Average Error: 2.7 → 0.4
Time: 4.1s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.8941292308796897 \cdot 10^{-61} \lor \neg \left(z \le 1.6470200371492856 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -9.8941292308796897 \cdot 10^{-61} \lor \neg \left(z \le 1.6470200371492856 \cdot 10^{-93}\right):\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{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 (((z <= -9.89412923087969e-61) || !(z <= 1.6470200371492856e-93))) {
		VAR = ((x * (sin(y) * (1.0 / 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

Original2.7
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 z < -9.89412923087969e-61 or 1.6470200371492856e-93 < z

    1. Initial program 0.3

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

    3. Applied div-inv0.4

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

    if -9.89412923087969e-61 < z < 1.6470200371492856e-93

    1. Initial program 7.6

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

    3. Applied *-un-lft-identity7.6

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.8941292308796897 \cdot 10^{-61} \lor \neg \left(z \le 1.6470200371492856 \cdot 10^{-93}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 +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))