Average Error: 7.8 → 0.4
Time: 5.9s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -261095818.6417586803436279296875:\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{x}}{z}\\ \mathbf{elif}\;z \le 60.4393804861111334503220859915018081665:\\ \;\;\;\;\frac{\left(\cosh x \cdot y\right) \cdot \frac{1}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -261095818.6417586803436279296875:\\
\;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{x}}{z}\\

\mathbf{elif}\;z \le 60.4393804861111334503220859915018081665:\\
\;\;\;\;\frac{\left(\cosh x \cdot y\right) \cdot \frac{1}{x}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r499842 = x;
        double r499843 = cosh(r499842);
        double r499844 = y;
        double r499845 = r499844 / r499842;
        double r499846 = r499843 * r499845;
        double r499847 = z;
        double r499848 = r499846 / r499847;
        return r499848;
}
↓
double f(double x, double y, double z) {
        double r499849 = z;
        double r499850 = -261095818.64175868;
        bool r499851 = r499849 <= r499850;
        double r499852 = x;
        double r499853 = cosh(r499852);
        double r499854 = y;
        double r499855 = r499853 * r499854;
        double r499856 = 1.0;
        double r499857 = r499856 / r499852;
        double r499858 = r499857 / r499849;
        double r499859 = r499855 * r499858;
        double r499860 = 60.43938048611113;
        bool r499861 = r499849 <= r499860;
        double r499862 = r499855 * r499857;
        double r499863 = r499862 / r499849;
        double r499864 = r499849 * r499852;
        double r499865 = r499855 / r499864;
        double r499866 = r499861 ? r499863 : r499865;
        double r499867 = r499851 ? r499859 : r499866;
        return r499867;
}

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

Original7.8
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935152855236908684227749499669 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -261095818.64175868

    1. Initial program 12.2

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

    3. Applied div-inv12.3

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

    4. Applied associate-*r*12.3

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

    6. Applied *-un-lft-identity12.3

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

    7. Applied times-frac0.4

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

    8. Simplified0.4

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

    if -261095818.64175868 < z < 60.43938048611113

    1. Initial program 0.3

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

    3. Applied div-inv0.4

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

    4. Applied associate-*r*0.4

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

    if 60.43938048611113 < z

    1. Initial program 11.7

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

    3. Applied associate-*r/11.7

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

    4. Applied associate-/l/0.4

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -261095818.6417586803436279296875:\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{x}}{z}\\ \mathbf{elif}\;z \le 60.4393804861111334503220859915018081665:\\ \;\;\;\;\frac{\left(\cosh x \cdot y\right) \cdot \frac{1}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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))