Average Error: 2.6 → 0.2
Time: 6.4s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.62297845209075496 \cdot 10^{41}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}}{z}\\ \mathbf{elif}\;z \le 1.7046640976337448 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.62297845209075496 \cdot 10^{41}:\\
\;\;\;\;\frac{x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}}{z}\\

\mathbf{elif}\;z \le 1.7046640976337448 \cdot 10^{-17}:\\
\;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\

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

\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 ((z <= -2.622978452090755e+41)) {
		VAR = (((double) (x * ((1.0 / y) / (1.0 / ((double) sin(y)))))) / z);
	} else {
		double VAR_1;
		if ((z <= 1.7046640976337448e-17)) {
			VAR_1 = (x / ((double) (z * (y / ((double) sin(y))))));
		} else {
			VAR_1 = ((x / (y / ((double) sin(y)))) / z);
		}
		VAR = VAR_1;
	}
	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
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -2.62297845209075496e41

    1. Initial program 0.1

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

    3. Applied clear-num0.1

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

    5. Applied div-inv0.2

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

    6. Applied associate-/r*0.1

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

    if -2.62297845209075496e41 < z < 1.7046640976337448e-17

    1. Initial program 5.4

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

    3. Applied associate-/l*0.3

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

    4. Simplified0.3

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

    if 1.7046640976337448e-17 < z

    1. Initial program 0.2

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

    3. Applied clear-num0.2

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

    5. Applied *-un-lft-identity0.2

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

    6. Applied associate-/r*0.2

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

    7. Simplified0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.62297845209075496 \cdot 10^{41}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}}{z}\\ \mathbf{elif}\;z \le 1.7046640976337448 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))