Average Error: 7.4 → 0.3
Time: 5.9s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \leq -\infty:\\ \;\;\;\;\frac{\cosh x}{\frac{x}{\frac{y}{z}}}\\ \mathbf{elif}\;\cosh x \cdot \frac{y}{x} \leq 5.032371106752183 \cdot 10^{+276}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\cosh x \cdot \frac{y}{x} \leq -\infty:\\
\;\;\;\;\frac{\cosh x}{\frac{x}{\frac{y}{z}}}\\

\mathbf{elif}\;\cosh x \cdot \frac{y}{x} \leq 5.032371106752183 \cdot 10^{+276}:\\
\;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* (cosh x) (/ y x)) (- INFINITY))
   (/ (cosh x) (/ x (/ y z)))
   (if (<= (* (cosh x) (/ y x)) 5.032371106752183e+276)
     (* (cosh x) (/ (/ y x) z))
     (/ (* (cosh x) y) (* x 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 ((cosh(x) * (y / x)) <= -((double) INFINITY)) {
		tmp = cosh(x) / (x / (y / z));
	} else if ((cosh(x) * (y / x)) <= 5.032371106752183e+276) {
		tmp = cosh(x) * ((y / x) / z);
	} else {
		tmp = (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

Original7.4
Target0.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y < 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-*r/_binary64_956864.0

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

    4. Applied associate-/l/_binary64_95730.6

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

    5. Simplified0.6

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

    7. Applied associate-/l*_binary64_95710.5

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

    8. Simplified0.5

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

    if -inf.0 < (*.f64 (cosh.f64 x) (/.f64 y x)) < 5.0323711067521825e276

    1. Initial program 0.3

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

    3. Applied *-un-lft-identity_binary64_96260.3

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

    4. Applied times-frac_binary64_96320.3

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

    5. Simplified0.3

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

    if 5.0323711067521825e276 < (*.f64 (cosh.f64 x) (/.f64 y x))

    1. Initial program 46.8

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

    3. Applied associate-*r/_binary64_956846.8

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

    4. Applied associate-/l/_binary64_95730.4

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

    5. Simplified0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \leq -\infty:\\ \;\;\;\;\frac{\cosh x}{\frac{x}{\frac{y}{z}}}\\ \mathbf{elif}\;\cosh x \cdot \frac{y}{x} \leq 5.032371106752183 \cdot 10^{+276}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020354 
(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))