Average Error: 7.5 → 0.5
Time: 4.5s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.2032535890096534 \cdot 10^{-34} \lor \neg \left(y \leq 3.732881937329904 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{\frac{z}{\frac{y}{x}}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.2032535890096534 \cdot 10^{-34} \lor \neg \left(y \leq 3.732881937329904 \cdot 10^{-31}\right):\\
\;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.2032535890096534e-34) (not (<= y 3.732881937329904e-31)))
   (/ (* y (cosh x)) (* x z))
   (/ (cosh x) (/ z (/ y x)))))
double code(double x, double y, double z) {
	return (cosh(x) * (y / x)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2032535890096534e-34) || !(y <= 3.732881937329904e-31)) {
		tmp = (y * cosh(x)) / (x * z);
	} else {
		tmp = cosh(x) / (z / (y / x));
	}
	return tmp;
}

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

Derivation

  1. Split input into 2 regimes

  2. if y < -1.2032535890096534e-34 or 3.7328819373299038e-31 < y

    1. Initial program 18.0

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

    3. Applied associate-*r/_binary6418.0

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

    4. Applied associate-/l/_binary640.5

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

    5. Simplified0.5

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

    if -1.2032535890096534e-34 < y < 3.7328819373299038e-31

    1. Initial program 0.3

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

    3. Applied associate-/l*_binary640.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2032535890096534 \cdot 10^{-34} \lor \neg \left(y \leq 3.732881937329904 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{\frac{z}{\frac{y}{x}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020260 
(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))