Average Error: 7.7 → 1.2
Time: 3.2s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -494.30008968649463:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{elif}\;y \leq 1.451586002073307 \cdot 10^{-137}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -494.30008968649463:\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

\mathbf{elif}\;y \leq 1.451586002073307 \cdot 10^{-137}:\\
\;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{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 <= -494.30008968649463)) {
		VAR = ((double) (((double) cosh(x)) * (y / ((double) (x * z)))));
	} else {
		double VAR_1;
		if ((y <= 1.451586002073307e-137)) {
			VAR_1 = ((double) (((double) cosh(x)) * ((y / x) / z)));
		} else {
			VAR_1 = (((double) (((double) cosh(x)) * (y / z))) / 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

Original7.7
Target0.4
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y < 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -494.30008968649463

    1. Initial program 21.3

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

    2. Simplified0.3

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

    if -494.30008968649463 < y < 1.451586002073307e-137

    1. Initial program 0.3

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

    2. Simplified11.4

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

    4. Applied associate-/r*0.3

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

    if 1.451586002073307e-137 < y

    1. Initial program 12.3

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

    2. Simplified2.5

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

    4. Applied *-un-lft-identity2.5

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

    5. Applied times-frac3.2

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

    6. Applied associate-*r*3.2

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

    7. Simplified3.2

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

    9. Applied associate-*l/3.1

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -494.30008968649463:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{elif}\;y \leq 1.451586002073307 \cdot 10^{-137}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \end{array}\]

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))