Average Error: 7.5 → 0.5
Time: 3.3s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -5.479021814815761 \cdot 10^{+53} \lor \neg \left(z \leq 8.289021693904929 \cdot 10^{-41}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -5.479021814815761 \cdot 10^{+53} \lor \neg \left(z \leq 8.289021693904929 \cdot 10^{-41}\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.479021814815761e+53) (not (<= z 8.289021693904929e-41)))
   (* (cosh x) (/ y (* z x)))
   (/ (* (cosh x) (/ y x)) z)))
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 tmp;
	if (((z <= -5.479021814815761e+53) || !(z <= 8.289021693904929e-41))) {
		tmp = ((double) (((double) cosh(x)) * (y / ((double) (z * x)))));
	} else {
		tmp = (((double) (((double) cosh(x)) * (y / x))) / 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

Original7.5
Target0.5
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 < -5.47902181481576139e53 or 8.28902169390492894e-41 < z

    1. Initial program Error: 11.6 bits

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

    2. SimplifiedError: 0.4 bits

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

    if -5.47902181481576139e53 < z < 8.28902169390492894e-41

    1. Initial program Error: 0.7 bits

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

  4. Final simplificationError: 0.5 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.479021814815761 \cdot 10^{+53} \lor \neg \left(z \leq 8.289021693904929 \cdot 10^{-41}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(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))