Average Error: 2.8 → 1.9
Time: 3.4s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le 1.52373213010746362 \cdot 10^{-141} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 2.8550563551916007 \cdot 10^{103}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sin y}{\sqrt[3]{y}}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le 1.52373213010746362 \cdot 10^{-141} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 2.8550563551916007 \cdot 10^{103}\right):\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sin y}{\sqrt[3]{y}}}{z}\\

\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 (((((double) (x * ((double) (((double) sin(y)) / y)))) <= 1.5237321301074636e-141) || !(((double) (x * ((double) (((double) sin(y)) / y)))) <= 2.8550563551916007e+103))) {
		VAR = ((double) (x / ((double) (z / ((double) (((double) sin(y)) / y))))));
	} else {
		VAR = ((double) (((double) (((double) (x / ((double) (((double) cbrt(y)) * ((double) cbrt(y)))))) * ((double) (((double) sin(y)) / ((double) cbrt(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

Original2.8
Target0.3
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < 1.52373213010746362e-141 or 2.8550563551916007e103 < (* x (/ (sin y) y))

    1. Initial program 3.5

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

    3. Applied associate-/l*2.1

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

    if 1.52373213010746362e-141 < (* x (/ (sin y) y)) < 2.8550563551916007e103

    1. Initial program 0.2

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

    3. Applied add-cube-cbrt1.3

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

    4. Applied *-un-lft-identity1.3

      \[\leadsto \frac{x \cdot \frac{\color{blue}{1 \cdot \sin y}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{z}\]

    5. Applied times-frac1.3

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sin y}{\sqrt[3]{y}}\right)}}{z}\]

    6. Applied associate-*r*1.3

      \[\leadsto \frac{\color{blue}{\left(x \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sin y}{\sqrt[3]{y}}}}{z}\]

    7. Simplified1.3

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le 1.52373213010746362 \cdot 10^{-141} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 2.8550563551916007 \cdot 10^{103}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sin y}{\sqrt[3]{y}}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(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))