Average Error: 8.1 → 0.8
Time: 4.3s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -1.80440294004069 \cdot 10^{221}:\\ \;\;\;\;\cosh x \cdot \left(\frac{1}{x} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le 1.94499063359633262 \cdot 10^{-105}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -1.80440294004069 \cdot 10^{221}:\\
\;\;\;\;\cosh x \cdot \left(\frac{1}{x} \cdot \frac{y}{z}\right)\\

\mathbf{elif}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le 1.94499063359633262 \cdot 10^{-105}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\

\mathbf{else}:\\
\;\;\;\;\cosh x \cdot \frac{\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 (((((double) (((double) cosh(x)) * (y / x))) / z) <= -1.80440294004069e+221)) {
		VAR = ((double) (((double) cosh(x)) * ((double) ((1.0 / x) * (y / z)))));
	} else {
		double VAR_1;
		if (((((double) (((double) cosh(x)) * (y / x))) / z) <= 1.9449906335963326e-105)) {
			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

Original8.1
Target0.5
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (cosh x) (/ y x)) z) < -1.80440294004069e221

    1. Initial program 33.7

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

    2. Simplified13.6

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

    4. Applied *-un-lft-identity13.6

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

    5. Applied times-frac0.4

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

    if -1.80440294004069e221 < (/ (* (cosh x) (/ y x)) z) < 1.94499063359633262e-105

    1. Initial program 0.2

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

    if 1.94499063359633262e-105 < (/ (* (cosh x) (/ y x)) z)

    1. Initial program 10.7

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

    2. Simplified8.5

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

    4. Applied *-un-lft-identity8.5

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

    5. Applied times-frac1.7

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

    7. Applied associate-*l/1.6

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

    8. Simplified1.6

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le -1.80440294004069 \cdot 10^{221}:\\ \;\;\;\;\cosh x \cdot \left(\frac{1}{x} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \le 1.94499063359633262 \cdot 10^{-105}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))