Average Error: 7.5 → 0.6
Time: 4.8s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.19074771996601305 \cdot 10^{61}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \mathbf{elif}\;y \le 9.8005472850728346 \cdot 10^{-64}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.19074771996601305 \cdot 10^{61}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\

\mathbf{elif}\;y \le 9.8005472850728346 \cdot 10^{-64}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\

\mathbf{else}:\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot 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 <= -1.190747719966013e+61)) {
		VAR = ((double) (((double) (((double) cosh(x)) * ((double) (y / z)))) / x));
	} else {
		double VAR_1;
		if ((y <= 9.800547285072835e-64)) {
			VAR_1 = ((double) (((double) (((double) cosh(x)) * ((double) (y / x)))) / z));
		} else {
			VAR_1 = ((double) (((double) cosh(x)) * ((double) (y / ((double) (x * z))))));
		}
		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

Original7.5
Target0.4
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.19074771996601305e61

    1. Initial program 27.6

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

    3. Applied div-inv27.7

      \[\leadsto \color{blue}{\left(\cosh x \cdot \frac{y}{x}\right) \cdot \frac{1}{z}}\]
    4. Using strategy rm

    5. Applied associate-*r/27.7

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

    6. Applied associate-*l/0.5

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

    7. Simplified0.4

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

    if -1.19074771996601305e61 < y < 9.8005472850728346e-64

    1. Initial program 0.6

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

    if 9.8005472850728346e-64 < y

    1. Initial program 15.1

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

    2. Simplified0.9

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.19074771996601305 \cdot 10^{61}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{z}}{x}\\ \mathbf{elif}\;y \le 9.8005472850728346 \cdot 10^{-64}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))