
        double r213121 = -9.063606018637908e+284;
        bool r213122 = r213120 <= r213121;
        double r213123 = c0;
        double r213124 = A;
        double r213125 = cbrt(r213124);
        double r213126 = r213125 * r213125;
        double r213127 = r213126 / r213118;
        double r213128 = sqrt(r213127);
        double r213129 = r213123 * r213128;
        double r213130 = r213125 / r213119;
        double r213131 = sqrt(r213130);
        double r213132 = r213129 * r213131;
        double r213133 = -3.0825749194176958e-195;
        bool r213134 = r213120 <= r213133;
        double r213135 = r213124 / r213120;
        double r213136 = cbrt(r213135);
        double r213137 = fabs(r213136);
        double r213138 = r213137 * r213123;
        double r213139 = sqrt(r213136);
        double r213140 = r213138 * r213139;
        double r213141 = 6.9009409587909e-318;
        bool r213142 = r213120 <= r213141;
        double r213143 = r213124 / r213118;
        double r213144 = 1.0;
        double r213145 = r213144 / r213119;
        double r213146 = r213143 * r213145;
        double r213147 = sqrt(r213146);
        double r213148 = r213123 * r213147;
        double r213149 = 1.3470627133444004e+300;
        bool r213150 = r213120 <= r213149;
        double r213151 = sqrt(r213124);
        double r213152 = sqrt(r213120);
        double r213153 = r213151 / r213152;
        double r213154 = r213123 * r213153;
        double r213155 = sqrt(r213143);
        double r213156 = sqrt(r213119);
        double r213157 = r213155 / r213156;
        double r213158 = r213123 * r213157;
        double r213159 = r213150 ? r213154 : r213158;
        double r213160 = r213142 ? r213148 : r213159;
        double r213161 = r213134 ? r213140 : r213160;
        double r213162 = r213122 ? r213132 : r213161;
        return r213162;
}

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 5 regimes

  2. if (* V l) < -9.063606018637908e+284

    1. Initial program 39.1

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

    3. Applied add-cube-cbrt39.2

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

    4. Applied times-frac22.6

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

    5. Applied sqrt-prod35.2

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

    6. Applied associate-*r*35.5

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

    if -9.063606018637908e+284 < (* V l) < -3.0825749194176958e-195

    1. Initial program 7.9

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

    3. Applied add-cube-cbrt8.3

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

    4. Applied sqrt-prod8.3

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

    5. Applied associate-*r*8.3

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

    6. Simplified8.3

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

    if -3.0825749194176958e-195 < (* V l) < 6.9009409587909e-318

    1. Initial program 46.9

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

    3. Applied add-cube-cbrt47.1

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

    4. Applied times-frac28.8

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

    6. Applied div-inv28.9

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

    7. Applied associate-*r*29.2

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

    8. Simplified28.9

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

    if 6.9009409587909e-318 < (* V l) < 1.3470627133444004e+300

    1. Initial program 10.5

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

    3. Applied sqrt-div0.5

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

    if 1.3470627133444004e+300 < (* V l)

    1. Initial program 38.5

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

    3. Applied add-cube-cbrt38.6

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

    4. Applied times-frac21.7

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

    6. Applied div-inv21.7

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

    7. Applied associate-*r*21.7

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

    8. Simplified21.5

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

    10. Applied un-div-inv21.5

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

    11. Applied sqrt-div36.9

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification12.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -9.06360601863790799 \cdot 10^{284}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le -3.08257491941769578 \cdot 10^{-195}:\\ \;\;\;\;\left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot c0\right) \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\\ \mathbf{elif}\;V \cdot \ell \le 6.900941 \cdot 10^{-318}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 1.3470627133444004 \cdot 10^{300}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))