Average Error: 3.0 → 0.8
Time: 4.5s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.1728892342568057 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{elif}\;z \le 1.32101974044890363 \cdot 10^{187}:\\ \;\;\;\;\frac{x \cdot 1}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.1728892342568057 \cdot 10^{-27}:\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

\mathbf{elif}\;z \le 1.32101974044890363 \cdot 10^{187}:\\
\;\;\;\;\frac{x \cdot 1}{z \cdot \frac{y}{\sin y}}\\

\mathbf{else}:\\
\;\;\;\;{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r572870 = x;
        double r572871 = y;
        double r572872 = sin(r572871);
        double r572873 = r572872 / r572871;
        double r572874 = r572870 * r572873;
        double r572875 = z;
        double r572876 = r572874 / r572875;
        return r572876;
}
↓
double f(double x, double y, double z) {
        double r572877 = z;
        double r572878 = -1.1728892342568057e-27;
        bool r572879 = r572877 <= r572878;
        double r572880 = x;
        double r572881 = y;
        double r572882 = sin(r572881);
        double r572883 = 1.0;
        double r572884 = r572883 / r572881;
        double r572885 = r572882 * r572884;
        double r572886 = r572880 * r572885;
        double r572887 = r572886 / r572877;
        double r572888 = 1.3210197404489036e+187;
        bool r572889 = r572877 <= r572888;
        double r572890 = r572880 * r572883;
        double r572891 = r572881 / r572882;
        double r572892 = r572877 * r572891;
        double r572893 = r572890 / r572892;
        double r572894 = r572880 / r572891;
        double r572895 = pow(r572894, r572883);
        double r572896 = r572883 / r572877;
        double r572897 = r572895 * r572896;
        double r572898 = r572889 ? r572893 : r572897;
        double r572899 = r572879 ? r572887 : r572898;
        return r572899;
}

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
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.1728892342568057e-27

    1. Initial program 0.2

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

    3. Applied div-inv0.3

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

    if -1.1728892342568057e-27 < z < 1.3210197404489036e+187

    1. Initial program 4.8

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

    3. Applied clear-num4.9

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

    5. Applied associate-*r/4.8

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

    6. Applied associate-/l/1.1

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

    if 1.3210197404489036e+187 < z

    1. Initial program 0.1

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

    3. Applied clear-num0.1

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

    5. Applied pow10.1

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

    6. Applied pow10.1

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

    7. Applied pow-prod-down0.1

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

    8. Simplified0.1

      \[\leadsto \frac{{\color{blue}{\left(\frac{x}{\frac{y}{\sin y}}\right)}}^{1}}{z}\]
    9. Using strategy rm

    10. Applied div-inv0.2

      \[\leadsto \color{blue}{{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.1728892342568057 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{elif}\;z \le 1.32101974044890363 \cdot 10^{187}:\\ \;\;\;\;\frac{x \cdot 1}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x}{\frac{y}{\sin y}}\right)}^{1} \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 
(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))