Average Error: 7.3 → 0.5
Time: 4.3s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -0.0040413612276975971 \lor \neg \left(y \le 1.58436151836249327 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\sqrt{\cosh x} \cdot \sqrt{\cosh x}\right) \cdot \frac{y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -0.0040413612276975971 \lor \neg \left(y \le 1.58436151836249327 \cdot 10^{-57}\right):\\
\;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(\sqrt{\cosh x} \cdot \sqrt{\cosh x}\right) \cdot \frac{y}{x}}{z}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (((double) cosh(x)) * ((double) (y / x)))) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((y <= -0.004041361227697597) || !(y <= 1.5843615183624933e-57))) {
		VAR = ((double) (((double) (((double) (((double) cosh(x)) * y)) / z)) / x));
	} else {
		VAR = ((double) (((double) (((double) (((double) sqrt(((double) cosh(x)))) * ((double) sqrt(((double) cosh(x)))))) * ((double) (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

Original7.3
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 y < -0.0040413612276975971 or 1.58436151836249327e-57 < y

    1. Initial program 17.6

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

    3. Applied associate-*r/17.6

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

    4. Applied associate-/l/0.5

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

    6. Applied associate-/r*0.7

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

    if -0.0040413612276975971 < y < 1.58436151836249327e-57

    1. Initial program 0.3

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

    3. Applied add-sqr-sqrt0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -0.0040413612276975971 \lor \neg \left(y \le 1.58436151836249327 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\sqrt{\cosh x} \cdot \sqrt{\cosh x}\right) \cdot \frac{y}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020173 
(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))