Average Error: 2.7 → 0.7
Time: 4.5s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z} \]
↓
\[\begin{array}{l} t_0 := \frac{\sin y}{y}\\ t_1 := x \cdot t_0\\ \mathbf{if}\;t_1 \leq -3.4923241998744487 \cdot 10^{-11} \lor \neg \left(t_1 \leq 1.9458890264629313 \cdot 10^{-279}\right):\\ \;\;\;\;\frac{t_1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
t_0 := \frac{\sin y}{y}\\
t_1 := x \cdot t_0\\
\mathbf{if}\;t_1 \leq -3.4923241998744487 \cdot 10^{-11} \lor \neg \left(t_1 \leq 1.9458890264629313 \cdot 10^{-279}\right):\\
\;\;\;\;\frac{t_1}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{t_0}}\\


\end{array}

(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)) (t_1 (* x t_0)))
   (if (or (<= t_1 -3.4923241998744487e-11)
           (not (<= t_1 1.9458890264629313e-279)))
     (/ t_1 z)
     (/ x (/ z t_0)))))
double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / z;
}
↓
double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double t_1 = x * t_0;
	double tmp;
	if ((t_1 <= -3.4923241998744487e-11) || !(t_1 <= 1.9458890264629313e-279)) {
		tmp = t_1 / z;
	} else {
		tmp = x / (z / t_0);
	}
	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
Target0.3
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 (*.f64 x (/.f64 (sin.f64 y) y)) < -3.4923241998744487e-11 or 1.9458890264629313e-279 < (*.f64 x (/.f64 (sin.f64 y) y))

    1. Initial program 0.2

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

    3. Applied *-commutative_binary640.2

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

    if -3.4923241998744487e-11 < (*.f64 x (/.f64 (sin.f64 y) y)) < 1.9458890264629313e-279

    1. Initial program 6.1

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

    3. Applied associate-/l*_binary641.5

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -3.4923241998744487 \cdot 10^{-11} \lor \neg \left(x \cdot \frac{\sin y}{y} \leq 1.9458890264629313 \cdot 10^{-279}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array} \]

Reproduce

herbie shell --seed 2021207 
(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))