Average Error: 2.6 → 0.4
Time: 4.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -9.58817383040854995 \cdot 10^{-299} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le 0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sin y}{y \cdot z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -9.58817383040854995 \cdot 10^{-299} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le 0.0\right):\\
\;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((x * (sin(y) / y)) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((((x * (sin(y) / y)) / z) <= -9.58817383040855e-299) || !(((x * (sin(y) / y)) / z) <= 0.0))) {
		VAR = ((x * (1.0 / (y / sin(y)))) / z);
	} else {
		VAR = (x * (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

Original2.6
Target0.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (/ (sin y) y)) z) < -9.58817383040855e-299 or 0.0 < (/ (* x (/ (sin y) y)) z)

    1. Initial program 0.4

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

    3. Applied clear-num0.4

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

    if -9.58817383040855e-299 < (/ (* x (/ (sin y) y)) z) < 0.0

    1. Initial program 8.7

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

    3. Applied *-un-lft-identity8.7

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

    7. Applied div-inv0.3

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

    8. Applied associate-/l*0.3

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

    9. Simplified0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -9.58817383040854995 \cdot 10^{-299} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le 0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sin y}{y \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(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 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))