\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -2548401331254628.0:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;z \le 4.164739628396679 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \left(\frac{\frac{1}{2}}{e^{x}} + e^{x} \cdot \frac{1}{2}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]

\frac{\cosh x \cdot \frac{y}{x}}{z}

↓

\begin{array}{l}
\mathbf{if}\;z \le -2548401331254628.0:\\
\;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\

\mathbf{elif}\;z \le 4.164739628396679 \cdot 10^{+36}:\\
\;\;\;\;\frac{\frac{y}{x} \cdot \left(\frac{\frac{1}{2}}{e^{x}} + e^{x} \cdot \frac{1}{2}\right)}{z}\\

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

\end{array}

double f(double x, double y, double z) {
        double r10027850 = x;
        double r10027851 = cosh(r10027850);
        double r10027852 = y;
        double r10027853 = r10027852 / r10027850;
        double r10027854 = r10027851 * r10027853;
        double r10027855 = z;
        double r10027856 = r10027854 / r10027855;
        return r10027856;
}

↓

double f(double x, double y, double z) {
        double r10027857 = z;
        double r10027858 = -2548401331254628.0;
        bool r10027859 = r10027857 <= r10027858;
        double r10027860 = x;
        double r10027861 = cosh(r10027860);
        double r10027862 = y;
        double r10027863 = r10027861 * r10027862;
        double r10027864 = r10027860 * r10027857;
        double r10027865 = r10027863 / r10027864;
        double r10027866 = 4.164739628396679e+36;
        bool r10027867 = r10027857 <= r10027866;
        double r10027868 = r10027862 / r10027860;
        double r10027869 = 0.5;
        double r10027870 = exp(r10027860);
        double r10027871 = r10027869 / r10027870;
        double r10027872 = r10027870 * r10027869;
        double r10027873 = r10027871 + r10027872;
        double r10027874 = r10027868 * r10027873;
        double r10027875 = r10027874 / r10027857;
        double r10027876 = r10027867 ? r10027875 : r10027865;
        double r10027877 = r10027859 ? r10027865 : r10027876;
        return r10027877;
}

Original	7.3
Target	0.4
Herbie	0.4

Derivation

Split input into 2 regimes
if z < -2548401331254628.0 or 4.164739628396679e+36 < z
1. Initial program 11.6
  \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
2. Using strategy rm
3. Applied associate-*r/11.6
  \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z}\]
4. Applied associate-/l/0.3
  \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}}\]
if -2548401331254628.0 < z < 4.164739628396679e+36
1. Initial program 0.6
  \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
2. Taylor expanded around inf 0.6
  \[\leadsto \frac{\color{blue}{\frac{\left(\frac{1}{2} \cdot e^{x} + \frac{1}{2} \cdot e^{-x}\right) \cdot y}{x}}}{z}\]
3. Simplified0.6
  \[\leadsto \frac{\color{blue}{\frac{y}{x} \cdot \left(\frac{\frac{1}{2}}{e^{x}} + e^{x} \cdot \frac{1}{2}\right)}}{z}\]
Recombined 2 regimes into one program.
Final simplification0.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2548401331254628.0:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;z \le 4.164739628396679 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \left(\frac{\frac{1}{2}}{e^{x}} + e^{x} \cdot \frac{1}{2}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(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))

Error

Try it out

Target

Derivation

`if z < -2548401331254628.0 or 4.164739628396679e+36 < z`

`if -2548401331254628.0 < z < 4.164739628396679e+36`

Reproduce

In
Out