Average Error: 19.0 → 12.4
Time: 21.0s
Precision: 64
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.525116185303215368597471651084471020441 \cdot 10^{-53}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 7.007658098774069688740450968037780966441 \cdot 10^{273}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \le -1.525116185303215368597471651084471020441 \cdot 10^{-53}:\\
\;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\

\mathbf{elif}\;V \cdot \ell \le 0.0:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \le 7.007658098774069688740450968037780966441 \cdot 10^{273}:\\
\;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\

\end{array}
double f(double c0, double A, double V, double l) {
        double r7285208 = c0;
        double r7285209 = A;
        double r7285210 = V;
        double r7285211 = l;
        double r7285212 = r7285210 * r7285211;
        double r7285213 = r7285209 / r7285212;
        double r7285214 = sqrt(r7285213);
        double r7285215 = r7285208 * r7285214;
        return r7285215;
}
↓
double f(double c0, double A, double V, double l) {
        double r7285216 = V;
        double r7285217 = l;
        double r7285218 = r7285216 * r7285217;
        double r7285219 = -1.5251161853032154e-53;
        bool r7285220 = r7285218 <= r7285219;
        double r7285221 = A;
        double r7285222 = r7285221 / r7285218;
        double r7285223 = sqrt(r7285222);
        double r7285224 = sqrt(r7285223);
        double r7285225 = c0;
        double r7285226 = r7285224 * r7285225;
        double r7285227 = r7285224 * r7285226;
        double r7285228 = 0.0;
        bool r7285229 = r7285218 <= r7285228;
        double r7285230 = r7285221 / r7285216;
        double r7285231 = 1.0;
        double r7285232 = r7285231 / r7285217;
        double r7285233 = r7285230 * r7285232;
        double r7285234 = sqrt(r7285233);
        double r7285235 = r7285225 * r7285234;
        double r7285236 = 7.00765809877407e+273;
        bool r7285237 = r7285218 <= r7285236;
        double r7285238 = sqrt(r7285221);
        double r7285239 = sqrt(r7285218);
        double r7285240 = r7285238 / r7285239;
        double r7285241 = r7285240 * r7285225;
        double r7285242 = r7285237 ? r7285241 : r7285235;
        double r7285243 = r7285229 ? r7285235 : r7285242;
        double r7285244 = r7285220 ? r7285227 : r7285243;
        return r7285244;
}

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 3 regimes

  2. if (* V l) < -1.5251161853032154e-53

    1. Initial program 14.6

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

    3. Applied add-sqr-sqrt14.6

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

    4. Applied sqrt-prod14.8

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

    5. Applied associate-*r*14.7

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

    if -1.5251161853032154e-53 < (* V l) < 0.0 or 7.00765809877407e+273 < (* V l)

    1. Initial program 34.5

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

    3. Applied add-cube-cbrt34.7

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

    4. Applied times-frac23.7

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

    6. Applied div-inv23.7

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

    7. Applied associate-*r*24.3

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

    8. Simplified24.0

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

    if 0.0 < (* V l) < 7.00765809877407e+273

    1. Initial program 9.9

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

    3. Applied sqrt-div0.7

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

  4. Final simplification12.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.525116185303215368597471651084471020441 \cdot 10^{-53}:\\ \;\;\;\;\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right)\\ \mathbf{elif}\;V \cdot \ell \le 0.0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \le 7.007658098774069688740450968037780966441 \cdot 10^{273}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{V \cdot \ell}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))