Average Error: 7.9 → 0.5
Time: 4.2s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -\infty:\\ \;\;\;\;y \cdot \left(\frac{e^{x} + e^{-x}}{x} \cdot \frac{0.5}{z}\right)\\ \mathbf{elif}\;\cosh x \cdot \frac{y}{x} \le 2.6920714768591096 \cdot 10^{+155}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{z}{\cosh x \cdot y}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -\infty:\\
\;\;\;\;y \cdot \left(\frac{e^{x} + e^{-x}}{x} \cdot \frac{0.5}{z}\right)\\

\mathbf{elif}\;\cosh x \cdot \frac{y}{x} \le 2.6920714768591096 \cdot 10^{+155}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (((double) cosh(x)) * ((double) (y / x)))) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (((double) cosh(x)) * ((double) (y / x)))) <= ((double) -(((double) INFINITY))))) {
		VAR = ((double) (y * ((double) (((double) (((double) (((double) exp(x)) + ((double) exp(((double) -(x)))))) / x)) * ((double) (0.5 / z))))));
	} else {
		double VAR_1;
		if ((((double) (((double) cosh(x)) * ((double) (y / x)))) <= 2.6920714768591096e+155)) {
			VAR_1 = ((double) (((double) (((double) cosh(x)) * ((double) (y / x)))) / z));
		} else {
			VAR_1 = ((double) (1.0 / ((double) (x * ((double) (z / ((double) (((double) cosh(x)) * y))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original7.9
Target0.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (cosh x) (/ y x)) < -inf.0

    1. Initial program 64.0

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

    2. Taylor expanded around inf 0.7

      \[\leadsto \color{blue}{\frac{\left(0.5 \cdot e^{-x} + 0.5 \cdot e^{x}\right) \cdot y}{z \cdot x}}\]

    3. Simplified0.7

      \[\leadsto \color{blue}{y \cdot \left(\frac{e^{x} + e^{-x}}{x} \cdot \frac{0.5}{z}\right)}\]

    if -inf.0 < (* (cosh x) (/ y x)) < 2.69207147685910959e155

    1. Initial program 0.3

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

    if 2.69207147685910959e155 < (* (cosh x) (/ y x))

    1. Initial program 23.2

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

    3. Applied clear-num23.3

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

    4. Simplified1.9

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -\infty:\\ \;\;\;\;y \cdot \left(\frac{e^{x} + e^{-x}}{x} \cdot \frac{0.5}{z}\right)\\ \mathbf{elif}\;\cosh x \cdot \frac{y}{x} \le 2.6920714768591096 \cdot 10^{+155}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{z}{\cosh x \cdot y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))