Average Error: 2.5 → 2.6
Time: 7.4s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \le -4.8358356144772814 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{z}}{y}\\ \mathbf{elif}\;\frac{\sin y}{y} \le 4.8956053390658603 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{1}{\frac{y}{\sin y}}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\sin y}{y} \le -4.8358356144772814 \cdot 10^{-280}:\\
\;\;\;\;x \cdot \frac{\frac{\sin y}{z}}{y}\\

\mathbf{elif}\;\frac{\sin y}{y} \le 4.8956053390658603 \cdot 10^{-95}:\\
\;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((x * (sin(y) / y)) / z);
}
↓
double code(double x, double y, double z) {
	double temp;
	if (((sin(y) / y) <= -4.835835614477281e-280)) {
		temp = (x * ((sin(y) / z) / y));
	} else {
		double temp_1;
		if (((sin(y) / y) <= 4.89560533906586e-95)) {
			temp_1 = (((x * sin(y)) / y) / z);
		} else {
			temp_1 = (x / (z / (1.0 / (y / sin(y)))));
		}
		temp = temp_1;
	}
	return temp;
}

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

Original2.5
Target0.3
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (sin y) y) < -4.835835614477281e-280

    1. Initial program 4.3

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

    3. Applied associate-/l*4.9

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

    5. Applied div-inv5.0

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

    6. Simplified4.4

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

    if -4.835835614477281e-280 < (/ (sin y) y) < 4.89560533906586e-95

    1. Initial program 6.1

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

    3. Applied associate-*r/6.2

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

    if 4.89560533906586e-95 < (/ (sin y) y)

    1. Initial program 0.3

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

    3. Applied associate-/l*0.4

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

    5. Applied clear-num0.4

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \le -4.8358356144772814 \cdot 10^{-280}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{z}}{y}\\ \mathbf{elif}\;\frac{\sin y}{y} \le 4.8956053390658603 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{1}{\frac{y}{\sin y}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(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))