Average Error: 7.3 → 0.3
Time: 4.0s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -12403175825184520:\\ \;\;\;\;\frac{\frac{\cosh x}{\frac{z}{y}}}{x}\\ \mathbf{elif}\;y \le 4.70989780554481168 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\frac{\cosh x \cdot y}{z}}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -12403175825184520:\\
\;\;\;\;\frac{\frac{\cosh x}{\frac{z}{y}}}{x}\\

\mathbf{elif}\;y \le 4.70989780554481168 \cdot 10^{-7}:\\
\;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{x}{\frac{\cosh x \cdot y}{z}}}\\

\end{array}
double f(double x, double y, double z) {
        double r462914 = x;
        double r462915 = cosh(r462914);
        double r462916 = y;
        double r462917 = r462916 / r462914;
        double r462918 = r462915 * r462917;
        double r462919 = z;
        double r462920 = r462918 / r462919;
        return r462920;
}
↓
double f(double x, double y, double z) {
        double r462921 = y;
        double r462922 = -1.240317582518452e+16;
        bool r462923 = r462921 <= r462922;
        double r462924 = x;
        double r462925 = cosh(r462924);
        double r462926 = z;
        double r462927 = r462926 / r462921;
        double r462928 = r462925 / r462927;
        double r462929 = r462928 / r462924;
        double r462930 = 4.7098978055448117e-07;
        bool r462931 = r462921 <= r462930;
        double r462932 = r462925 * r462921;
        double r462933 = r462932 / r462924;
        double r462934 = r462933 / r462926;
        double r462935 = 1.0;
        double r462936 = r462932 / r462926;
        double r462937 = r462924 / r462936;
        double r462938 = r462935 / r462937;
        double r462939 = r462931 ? r462934 : r462938;
        double r462940 = r462923 ? r462929 : r462939;
        return r462940;
}

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

Original7.3
Target0.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.240317582518452e+16

    1. Initial program 22.3

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

    3. Applied associate-*r/22.3

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

    4. Applied associate-/l/0.3

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

    6. Applied associate-/r*0.3

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

    8. Applied associate-/l*0.4

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

    if -1.240317582518452e+16 < y < 4.7098978055448117e-07

    1. Initial program 0.3

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

    3. Applied associate-*r/0.3

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

    4. Applied associate-/l/11.1

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

    6. Applied associate-/r*10.3

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

    8. Applied clear-num10.4

      \[\leadsto \color{blue}{\frac{1}{\frac{x}{\frac{\cosh x \cdot y}{z}}}}\]
    9. Using strategy rm

    10. Applied associate-/r/0.7

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

    11. Applied associate-/r*0.3

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

    12. Simplified0.3

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

    if 4.7098978055448117e-07 < y

    1. Initial program 20.3

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

    3. Applied associate-*r/20.4

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

    4. Applied associate-/l/0.5

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

    6. Applied associate-/r*0.5

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

    8. Applied clear-num0.6

      \[\leadsto \color{blue}{\frac{1}{\frac{x}{\frac{\cosh x \cdot y}{z}}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -12403175825184520:\\ \;\;\;\;\frac{\frac{\cosh x}{\frac{z}{y}}}{x}\\ \mathbf{elif}\;y \le 4.70989780554481168 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\frac{\cosh x \cdot y}{z}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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))