Average Error: 2.7 → 0.9
Time: 4.2s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -3.569106272538475 \cdot 10^{-295}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \cdot \frac{\sin y}{y} \leq 3.5421287694234906 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot \sin y}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -3.569106272538475 \cdot 10^{-295}:\\
\;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\

\mathbf{elif}\;x \cdot \frac{\sin y}{y} \leq 3.5421287694234906 \cdot 10^{-280}:\\
\;\;\;\;\frac{x \cdot \sin y}{y \cdot z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* x (/ (sin y) y)) -3.569106272538475e-295)
   (/ (* x (/ 1.0 (/ y (sin y)))) z)
   (if (<= (* x (/ (sin y) y)) 3.5421287694234906e-280)
     (/ (* x (sin y)) (* y z))
     (/ (* x (/ (sin y) y)) z))))
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 ((x * (sin(y) / y)) <= -3.569106272538475e-295) {
		tmp = (x * (1.0 / (y / sin(y)))) / z;
	} else if ((x * (sin(y) / y)) <= 3.5421287694234906e-280) {
		tmp = (x * sin(y)) / (y * z);
	} else {
		tmp = (x * (sin(y) / y)) / z;
	}
	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

Original2.7
Target0.3
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 x (/.f64 (sin.f64 y) y)) < -3.56910627253847484e-295

    1. Initial program 0.1

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

    3. Applied clear-num_binary640.2

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

    if -3.56910627253847484e-295 < (*.f64 x (/.f64 (sin.f64 y) y)) < 3.5421287694234906e-280

    1. Initial program 14.4

      \[\frac{x \cdot \frac{\sin y}{y}}{z}\]

    2. Taylor expanded around 0 4.0

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

    3. Simplified4.0

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

    if 3.5421287694234906e-280 < (*.f64 x (/.f64 (sin.f64 y) y))

    1. Initial program 0.2

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -3.569106272538475 \cdot 10^{-295}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \cdot \frac{\sin y}{y} \leq 3.5421287694234906 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot \sin y}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021110 
(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))