Average Error: 2.6 → 0.2
Time: 4.1s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -1.42142806571902 \cdot 10^{-299} \lor \neg \left(x \cdot \frac{\sin y}{y} \leq 2.3848349616302 \cdot 10^{-315}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{z}}{y}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -1.42142806571902 \cdot 10^{-299} \lor \neg \left(x \cdot \frac{\sin y}{y} \leq 2.3848349616302 \cdot 10^{-315}\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

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

\end{array}
double code(double x, double y, double z) {
	return (((double) (x * (((double) sin(y)) / y))) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((((double) (x * (((double) sin(y)) / y))) <= -1.42142806571902e-299) || !(((double) (x * (((double) sin(y)) / y))) <= 2.3848349616302e-315))) {
		VAR = (((double) (x * (((double) sin(y)) / y))) / z);
	} else {
		VAR = (((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

Original2.6
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -1.42142806571902006e-299 or 2.384834962e-315 < (* x (/ (sin y) y))

    1. Initial program Error: 0.2 bits

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

    if -1.42142806571902006e-299 < (* x (/ (sin y) y)) < 2.384834962e-315

    1. Initial program Error: 16.7 bits

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

    3. Applied div-invError: 16.7 bits

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

    5. Applied associate-*r/Error: 17.2 bits

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

    6. Applied associate-*l/Error: 0.7 bits

      \[\leadsto \color{blue}{\frac{\left(x \cdot \sin y\right) \cdot \frac{1}{z}}{y}}\]

    7. SimplifiedError: 0.4 bits

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

  4. Final simplificationError: 0.2 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -1.42142806571902 \cdot 10^{-299} \lor \neg \left(x \cdot \frac{\sin y}{y} \leq 2.3848349616302 \cdot 10^{-315}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{z}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(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))