Average Error: 2.6 → 0.3
Time: 12.8s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.61269932403100551 \cdot 10^{63} \lor \neg \left(z \le 1.27184561188259121 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.61269932403100551 \cdot 10^{63} \lor \neg \left(z \le 1.27184561188259121 \cdot 10^{-17}\right):\\
\;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{z \cdot \frac{y}{\sin 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 (((z <= -4.6126993240310055e+63) || !(z <= 1.2718456118825912e-17))) {
		VAR = ((x / (y / ((double) sin(y)))) / z);
	} else {
		VAR = (x / ((double) (z * (y / ((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

Original2.6
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.61269932403100551e63 or 1.27184561188259121e-17 < z

    1. Initial program 0.1

      \[\frac{x \cdot \frac{\sin y}{y}}{z}\]
    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-div-inv0.1

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

    if -4.61269932403100551e63 < z < 1.27184561188259121e-17

    1. Initial program 5.2

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

    3. Applied associate-/l*0.4

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

    4. Simplified0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.61269932403100551 \cdot 10^{63} \lor \neg \left(z \le 1.27184561188259121 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array}\]

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))