Average Error: 7.4 → 0.4
Time: 4.0s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -7.1339183193240772 \cdot 10^{58} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \le 1.2670938134229954 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -7.1339183193240772 \cdot 10^{58} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \le 1.2670938134229954 \cdot 10^{-24}\right):\\
\;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\

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

\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) (((double) cosh(x)) * ((double) (y / x)))) / z)) <= -7.133918319324077e+58) || !(((double) (((double) (((double) cosh(x)) * ((double) (y / x)))) / z)) <= 1.2670938134229954e-24))) {
		VAR = ((double) (((double) (((double) (((double) cosh(x)) * y)) / z)) / x));
	} else {
		VAR = ((double) (((double) cosh(x)) * ((double) (y / ((double) (x * z))))));
	}
	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

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

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (cosh x) (/ y x)) z) < -7.1339183193240772e58 or 1.2670938134229954e-24 < (/ (* (cosh x) (/ y x)) z)

    1. Initial program 13.1

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

    3. Applied div-inv13.2

      \[\leadsto \color{blue}{\left(\cosh x \cdot \frac{y}{x}\right) \cdot \frac{1}{z}}\]
    4. Using strategy rm

    5. Applied associate-*r/13.2

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

    6. Applied associate-*l/0.5

      \[\leadsto \color{blue}{\frac{\left(\cosh x \cdot y\right) \cdot \frac{1}{z}}{x}}\]

    7. Simplified0.4

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

    if -7.1339183193240772e58 < (/ (* (cosh x) (/ y x)) z) < 1.2670938134229954e-24

    1. Initial program 0.2

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

    3. Applied *-un-lft-identity0.2

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

    6. Simplified0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -7.1339183193240772 \cdot 10^{58} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \le 1.2670938134229954 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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))