Average Error: 7.6 → 0.8
Time: 4.4s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.6001095201590717 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{\cosh x}{z \cdot x}\\ \mathbf{elif}\;z \leq 2.15700900459188 \cdot 10^{-39}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \cosh x}{z \cdot x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.6001095201590717 \cdot 10^{+86}:\\
\;\;\;\;y \cdot \frac{\cosh x}{z \cdot x}\\

\mathbf{elif}\;z \leq 2.15700900459188 \cdot 10^{-39}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6001095201590717e+86)
   (* y (/ (cosh x) (* z x)))
   (if (<= z 2.15700900459188e-39)
     (/ (* (cosh x) (/ y x)) z)
     (/ (* y (cosh x)) (* z 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 (z <= -1.6001095201590717e+86) {
		tmp = y * (cosh(x) / (z * x));
	} else if (z <= 2.15700900459188e-39) {
		tmp = (cosh(x) * (y / x)) / z;
	} else {
		tmp = (y * cosh(x)) / (z * 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

Original7.6
Target0.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y < 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.6001095201590717e86

    1. Initial program 14.6

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

    3. Applied associate-/l*_binary64_1275215.2

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

    5. Applied div-inv_binary64_1280415.2

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

    6. Applied *-un-lft-identity_binary64_1280715.2

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

    7. Applied times-frac_binary64_128131.0

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

    8. Applied *-un-lft-identity_binary64_128071.0

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

    9. Applied times-frac_binary64_128130.5

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

    10. Simplified0.4

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

    11. Simplified0.4

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

    if -1.6001095201590717e86 < z < 2.15700900459187988e-39

    1. Initial program 1.4

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

    if 2.15700900459187988e-39 < z

    1. Initial program 9.7

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

    3. Applied associate-*r/_binary64_127499.7

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

    4. Applied associate-/l/_binary64_127540.5

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

    5. Simplified0.5

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6001095201590717 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{\cosh x}{z \cdot x}\\ \mathbf{elif}\;z \leq 2.15700900459188 \cdot 10^{-39}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \cosh x}{z \cdot x}\\ \end{array}\]

Reproduce

herbie shell --seed 2020292 
(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))