Average Error: 2.5 → 1.2
Time: 4.2s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.49450524163551911 \cdot 10^{46} \lor \neg \left(z \le 1.43141062544078479 \cdot 10^{27}\right):\\ \;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\sin y}{\sqrt[3]{z} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{z}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.49450524163551911 \cdot 10^{46} \lor \neg \left(z \le 1.43141062544078479 \cdot 10^{27}\right):\\
\;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\sin y}{\sqrt[3]{z} \cdot y}\\

\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 <= -4.494505241635519e+46) || !(z <= 1.4314106254407848e+27))) {
		VAR = ((double) (((double) (x / ((double) (((double) cbrt(z)) * ((double) cbrt(z)))))) * ((double) (((double) sin(y)) / ((double) (((double) cbrt(z)) * y))))));
	} 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

Original2.5
Target0.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.49450524163551911e46 or 1.43141062544078479e27 < z

    1. Initial program 0.1

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

    3. Applied add-cube-cbrt0.7

      \[\leadsto \frac{x \cdot \frac{\sin y}{y}}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied times-frac1.7

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\frac{\sin y}{y}}{\sqrt[3]{z}}}\]

    5. Simplified2.0

      \[\leadsto \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \color{blue}{\frac{\sin y}{y \cdot \sqrt[3]{z}}}\]

    if -4.49450524163551911e46 < z < 1.43141062544078479e27

    1. Initial program 4.8

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

    3. Applied associate-/l*0.3

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

    4. Simplified0.5

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.49450524163551911 \cdot 10^{46} \lor \neg \left(z \le 1.43141062544078479 \cdot 10^{27}\right):\\ \;\;\;\;\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\sin y}{\sqrt[3]{z} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{z}{\sin y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))