Average Error: 2.7 → 0.9
Time: 3.4s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -28100484199212.992:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{elif}\;z \leq 4.748493217637233 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -28100484199212.992:\\
\;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\

\mathbf{elif}\;z \leq 4.748493217637233 \cdot 10^{-12}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= z -28100484199212.992)
   (/ (/ (* x (sin y)) y) z)
   (if (<= z 4.748493217637233e-12)
     (/ x (/ z (/ (sin y) y)))
     (* (/ (sin y) y) (/ x z)))))
double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (z <= -28100484199212.992) {
		tmp = ((x * sin(y)) / y) / z;
	} else if (z <= 4.748493217637233e-12) {
		tmp = x / (z / (sin(y) / y));
	} else {
		tmp = (sin(y) / y) * (x / z);
	}
	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
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -28100484199212.992

    1. Initial program 0.1

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

    3. Applied associate-*r/_binary642.7

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

    if -28100484199212.992 < z < 4.748493217637233e-12

    1. Initial program 5.7

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

    3. Applied associate-/l*_binary640.2

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

    if 4.748493217637233e-12 < z

    1. Initial program 0.1

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

    3. Applied associate-/l*_binary644.7

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

    5. Applied associate-/r/_binary640.1

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -28100484199212.992:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{elif}\;z \leq 4.748493217637233 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020233 
(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))