Average Error: 7.7 → 0.6
Time: 3.9s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -1.20372722107833069 \cdot 10^{215}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;\cosh x \cdot \frac{y}{x} \le 8.05838683923620923 \cdot 10^{156}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{x}}{\frac{\frac{z}{e^{-1 \cdot x} + e^{x}}}{y}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -1.20372722107833069 \cdot 10^{215}:\\
\;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\

\mathbf{elif}\;\cosh x \cdot \frac{y}{x} \le 8.05838683923620923 \cdot 10^{156}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{\frac{1}{2}}{x}}{\frac{\frac{z}{e^{-1 \cdot x} + e^{x}}}{y}}\\

\end{array}
double code(double x, double y, double z) {
	return ((cosh(x) * (y / x)) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((cosh(x) * (y / x)) <= -1.2037272210783307e+215)) {
		VAR = ((cosh(x) * y) / (x * z));
	} else {
		double VAR_1;
		if (((cosh(x) * (y / x)) <= 8.058386839236209e+156)) {
			VAR_1 = ((cosh(x) * (y / x)) / z);
		} else {
			VAR_1 = ((0.5 / x) / ((z / (exp((-1.0 * x)) + exp(x))) / y));
		}
		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
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 (* (cosh x) (/ y x)) < -1.2037272210783307e+215

    1. Initial program 31.2

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

    3. Applied div-inv31.3

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

    5. Applied associate-*r/31.3

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

    6. Applied frac-times0.7

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

    7. Simplified0.7

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

    if -1.2037272210783307e+215 < (* (cosh x) (/ y x)) < 8.058386839236209e+156

    1. Initial program 0.3

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

    if 8.058386839236209e+156 < (* (cosh x) (/ y x))

    1. Initial program 22.2

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

    2. Taylor expanded around inf 22.2

      \[\leadsto \frac{\color{blue}{\frac{y \cdot \left(\frac{1}{2} \cdot e^{x} + \frac{1}{2} \cdot e^{-x}\right)}{x}}}{z}\]

    3. Simplified22.3

      \[\leadsto \frac{\color{blue}{\frac{\frac{1}{2} \cdot \left(e^{-1 \cdot x} + e^{x}\right)}{\frac{x}{y}}}}{z}\]
    4. Using strategy rm

    5. Applied div-inv22.3

      \[\leadsto \frac{\frac{\frac{1}{2} \cdot \left(e^{-1 \cdot x} + e^{x}\right)}{\color{blue}{x \cdot \frac{1}{y}}}}{z}\]

    6. Applied times-frac22.3

      \[\leadsto \frac{\color{blue}{\frac{\frac{1}{2}}{x} \cdot \frac{e^{-1 \cdot x} + e^{x}}{\frac{1}{y}}}}{z}\]

    7. Applied associate-/l*2.1

      \[\leadsto \color{blue}{\frac{\frac{\frac{1}{2}}{x}}{\frac{z}{\frac{e^{-1 \cdot x} + e^{x}}{\frac{1}{y}}}}}\]

    8. Simplified1.9

      \[\leadsto \frac{\frac{\frac{1}{2}}{x}}{\color{blue}{\frac{\frac{z}{e^{-1 \cdot x} + e^{x}}}{y}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -1.20372722107833069 \cdot 10^{215}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;\cosh x \cdot \frac{y}{x} \le 8.05838683923620923 \cdot 10^{156}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{x}}{\frac{\frac{z}{e^{-1 \cdot x} + e^{x}}}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 
(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))