Average Error: 2.6 → 0.5
Time: 3.5s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -1.0256658177533403 \cdot 10^{-39} \lor \neg \left(x \leq 1.0187343895406232 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot \frac{y}{\sin y}}{x}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -1.0256658177533403 \cdot 10^{-39} \lor \neg \left(x \leq 1.0187343895406232 \cdot 10^{-25}\right):\\
\;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.0256658177533403e-39) (not (<= x 1.0187343895406232e-25)))
   (/ (/ (* x (sin y)) y) z)
   (/ 1.0 (/ (* z (/ y (sin y))) x))))
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 ((x <= -1.0256658177533403e-39) || !(x <= 1.0187343895406232e-25)) {
		tmp = ((x * sin(y)) / y) / z;
	} else {
		tmp = 1.0 / ((z * (y / sin(y))) / x);
	}
	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
Target0.3
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.0256658177533403e-39 or 1.01873438954062316e-25 < x

    1. Initial program 0.2

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

    3. Applied associate-*r/_binary640.4

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

    if -1.0256658177533403e-39 < x < 1.01873438954062316e-25

    1. Initial program 5.1

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

    3. Applied clear-num_binary645.5

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

    5. Applied div-inv_binary646.0

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

    6. Simplified6.0

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

    8. Applied associate-*r/_binary640.8

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.0256658177533403 \cdot 10^{-39} \lor \neg \left(x \leq 1.0187343895406232 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z \cdot \frac{y}{\sin y}}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020224 
(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))