Average Error: 2.7 → 0.8
Time: 5.6s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -1.0705577612094227 \cdot 10^{-168}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \cdot \frac{\sin y}{y} \leq 5.233769824510889 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -1.0705577612094227 \cdot 10^{-168}:\\
\;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\

\mathbf{elif}\;x \cdot \frac{\sin y}{y} \leq 5.233769824510889 \cdot 10^{-23}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x \cdot \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)) -1.0705577612094227e-168)
   (/ (* x (/ 1.0 (/ y (sin y)))) z)
   (if (<= (* x (/ (sin y) y)) 5.233769824510889e-23)
     (/ x (/ z (/ (sin y) y)))
     (/ (/ (* x (sin y)) y) z))))
double code(double x, double y, double z) {
	return (((double) (x * (((double) sin(y)) / y))) / z);
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((((double) (x * (((double) sin(y)) / y))) <= -1.0705577612094227e-168)) {
		tmp = (((double) (x * (1.0 / (y / ((double) sin(y)))))) / z);
	} else {
		double tmp_1;
		if ((((double) (x * (((double) sin(y)) / y))) <= 5.233769824510889e-23)) {
			tmp_1 = (x / (z / (((double) sin(y)) / y)));
		} else {
			tmp_1 = ((((double) (x * ((double) sin(y)))) / y) / z);
		}
		tmp = tmp_1;
	}
	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
Target0.2
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 x (/.f64 (sin.f64 y) y)) < -1.07055776120942271e-168

    1. Initial program 0.2

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

    3. Applied clear-num_binary640.2

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

    if -1.07055776120942271e-168 < (*.f64 x (/.f64 (sin.f64 y) y)) < 5.2337698245108889e-23

    1. Initial program 5.1

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

    3. Applied associate-/l*_binary641.4

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

    if 5.2337698245108889e-23 < (*.f64 x (/.f64 (sin.f64 y) y))

    1. Initial program 0.2

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

    3. Applied associate-*r/_binary640.2

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -1.0705577612094227 \cdot 10^{-168}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \cdot \frac{\sin y}{y} \leq 5.233769824510889 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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))