Average Error: 2.7 → 0.9
Time: 3.9s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -7.501794388521635 \cdot 10^{67} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le 6.13088843254250892 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{z}}{y}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -7.501794388521635 \cdot 10^{67} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le 6.13088843254250892 \cdot 10^{-167}\right):\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

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

\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) (((double) (x * ((double) (((double) sin(y)) / y)))) / z)) <= -7.501794388521635e+67) || !(((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z)) <= 6.130888432542509e-167))) {
		VAR = ((double) (x / ((double) (z / ((double) (((double) sin(y)) / y))))));
	} else {
		VAR = ((double) (((double) sin(y)) * ((double) (((double) (x / z)) / y))));
	}
	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

Original2.7
Target0.3
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (/ (sin y) y)) z) < -7.501794388521635e67 or 6.13088843254250892e-167 < (/ (* x (/ (sin y) y)) z)

    1. Initial program 0.4

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

    3. Applied associate-/l*1.4

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

    if -7.501794388521635e67 < (/ (* x (/ (sin y) y)) z) < 6.13088843254250892e-167

    1. Initial program 4.4

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

    3. Applied associate-/l*4.5

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

    5. Applied div-inv4.5

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

    6. Applied *-un-lft-identity4.5

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

    7. Applied times-frac6.4

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

    8. Applied *-un-lft-identity6.4

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

    9. Applied times-frac6.7

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

    10. Simplified6.7

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

    11. Simplified0.6

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -7.501794388521635 \cdot 10^{67} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le 6.13088843254250892 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{z}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020149 
(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))