Average Error: 7.7 → 0.5
Time: 3.1s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -160614062.07336497 \lor \neg \left(z \leq 2.1824738903714276 \cdot 10^{+66}\right):\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{1}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x} \cdot \frac{y}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -160614062.07336497 \lor \neg \left(z \leq 2.1824738903714276 \cdot 10^{+66}\right):\\
\;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{1}{z \cdot x}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -160614062.07336497) (not (<= z 2.1824738903714276e+66)))
   (* (* (cosh x) y) (/ 1.0 (* z x)))
   (* (/ (cosh x) x) (/ y z))))
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 ((z <= -160614062.07336497) || !(z <= 2.1824738903714276e+66)) {
		tmp = (cosh(x) * y) * (1.0 / (z * x));
	} else {
		tmp = (cosh(x) / x) * (y / z);
	}
	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

Original7.7
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 z < -160614062.07336497 or 2.18247389037142757e66 < z

    1. Initial program 12.6

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

    3. Applied associate-*r/_binary6412.6

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

    4. Applied associate-/l/_binary640.3

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

    5. Simplified0.3

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

    7. Applied div-inv_binary640.4

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

    if -160614062.07336497 < z < 2.18247389037142757e66

    1. Initial program 1.0

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

    3. Applied associate-*r/_binary641.0

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

    4. Applied associate-/l/_binary6415.9

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

    5. Simplified15.9

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

    7. Applied times-frac_binary640.7

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -160614062.07336497 \lor \neg \left(z \leq 2.1824738903714276 \cdot 10^{+66}\right):\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{1}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x} \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020224 
(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))