Average Error: 2.6 → 2.6
Time: 3.6s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \le 3.5650135889674179 \cdot 10^{-238}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\sin y}{y} \le 3.5650135889674179 \cdot 10^{-238}:\\
\;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (((double) sin(y)) / y)) <= 3.565013588967418e-238)) {
		VAR = ((double) (((double) (((double) sin(y)) / z)) * ((double) (x / y))));
	} else {
		VAR = ((double) (x * ((double) (((double) (((double) sin(y)) / y)) / z))));
	}
	return VAR;
}

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

Original2.6
Target0.3
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (sin y) y) < 3.5650135889674179e-238

    1. Initial program 5.2

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

    3. Applied associate-/l*6.0

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

    5. Applied associate-/r/6.0

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

    6. Applied *-un-lft-identity6.0

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

    7. Applied times-frac5.2

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

    8. Simplified5.2

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

    if 3.5650135889674179e-238 < (/ (sin y) y)

    1. Initial program 1.3

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

    3. Applied *-un-lft-identity1.3

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

    4. Applied times-frac1.4

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

    5. Simplified1.4

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \le 3.5650135889674179 \cdot 10^{-238}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))