Average Error: 7.5 → 0.3
Time: 18.8s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.7528430636640835 \cdot 10^{-45}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;z \le 1.1146827486934066 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{y}{\frac{x}{\cosh x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.7528430636640835 \cdot 10^{-45}:\\
\;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\

\mathbf{elif}\;z \le 1.1146827486934066 \cdot 10^{-11}:\\
\;\;\;\;\frac{\frac{y}{\frac{x}{\cosh x}}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r26082926 = x;
        double r26082927 = cosh(r26082926);
        double r26082928 = y;
        double r26082929 = r26082928 / r26082926;
        double r26082930 = r26082927 * r26082929;
        double r26082931 = z;
        double r26082932 = r26082930 / r26082931;
        return r26082932;
}
↓
double f(double x, double y, double z) {
        double r26082933 = z;
        double r26082934 = -4.7528430636640835e-45;
        bool r26082935 = r26082933 <= r26082934;
        double r26082936 = x;
        double r26082937 = cosh(r26082936);
        double r26082938 = y;
        double r26082939 = r26082937 * r26082938;
        double r26082940 = r26082936 * r26082933;
        double r26082941 = r26082939 / r26082940;
        double r26082942 = 1.1146827486934066e-11;
        bool r26082943 = r26082933 <= r26082942;
        double r26082944 = r26082936 / r26082937;
        double r26082945 = r26082938 / r26082944;
        double r26082946 = r26082945 / r26082933;
        double r26082947 = r26082943 ? r26082946 : r26082941;
        double r26082948 = r26082935 ? r26082941 : r26082947;
        return r26082948;
}

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

Original7.5
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 < -4.7528430636640835e-45 or 1.1146827486934066e-11 < z

    1. Initial program 10.7

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

    3. Applied associate-*r/10.7

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

    4. Applied associate-/l/0.4

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

    if -4.7528430636640835e-45 < z < 1.1146827486934066e-11

    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

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.7528430636640835 \cdot 10^{-45}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;z \le 1.1146827486934066 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{y}{\frac{x}{\cosh x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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))