Average Error: 2.7 → 0.2
Time: 4.6s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -8.27881371708331471 \cdot 10^{-306} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 3.49340538877379705 \cdot 10^{-307}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{z}}{y}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -8.27881371708331471 \cdot 10^{-306} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 3.49340538877379705 \cdot 10^{-307}\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

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

\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) (x * ((double) (((double) sin(y)) / y)))) <= -8.278813717083315e-306) || !(((double) (x * ((double) (((double) sin(y)) / y)))) <= 3.493405388773797e-307))) {
		VAR = ((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z));
	} else {
		VAR = ((double) (((double) (((double) (x * ((double) sin(y)))) / z)) / y));
	}
	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

Original2.7
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -8.278813717083315e-306 or 3.493405388773797e-307 < (* x (/ (sin y) y))

    1. Initial program 0.2

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

    if -8.278813717083315e-306 < (* x (/ (sin y) y)) < 3.493405388773797e-307

    1. Initial program 18.1

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

    3. Applied clear-num18.2

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot \frac{\sin y}{y}}}}\]
    4. Using strategy rm

    5. Applied associate-*r/18.7

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

    6. Applied associate-/r/1.2

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

    7. Applied associate-/r*0.8

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

    8. Simplified0.7

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -8.27881371708331471 \cdot 10^{-306} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 3.49340538877379705 \cdot 10^{-307}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{z}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020122 
(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 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

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