Average Error: 2.7 → 0.3
Time: 7.5s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \leq -6.024516597309163 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{x}}}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{elif}\;\frac{x \cdot \frac{\sin y}{y}}{z} \leq 1.698103388791305 \cdot 10^{-21}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \leq -6.024516597309163 \cdot 10^{+61}:\\
\;\;\;\;\frac{\frac{1}{\frac{1}{x}}}{\frac{z}{\frac{\sin y}{y}}}\\

\mathbf{elif}\;\frac{x \cdot \frac{\sin y}{y}}{z} \leq 1.698103388791305 \cdot 10^{-21}:\\
\;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (/ (sin y) y)) z) -6.024516597309163e+61)
   (/ (/ 1.0 (/ 1.0 x)) (/ z (/ (sin y) y)))
   (if (<= (/ (* x (/ (sin y) y)) z) 1.698103388791305e-21)
     (* (/ (sin y) y) (/ x z))
     (/ (* x (/ (sin y) y)) z))))
double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (((x * (sin(y) / y)) / z) <= -6.024516597309163e+61) {
		tmp = (1.0 / (1.0 / x)) / (z / (sin(y) / y));
	} else if (((x * (sin(y) / y)) / z) <= 1.698103388791305e-21) {
		tmp = (sin(y) / y) * (x / z);
	} else {
		tmp = (x * (sin(y) / y)) / z;
	}
	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
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 (*.f64 x (/.f64 (sin.f64 y) y)) z) < -6.02451659730916294e61

    1. Initial program 0.2

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

    3. Applied clear-num_binary640.4

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

    4. Simplified2.0

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{x \cdot \sin y}{y}}}}\]
    5. Using strategy rm

    6. Applied *-un-lft-identity_binary642.0

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

    7. Applied times-frac_binary640.4

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

    8. Applied *-un-lft-identity_binary640.4

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

    9. Applied times-frac_binary640.4

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

    10. Applied associate-/r*_binary640.3

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

    if -6.02451659730916294e61 < (/.f64 (*.f64 x (/.f64 (sin.f64 y) y)) z) < 1.698103388791305e-21

    1. Initial program 3.8

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

    3. Applied clear-num_binary644.4

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

    4. Simplified10.4

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{x \cdot \sin y}{y}}}}\]
    5. Using strategy rm

    6. Applied *-un-lft-identity_binary6410.4

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

    7. Applied times-frac_binary644.4

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

    8. Applied associate-/r*_binary641.0

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

    9. Simplified1.0

      \[\leadsto \frac{1}{\frac{\color{blue}{\frac{z}{x}}}{\frac{\sin y}{y}}}\]
    10. Using strategy rm

    11. Applied div-inv_binary641.0

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

    12. Applied add-cube-cbrt_binary641.0

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{z}{x} \cdot \frac{1}{\frac{\sin y}{y}}}\]

    13. Applied times-frac_binary640.6

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{z}{x}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\frac{\sin y}{y}}}}\]

    14. Simplified0.3

      \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\frac{\sin y}{y}}}\]

    15. Simplified0.3

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

    if 1.698103388791305e-21 < (/.f64 (*.f64 x (/.f64 (sin.f64 y) y)) z)

    1. Initial program 0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \leq -6.024516597309163 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{1}{\frac{1}{x}}}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{elif}\;\frac{x \cdot \frac{\sin y}{y}}{z} \leq 1.698103388791305 \cdot 10^{-21}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021155 
(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))