Average Error: 2.7 → 1.6
Time: 3.6s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.011301261708857 \cdot 10^{30}:\\ \;\;\;\;\left(x \cdot \frac{1}{\frac{y}{\sin y}}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.011301261708857 \cdot 10^{30}:\\
\;\;\;\;\left(x \cdot \frac{1}{\frac{y}{\sin y}}\right) \cdot \frac{1}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{y}{\sin 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 ((x <= -8.011301261708857e+30)) {
		VAR = ((double) (((double) (x * ((double) (1.0 / ((double) (y / ((double) sin(y)))))))) * ((double) (1.0 / z))));
	} else {
		VAR = ((double) (((double) (x / z)) / ((double) (y / ((double) sin(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

Original2.7
Target0.3
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -8.011301261708857e30

    1. Initial program 0.2

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

    3. Applied div-inv0.4

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

    5. Applied clear-num0.4

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

    if -8.011301261708857e30 < x

    1. Initial program 3.3

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

    3. Applied div-inv3.4

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

    5. Applied clear-num3.4

      \[\leadsto \left(x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\right) \cdot \frac{1}{z}\]
    6. Using strategy rm

    7. Applied un-div-inv3.4

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

    8. Applied associate-*l/2.1

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

    9. Simplified1.9

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.011301261708857 \cdot 10^{30}:\\ \;\;\;\;\left(x \cdot \frac{1}{\frac{y}{\sin y}}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y}{\sin y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(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))