Average Error: 2.6 → 2.8
Time: 3.6s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 9.93766968672907486 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \sin y} \cdot y}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le 9.93766968672907486 \cdot 10^{-17}:\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot \sin y} \cdot y}\\

\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 ((y <= 9.937669686729075e-17)) {
		VAR = ((double) (((double) (x * ((double) (((double) sin(y)) * ((double) (1.0 / y)))))) / z));
	} else {
		VAR = ((double) (1.0 / ((double) (((double) (z / ((double) (x * ((double) sin(y)))))) * y))));
	}
	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

Original2.6
Target0.3
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 9.937669686729075e-17

    1. Initial program 1.7

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

    3. Applied div-inv1.8

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

    if 9.937669686729075e-17 < y

    1. Initial program 5.1

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

    3. Applied clear-num5.4

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

    5. Applied associate-*r/5.4

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

    6. Applied associate-/r/5.3

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{x \cdot \sin y} \cdot y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 9.93766968672907486 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \sin y} \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020121 
(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 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))