Average Error: 7.8 → 0.3
Time: 9.5s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq -1.2588588295461347 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{x}{\cosh x}}\\ \mathbf{elif}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 2.856324000879487 \cdot 10^{+274}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \left(\frac{y}{z} \cdot \frac{1}{x}\right)\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq -1.2588588295461347 \cdot 10^{+88}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{x}{\cosh x}}\\

\mathbf{elif}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 2.856324000879487 \cdot 10^{+274}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\

\mathbf{else}:\\
\;\;\;\;\cosh x \cdot \left(\frac{y}{z} \cdot \frac{1}{x}\right)\\

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* (cosh x) (/ y x)) z) -1.2588588295461347e+88)
   (/ (/ y z) (/ x (cosh x)))
   (if (<= (/ (* (cosh x) (/ y x)) z) 2.856324000879487e+274)
     (/ (* (cosh x) (/ y x)) z)
     (* (cosh x) (* (/ y z) (/ 1.0 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 (((cosh(x) * (y / x)) / z) <= -1.2588588295461347e+88) {
		tmp = (y / z) / (x / cosh(x));
	} else if (((cosh(x) * (y / x)) / z) <= 2.856324000879487e+274) {
		tmp = (cosh(x) * (y / x)) / z;
	} else {
		tmp = cosh(x) * ((y / z) * (1.0 / 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

Original7.8
Target0.4
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 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < -1.2588588295461347e88

    1. Initial program 17.8

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

    2. Simplified0.3

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

    if -1.2588588295461347e88 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 2.85632400087948709e274

    1. Initial program 0.2

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

    if 2.85632400087948709e274 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

    1. Initial program 47.9

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

    2. Simplified7.2

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

    4. Applied *-un-lft-identity_binary64_215617.2

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

    5. Applied times-frac_binary64_215670.4

      \[\leadsto \cosh x \cdot \color{blue}{\left(\frac{1}{x} \cdot \frac{y}{z}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq -1.2588588295461347 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{x}{\cosh x}}\\ \mathbf{elif}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 2.856324000879487 \cdot 10^{+274}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \left(\frac{y}{z} \cdot \frac{1}{x}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021176 
(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))