Average Error: 2.9 → 0.9
Time: 9.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.6091788831885175 \cdot 10^{198}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} \cdot \sin y\right)}{z}\\ \mathbf{elif}\;z \le 8.27444862348079715 \cdot 10^{120}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.6091788831885175 \cdot 10^{198}:\\
\;\;\;\;\frac{x \cdot \left(\frac{1}{y} \cdot \sin y\right)}{z}\\

\mathbf{elif}\;z \le 8.27444862348079715 \cdot 10^{120}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r508883 = x;
        double r508884 = y;
        double r508885 = sin(r508884);
        double r508886 = r508885 / r508884;
        double r508887 = r508883 * r508886;
        double r508888 = z;
        double r508889 = r508887 / r508888;
        return r508889;
}
↓
double f(double x, double y, double z) {
        double r508890 = z;
        double r508891 = -6.609178883188517e+198;
        bool r508892 = r508890 <= r508891;
        double r508893 = x;
        double r508894 = 1.0;
        double r508895 = y;
        double r508896 = r508894 / r508895;
        double r508897 = sin(r508895);
        double r508898 = r508896 * r508897;
        double r508899 = r508893 * r508898;
        double r508900 = r508899 / r508890;
        double r508901 = 8.274448623480797e+120;
        bool r508902 = r508890 <= r508901;
        double r508903 = r508897 / r508895;
        double r508904 = r508890 / r508903;
        double r508905 = r508893 / r508904;
        double r508906 = r508895 / r508897;
        double r508907 = r508894 / r508906;
        double r508908 = r508893 * r508907;
        double r508909 = r508908 / r508890;
        double r508910 = r508902 ? r508905 : r508909;
        double r508911 = r508892 ? r508900 : r508910;
        return r508911;
}

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

Original2.9
Target0.2
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 3 regimes

  2. if z < -6.609178883188517e+198

    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 div-inv0.2

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

    6. Applied add-cube-cbrt0.2

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

    7. Applied times-frac0.1

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

    8. Simplified0.1

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

    9. Simplified0.1

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

    if -6.609178883188517e+198 < z < 8.274448623480797e+120

    1. Initial program 3.9

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

    3. Applied clear-num3.9

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

    5. Applied associate-/l*1.3

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

    6. Simplified1.2

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

    if 8.274448623480797e+120 < z

    1. Initial program 0.1

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

    3. Applied clear-num0.1

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.6091788831885175 \cdot 10^{198}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} \cdot \sin y\right)}{z}\\ \mathbf{elif}\;z \le 8.27444862348079715 \cdot 10^{120}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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))