Average Error: 7.9 → 0.4
Time: 4.1s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.252876066324285 \cdot 10^{-34}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{elif}\;y \leq 8.583768275425656 \cdot 10^{+21}:\\ \;\;\;\;\left(\cosh x \cdot \frac{y}{x}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{z}{y \cdot \cosh x}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.252876066324285 \cdot 10^{-34}:\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

\mathbf{elif}\;y \leq 8.583768275425656 \cdot 10^{+21}:\\
\;\;\;\;\left(\cosh x \cdot \frac{y}{x}\right) \cdot \frac{1}{z}\\

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

\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 ((y <= -1.252876066324285e-34)) {
		VAR = ((double) (((double) cosh(x)) * (y / ((double) (x * z)))));
	} else {
		double VAR_1;
		if ((y <= 8.583768275425656e+21)) {
			VAR_1 = ((double) (((double) (((double) cosh(x)) * (y / x))) * (1.0 / z)));
		} else {
			VAR_1 = (1.0 / ((double) (x * (z / ((double) (y * ((double) cosh(x))))))));
		}
		VAR = VAR_1;
	}
	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
\[\begin{array}{l} \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y < 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.25287606632428499e-34

    1. Initial program 18.4

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

    2. Simplified0.5

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

    if -1.25287606632428499e-34 < y < 8.583768275425656e21

    1. Initial program 0.3

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

    3. Applied div-inv0.4

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

    if 8.583768275425656e21 < y

    1. Initial program 24.2

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

    3. Applied clear-num24.2

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

    4. Simplified0.4

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.252876066324285 \cdot 10^{-34}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{elif}\;y \leq 8.583768275425656 \cdot 10^{+21}:\\ \;\;\;\;\left(\cosh x \cdot \frac{y}{x}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \frac{z}{y \cdot \cosh x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))