Average Error: 2.8 → 0.3
Time: 6.4s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -3.2266964228689376 \cdot 10^{+81} \lor \neg \left(z \leq 3.946338514026135 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -3.2266964228689376 \cdot 10^{+81} \lor \neg \left(z \leq 3.946338514026135 \cdot 10^{-10}\right):\\
\;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.2266964228689376e+81) (not (<= z 3.946338514026135e-10)))
   (* (/ (sin y) y) (/ x z))
   (/ x (/ z (/ (sin y) y)))))
double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.2266964228689376e+81) || !(z <= 3.946338514026135e-10)) {
		tmp = (sin(y) / y) * (x / z);
	} else {
		tmp = x / (z / (sin(y) / y));
	}
	return tmp;
}

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
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.22669642286893759e81 or 3.94633851402613508e-10 < z

    1. Initial program 0.1

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

    3. Applied clear-num_binary640.8

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot \frac{\sin y}{y}}}}\]
    4. Using strategy rm

    5. Applied add-cube-cbrt_binary641.4

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

    6. Applied times-frac_binary642.7

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

    7. Applied add-cube-cbrt_binary642.7

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

    8. Applied times-frac_binary642.1

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

    9. Taylor expanded around inf 8.0

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

    10. Simplified0.1

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

    if -3.22669642286893759e81 < z < 3.94633851402613508e-10

    1. Initial program 5.2

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

    3. Applied associate-/l*_binary640.5

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2266964228689376 \cdot 10^{+81} \lor \neg \left(z \leq 3.946338514026135 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020219 
(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))