Average Error: 7.3 → 0.3
Time: 22.3s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -0.17773348789390944:\\ \;\;\;\;\frac{y}{z \cdot \frac{x}{\cosh x}}\\ \mathbf{elif}\;z \le 7.165052739410651 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{1}{\frac{\frac{x}{\cosh x}}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{x}{\cosh x}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -0.17773348789390944:\\
\;\;\;\;\frac{y}{z \cdot \frac{x}{\cosh x}}\\

\mathbf{elif}\;z \le 7.165052739410651 \cdot 10^{-33}:\\
\;\;\;\;\frac{\frac{1}{\frac{\frac{x}{\cosh x}}{y}}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r29085927 = x;
        double r29085928 = cosh(r29085927);
        double r29085929 = y;
        double r29085930 = r29085929 / r29085927;
        double r29085931 = r29085928 * r29085930;
        double r29085932 = z;
        double r29085933 = r29085931 / r29085932;
        return r29085933;
}
↓
double f(double x, double y, double z) {
        double r29085934 = z;
        double r29085935 = -0.17773348789390944;
        bool r29085936 = r29085934 <= r29085935;
        double r29085937 = y;
        double r29085938 = x;
        double r29085939 = cosh(r29085938);
        double r29085940 = r29085938 / r29085939;
        double r29085941 = r29085934 * r29085940;
        double r29085942 = r29085937 / r29085941;
        double r29085943 = 7.165052739410651e-33;
        bool r29085944 = r29085934 <= r29085943;
        double r29085945 = 1.0;
        double r29085946 = r29085940 / r29085937;
        double r29085947 = r29085945 / r29085946;
        double r29085948 = r29085947 / r29085934;
        double r29085949 = r29085944 ? r29085948 : r29085942;
        double r29085950 = r29085936 ? r29085942 : r29085949;
        return r29085950;
}

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
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -0.17773348789390944 or 7.165052739410651e-33 < z

    1. Initial program 10.8

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

    3. Applied *-un-lft-identity10.8

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

    4. Applied associate-/r*10.8

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

    5. Simplified10.8

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

    7. Applied associate-/l/0.3

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

    if -0.17773348789390944 < z < 7.165052739410651e-33

    1. Initial program 0.3

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

    3. Applied *-un-lft-identity0.3

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

    4. Applied associate-/r*0.3

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

    5. Simplified0.3

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

    7. Applied clear-num0.4

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\frac{x}{\cosh x}}{y}}}}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -0.17773348789390944:\\ \;\;\;\;\frac{y}{z \cdot \frac{x}{\cosh x}}\\ \mathbf{elif}\;z \le 7.165052739410651 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{1}{\frac{\frac{x}{\cosh x}}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{x}{\cosh x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

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