Average Error: 7.7 → 0.5
Time: 3.8s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.41253613397111438599433893468190853575 \cdot 10^{77} \lor \neg \left(z \le 1175910331545633266413439287296\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z} \cdot \cosh x}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.41253613397111438599433893468190853575 \cdot 10^{77} \lor \neg \left(z \le 1175910331545633266413439287296\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{y}{z} \cdot \cosh x}{x}\\

\end{array}
double f(double x, double y, double z) {
        double r716914 = x;
        double r716915 = cosh(r716914);
        double r716916 = y;
        double r716917 = r716916 / r716914;
        double r716918 = r716915 * r716917;
        double r716919 = z;
        double r716920 = r716918 / r716919;
        return r716920;
}
↓
double f(double x, double y, double z) {
        double r716921 = z;
        double r716922 = -4.4125361339711144e+77;
        bool r716923 = r716921 <= r716922;
        double r716924 = 1.1759103315456333e+30;
        bool r716925 = r716921 <= r716924;
        double r716926 = !r716925;
        bool r716927 = r716923 || r716926;
        double r716928 = x;
        double r716929 = cosh(r716928);
        double r716930 = y;
        double r716931 = r716928 * r716921;
        double r716932 = r716930 / r716931;
        double r716933 = r716929 * r716932;
        double r716934 = r716930 / r716921;
        double r716935 = r716934 * r716929;
        double r716936 = r716935 / r716928;
        double r716937 = r716927 ? r716933 : r716936;
        return r716937;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.7
Target0.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935152855236908684227749499669 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.4125361339711144e+77 or 1.1759103315456333e+30 < z

    1. Initial program 13.1

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity13.1

      \[\leadsto \frac{\cosh x \cdot \frac{y}{x}}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac13.1

      \[\leadsto \color{blue}{\frac{\cosh x}{1} \cdot \frac{\frac{y}{x}}{z}}\]

    5. Simplified13.1

      \[\leadsto \color{blue}{\cosh x} \cdot \frac{\frac{y}{x}}{z}\]

    6. Simplified0.3

      \[\leadsto \cosh x \cdot \color{blue}{\frac{y}{x \cdot z}}\]

    if -4.4125361339711144e+77 < z < 1.1759103315456333e+30

    1. Initial program 1.1

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity1.1

      \[\leadsto \frac{\cosh x \cdot \frac{y}{x}}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac1.1

      \[\leadsto \color{blue}{\frac{\cosh x}{1} \cdot \frac{\frac{y}{x}}{z}}\]

    5. Simplified1.1

      \[\leadsto \color{blue}{\cosh x} \cdot \frac{\frac{y}{x}}{z}\]

    6. Simplified14.8

      \[\leadsto \cosh x \cdot \color{blue}{\frac{y}{x \cdot z}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity14.8

      \[\leadsto \cosh x \cdot \frac{\color{blue}{1 \cdot y}}{x \cdot z}\]

    9. Applied times-frac0.8

      \[\leadsto \cosh x \cdot \color{blue}{\left(\frac{1}{x} \cdot \frac{y}{z}\right)}\]
    10. Using strategy rm

    11. Applied associate-*l/0.7

      \[\leadsto \cosh x \cdot \color{blue}{\frac{1 \cdot \frac{y}{z}}{x}}\]

    12. Applied associate-*r/0.7

      \[\leadsto \color{blue}{\frac{\cosh x \cdot \left(1 \cdot \frac{y}{z}\right)}{x}}\]

    13. Simplified0.7

      \[\leadsto \frac{\color{blue}{\frac{y}{z} \cdot \cosh x}}{x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.41253613397111438599433893468190853575 \cdot 10^{77} \lor \neg \left(z \le 1175910331545633266413439287296\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z} \cdot \cosh x}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.0385305359351529e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))