Average Error: 7.7 → 0.5
Time: 3.4s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.3649263236055999 \cdot 10^{-48} \lor \neg \left(z \le 3.8333035288502299 \cdot 10^{56}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{z} \cdot \frac{1}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.3649263236055999 \cdot 10^{-48} \lor \neg \left(z \le 3.8333035288502299 \cdot 10^{56}\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((cosh(x) * (y / x)) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -5.3649263236056e-48) || !(z <= 3.83330352885023e+56))) {
		VAR = (cosh(x) * (y / (x * z)));
	} else {
		VAR = (((cosh(x) * y) / z) * (1.0 / x));
	}
	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

Original7.7
Target0.5
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 2 regimes

  2. if z < -5.3649263236056e-48 or 3.83330352885023e+56 < z

    1. Initial program 11.7

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

    3. Applied *-un-lft-identity11.7

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

    4. Applied times-frac11.7

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

    5. Simplified11.7

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

    6. Simplified0.4

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

    if -5.3649263236056e-48 < z < 3.83330352885023e+56

    1. Initial program 0.6

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

    3. Applied associate-*r/0.6

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

    4. Applied associate-/l/18.7

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

    6. Applied associate-/r*0.6

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

    8. Applied div-inv0.7

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.3649263236055999 \cdot 10^{-48} \lor \neg \left(z \le 3.8333035288502299 \cdot 10^{56}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{z} \cdot \frac{1}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(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))