Average Error: 2.5 → 0.3
Time: 4.6s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z} \]
↓
\[\begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;x \leq -4.016258732507709 \cdot 10^{+34} \lor \neg \left(x \leq 1.339412821928085 \cdot 10^{-116}\right):\\ \;\;\;\;\frac{x \cdot t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
t_0 := \frac{\sin y}{y}\\
\mathbf{if}\;x \leq -4.016258732507709 \cdot 10^{+34} \lor \neg \left(x \leq 1.339412821928085 \cdot 10^{-116}\right):\\
\;\;\;\;\frac{x \cdot t_0}{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)))
   (if (or (<= x -4.016258732507709e+34) (not (<= x 1.339412821928085e-116)))
     (/ (* x t_0) 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 tmp;
	if ((x <= -4.016258732507709e+34) || !(x <= 1.339412821928085e-116)) {
		tmp = (x * t_0) / 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

Original2.5
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if x < -4.01625873250770897e34 or 1.3394128219280849e-116 < x

    1. Initial program 0.5

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

    2. Applied *-un-lft-identity_binary640.5

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

    3. Applied *-un-lft-identity_binary640.5

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

    4. Applied times-frac_binary640.5

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{1} \cdot \frac{\sin y}{y}\right)}}{z} \]

    5. Simplified0.5

      \[\leadsto \frac{x \cdot \left(\color{blue}{1} \cdot \frac{\sin y}{y}\right)}{z} \]

    if -4.01625873250770897e34 < x < 1.3394128219280849e-116

    1. Initial program 5.0

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

    2. Applied associate-/l*_binary640.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.016258732507709 \cdot 10^{+34} \lor \neg \left(x \leq 1.339412821928085 \cdot 10^{-116}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022088 
(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))