Average Error: 2.6 → 0.7
Time: 3.8s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -7.86796053966447 \cdot 10^{+81} \lor \neg \left(z \leq 1.5296300629480374 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{z}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -7.86796053966447 \cdot 10^{+81} \lor \neg \left(z \leq 1.5296300629480374 \cdot 10^{-87}\right):\\
\;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.86796053966447e+81) (not (<= z 1.5296300629480374e-87)))
   (/ (/ x (/ y (sin y))) z)
   (/ x (* y (/ z (sin y))))))
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 (((z <= -7.86796053966447e+81) || !(z <= 1.5296300629480374e-87))) {
		tmp = ((x / (y / ((double) sin(y)))) / z);
	} else {
		tmp = (x / ((double) (y * (z / ((double) sin(y))))));
	}
	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

Original2.6
Target0.2
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.8679605396644699e81 or 1.52963006294803742e-87 < z

    1. Initial program Error: 0.4 bits

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

    3. Applied clear-numError: 0.4 bits

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

    5. Applied un-div-invError: 0.4 bits

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

    if -7.8679605396644699e81 < z < 1.52963006294803742e-87

    1. Initial program Error: 5.3 bits

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

    3. Applied associate-/l*Error: 0.5 bits

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

    4. SimplifiedError: 1.1 bits

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

  4. Final simplificationError: 0.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.86796053966447 \cdot 10^{+81} \lor \neg \left(z \leq 1.5296300629480374 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{z}{\sin y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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))