Average Error: 7.9 → 0.4
Time: 4.6s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -8.6650042703662669 \cdot 10^{-45} \lor \neg \left(z \le 6.22728347851612269 \cdot 10^{-28}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{1}{x}}{\frac{z}{y}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -8.6650042703662669 \cdot 10^{-45} \lor \neg \left(z \le 6.22728347851612269 \cdot 10^{-28}\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\cosh x \cdot \frac{\frac{1}{x}}{\frac{z}{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 (((z <= -8.665004270366267e-45) || !(z <= 6.227283478516123e-28))) {
		VAR = ((double) (((double) cosh(x)) * ((double) (y / ((double) (x * z))))));
	} else {
		VAR = ((double) (((double) cosh(x)) * ((double) (((double) (1.0 / x)) / ((double) (z / y))))));
	}
	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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -8.6650042703662669e-45 or 6.22728347851612269e-28 < z

    1. Initial program 11.0

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

    3. Applied *-un-lft-identity11.0

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

    4. Applied times-frac11.0

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

    5. Simplified11.0

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

    6. Simplified0.4

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

    if -8.6650042703662669e-45 < z < 6.22728347851612269e-28

    1. Initial program 0.3

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

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

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

    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. Simplified23.3

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

    8. Applied clear-num23.3

      \[\leadsto \cosh x \cdot \color{blue}{\frac{1}{\frac{x \cdot z}{y}}}\]
    9. Using strategy rm

    10. Applied *-un-lft-identity23.3

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

    11. Applied times-frac0.4

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

    12. Applied associate-/r*0.4

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

    13. Simplified0.4

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.6650042703662669 \cdot 10^{-45} \lor \neg \left(z \le 6.22728347851612269 \cdot 10^{-28}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{1}{x}}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020168 
(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))