Average Error: 2.9 → 0.7
Time: 4.1s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z} \]
↓
\[\begin{array}{l} t_0 := \frac{\sin y}{y}\\ t_1 := \frac{x \cdot t_0}{z}\\ \mathbf{if}\;x \leq -2.0065446232001473 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.135949926575344 \cdot 10^{-59}:\\ \;\;\;\;t_0 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
t_0 := \frac{\sin y}{y}\\
t_1 := \frac{x \cdot t_0}{z}\\
\mathbf{if}\;x \leq -2.0065446232001473 \cdot 10^{+165}:\\
\;\;\;\;t_1\\

\mathbf{elif}\;x \leq 6.135949926575344 \cdot 10^{-59}:\\
\;\;\;\;t_0 \cdot \frac{x}{z}\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\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) z)))
   (if (<= x -2.0065446232001473e+165)
     t_1
     (if (<= x 6.135949926575344e-59) (* t_0 (/ x z)) t_1))))
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) / z;
	double tmp;
	if (x <= -2.0065446232001473e+165) {
		tmp = t_1;
	} else if (x <= 6.135949926575344e-59) {
		tmp = t_0 * (x / z);
	} else {
		tmp = t_1;
	}
	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

Original2.9
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 x < -2.0065446232001473e165 or 6.13594992657534381e-59 < x

    1. Initial program 0.3

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]

    if -2.0065446232001473e165 < x < 6.13594992657534381e-59

    1. Initial program 4.5

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]

    2. Applied egg-rr1.0

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.0065446232001473 \cdot 10^{+165}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{elif}\;x \leq 6.135949926575344 \cdot 10^{-59}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array} \]

Reproduce

herbie shell --seed 2022130 
(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))