Average Error: 8.1 → 0.4
Time: 3.2s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -0.09626506099155085 \lor \neg \left(y \leq 5.4305020927789424 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -0.09626506099155085 \lor \neg \left(y \leq 5.4305020927789424 \cdot 10^{-46}\right):\\
\;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.09626506099155085) (not (<= y 5.4305020927789424e-46)))
   (/ (* y (cosh x)) (* x z))
   (* (cosh x) (/ (/ y x) z))))
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 <= -0.09626506099155085) || !(y <= 5.4305020927789424e-46))) {
		VAR = (((double) (y * ((double) cosh(x)))) / ((double) (x * z)));
	} 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

Original8.1
Target0.5
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 2 regimes

  2. if y < -0.096265060991550855 or 5.4305020927789424e-46 < y

    1. Initial program 19.3

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

    2. Simplified0.5

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

    4. Applied associate-*r/0.5

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

    5. Simplified0.5

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

    if -0.096265060991550855 < y < 5.4305020927789424e-46

    1. Initial program 0.3

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

    2. Simplified11.6

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

    4. Applied associate-/r*0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.09626506099155085 \lor \neg \left(y \leq 5.4305020927789424 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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))