Average Error: 3.0 → 0.2
Time: 5.8s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -3.7814513636873637 \cdot 10^{-272} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 6.1789745427068699 \cdot 10^{-220}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{\sin y} \cdot \left(-z\right)}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -3.7814513636873637 \cdot 10^{-272} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 6.1789745427068699 \cdot 10^{-220}\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{-x}{\frac{y}{\sin y} \cdot \left(-z\right)}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((((double) (x * ((double) (((double) sin(y)) / y)))) <= -3.781451363687364e-272) || !(((double) (x * ((double) (((double) sin(y)) / y)))) <= 6.17897454270687e-220))) {
		VAR = ((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z));
	} else {
		VAR = ((double) (((double) -(x)) / ((double) (((double) (y / ((double) sin(y)))) * ((double) -(z))))));
	}
	return VAR;
}

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

Original3.0
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -3.781451363687364e-272 or 6.17897454270687e-220 < (* x (/ (sin y) y))

    1. Initial program 0.2

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

    if -3.781451363687364e-272 < (* x (/ (sin y) y)) < 6.17897454270687e-220

    1. Initial program 12.0

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

    3. Applied *-commutative12.0

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

    4. Applied associate-/l*0.4

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

    6. Applied clear-num0.4

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

    7. Applied associate-/r/0.2

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

    8. Simplified0.2

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

    10. Applied frac-2neg0.2

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

    11. Applied clear-num0.3

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

    12. Applied frac-times0.3

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

    13. Simplified0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -3.7814513636873637 \cdot 10^{-272} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 6.1789745427068699 \cdot 10^{-220}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{\sin y} \cdot \left(-z\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(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 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))