Average Error: 2.8 → 1.0
Time: 4.1s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.2486964666857625 \cdot 10^{-98} \lor \neg \left(z \le 3.4739938757762599 \cdot 10^{-196}\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{z}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.2486964666857625 \cdot 10^{-98} \lor \neg \left(z \le 3.4739938757762599 \cdot 10^{-196}\right):\\
\;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y \cdot \frac{z}{\sin 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 (((z <= -1.2486964666857625e-98) || !(z <= 3.47399387577626e-196))) {
		VAR = ((double) (((double) (((double) sin(y)) / y)) * ((double) (x / z))));
	} else {
		VAR = ((double) (x / ((double) (y * ((double) (z / ((double) sin(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

Original2.8
Target0.3
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.2486964666857625e-98 or 3.4739938757762599e-196 < z

    1. Initial program 1.0

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

    3. Applied associate-/l*3.6

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

    4. Simplified10.8

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

    6. Applied *-un-lft-identity10.8

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

    7. Applied times-frac11.5

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

    8. Simplified7.5

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

    10. Applied associate-*r*1.3

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

    11. Simplified1.3

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

    if -1.2486964666857625e-98 < z < 3.4739938757762599e-196

    1. Initial program 9.2

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

    3. Applied associate-/l*0.2

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

    4. Simplified0.3

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.2486964666857625 \cdot 10^{-98} \lor \neg \left(z \le 3.4739938757762599 \cdot 10^{-196}\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{z}{\sin y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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))