Average Error: 2.7 → 0.2
Time: 4.7s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -6.43386950189108172 \cdot 10^{-231} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 4.44659 \cdot 10^{-323}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -6.43386950189108172 \cdot 10^{-231} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 4.44659 \cdot 10^{-323}\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\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) (x * ((double) (((double) sin(y)) / y)))) <= -6.433869501891082e-231) || !(((double) (x * ((double) (((double) sin(y)) / y)))) <= 4.4465908125712e-323))) {
		VAR = ((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z));
	} 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

Original2.7
Target0.4
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)) < -6.43386950189108172e-231 or 4.44659e-323 < (* x (/ (sin y) y))

    1. Initial program 0.3

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

    if -6.43386950189108172e-231 < (* x (/ (sin y) y)) < 4.44659e-323

    1. Initial program 12.6

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

    3. Applied clear-num12.6

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

    5. Applied *-un-lft-identity12.6

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

    6. Applied times-frac0.3

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

    7. Simplified0.3

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

    8. Simplified0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -6.43386950189108172 \cdot 10^{-231} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 4.44659 \cdot 10^{-323}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))