Average Error: 2.6 → 0.3
Time: 4.0s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.270489758192143 \cdot 10^{-20} \lor \neg \left(z \leq 5.7234459696882616 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.270489758192143 \cdot 10^{-20} \lor \neg \left(z \leq 5.7234459696882616 \cdot 10^{-80}\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 -1.270489758192143e-20) (not (<= z 5.7234459696882616e-80)))
   (* (/ (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 <= -1.270489758192143e-20) || !(z <= 5.7234459696882616e-80)) {
		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

Original2.6
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 < -1.27048975819214297e-20 or 5.72344596968826157e-80 < z

    1. Initial program 0.3

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

    3. Applied add-cube-cbrt_binary641.0

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

    4. Applied times-frac_binary641.7

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

    5. Taylor expanded around inf 7.9

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

    6. Simplified0.3

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

    if -1.27048975819214297e-20 < z < 5.72344596968826157e-80

    1. Initial program 6.5

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

    3. Applied associate-/l*_binary640.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.270489758192143 \cdot 10^{-20} \lor \neg \left(z \leq 5.7234459696882616 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(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))