Average Error: 7.9 → 0.3
Time: 3.5s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -3.0964517336393437 \cdot 10^{307} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \le 222166518906540650000\right):\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -3.0964517336393437 \cdot 10^{307} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \le 222166518906540650000\right):\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\

\mathbf{else}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{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)) <= -3.0964517336393437e+307) || !(((double) (((double) (((double) cosh(x)) * ((double) (y / x)))) / z)) <= 2.2216651890654065e+20))) {
		VAR = ((double) (((double) (((double) cosh(x)) * ((double) (y / z)))) / x));
	} else {
		VAR = ((double) (((double) (((double) cosh(x)) * ((double) (y / 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

Original7.9
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (cosh x) (/ y x)) z) < -3.0964517336393437e307 or 222166518906540650000 < (/ (* (cosh x) (/ y x)) z)

    1. Initial program 23.4

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

    2. Simplified9.4

      \[\leadsto \color{blue}{\cosh x \cdot \frac{y}{x \cdot z}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity9.4

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

    5. Applied times-frac0.4

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

    6. Applied associate-*r*0.4

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

    7. Simplified0.4

      \[\leadsto \color{blue}{\frac{\cosh x}{x}} \cdot \frac{y}{z}\]
    8. Using strategy rm

    9. Applied associate-*l/0.4

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

    if -3.0964517336393437e307 < (/ (* (cosh x) (/ y x)) z) < 222166518906540650000

    1. Initial program 0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -3.0964517336393437 \cdot 10^{307} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \le 222166518906540650000\right):\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]

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))