Average Error: 7.5 → 0.4
Time: 52.4s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.986686670783298043324591018464960578634 \cdot 10^{-19}:\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{elif}\;z \le 7.189025362679728768411324688191991410865 \cdot 10^{-40}:\\ \;\;\;\;\left(\frac{y}{x} \cdot \cosh x\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.986686670783298043324591018464960578634 \cdot 10^{-19}:\\
\;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\

\mathbf{elif}\;z \le 7.189025362679728768411324688191991410865 \cdot 10^{-40}:\\
\;\;\;\;\left(\frac{y}{x} \cdot \cosh x\right) \cdot \frac{1}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r25521041 = x;
        double r25521042 = cosh(r25521041);
        double r25521043 = y;
        double r25521044 = r25521043 / r25521041;
        double r25521045 = r25521042 * r25521044;
        double r25521046 = z;
        double r25521047 = r25521045 / r25521046;
        return r25521047;
}
↓
double f(double x, double y, double z) {
        double r25521048 = z;
        double r25521049 = -1.986686670783298e-19;
        bool r25521050 = r25521048 <= r25521049;
        double r25521051 = y;
        double r25521052 = x;
        double r25521053 = cosh(r25521052);
        double r25521054 = r25521051 * r25521053;
        double r25521055 = r25521052 * r25521048;
        double r25521056 = r25521054 / r25521055;
        double r25521057 = 7.189025362679729e-40;
        bool r25521058 = r25521048 <= r25521057;
        double r25521059 = r25521051 / r25521052;
        double r25521060 = r25521059 * r25521053;
        double r25521061 = 1.0;
        double r25521062 = r25521061 / r25521048;
        double r25521063 = r25521060 * r25521062;
        double r25521064 = r25521058 ? r25521063 : r25521056;
        double r25521065 = r25521050 ? r25521056 : r25521064;
        return r25521065;
}

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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.986686670783298e-19 or 7.189025362679729e-40 < z

    1. Initial program 10.8

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

    3. Applied associate-*r/10.8

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

    4. Applied associate-/l/0.4

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

    if -1.986686670783298e-19 < z < 7.189025362679729e-40

    1. Initial program 0.3

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

    3. Applied div-inv0.4

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.986686670783298043324591018464960578634 \cdot 10^{-19}:\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{elif}\;z \le 7.189025362679728768411324688191991410865 \cdot 10^{-40}:\\ \;\;\;\;\left(\frac{y}{x} \cdot \cosh x\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(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))