Average Error: 2.7 → 0.4
Time: 3.2s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -8.50374847451689476 \cdot 10^{-275} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 1.7369308748153065 \cdot 10^{-300}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -8.50374847451689476 \cdot 10^{-275} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 1.7369308748153065 \cdot 10^{-300}\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\mathbf{else}:\\
\;\;\;\;\sin y \cdot \frac{x}{y \cdot 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) (x * ((double) (((double) sin(y)) / y)))) <= -8.503748474516895e-275) || !(((double) (x * ((double) (((double) sin(y)) / y)))) <= 1.7369308748153065e-300))) {
		VAR = ((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z));
	} else {
		VAR = ((double) (((double) sin(y)) * ((double) (x / ((double) (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

Original2.7
Target0.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -8.50374847451689476e-275 or 1.7369308748153065e-300 < (* x (/ (sin y) y))

    1. Initial program 0.2

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

    if -8.50374847451689476e-275 < (* x (/ (sin y) y)) < 1.7369308748153065e-300

    1. Initial program 15.0

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

    2. Taylor expanded around inf 3.3

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

    3. Simplified1.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -8.50374847451689476 \cdot 10^{-275} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 1.7369308748153065 \cdot 10^{-300}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))