Average Error: 7.7 → 0.3
Time: 3.9s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq -1.2655409549400952 \cdot 10^{+215} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 7.79880706110208 \cdot 10^{-24}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq -1.2655409549400952 \cdot 10^{+215} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 7.79880706110208 \cdot 10^{-24}\right):\\
\;\;\;\;\cosh x \cdot \frac{\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) cosh(x)) * (y / x))) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((((double) (((double) cosh(x)) * (y / x))) / z) <= -1.2655409549400952e+215) || !((((double) (((double) cosh(x)) * (y / x))) / z) <= 7.79880706110208e-24))) {
		VAR = ((double) (((double) cosh(x)) * ((y / z) / x)));
	} else {
		VAR = (((double) (((double) cosh(x)) * (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

Original7.7
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y < 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (cosh x) (/ y x)) z) < -1.2655409549400952e215 or 7.79880706110207929e-24 < (/ (* (cosh x) (/ y x)) z)

    1. Initial program Error: 17.7 bits

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

    2. SimplifiedError: 11.5 bits

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

    4. Applied add-cube-cbrtError: 12.4 bits

      \[\leadsto \cosh x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{x \cdot z}\]

    5. Applied times-fracError: 10.7 bits

      \[\leadsto \cosh x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{x} \cdot \frac{\sqrt[3]{y}}{z}\right)}\]

    6. SimplifiedError: 10.7 bits

      \[\leadsto \cosh x \cdot \left(\color{blue}{\left(\frac{\sqrt[3]{y}}{x} \cdot \sqrt[3]{y}\right)} \cdot \frac{\sqrt[3]{y}}{z}\right)\]
    7. Using strategy rm

    8. Applied associate-*l/Error: 10.7 bits

      \[\leadsto \cosh x \cdot \left(\color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{x}} \cdot \frac{\sqrt[3]{y}}{z}\right)\]

    9. Applied associate-*l/Error: 1.5 bits

      \[\leadsto \cosh x \cdot \color{blue}{\frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \frac{\sqrt[3]{y}}{z}}{x}}\]

    10. SimplifiedError: 0.4 bits

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

    if -1.2655409549400952e215 < (/ (* (cosh x) (/ y x)) z) < 7.79880706110207929e-24

    1. Initial program Error: 0.2 bits

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

  4. Final simplificationError: 0.3 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq -1.2655409549400952 \cdot 10^{+215} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 7.79880706110208 \cdot 10^{-24}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))