Average Error: 2.6 → 0.3
Time: 15.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \cdot x \le -9.952501648391637084358678946699592551584 \cdot 10^{-273}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{elif}\;\frac{\sin y}{y} \cdot x \le -0.0:\\ \;\;\;\;\left(\frac{1}{z} \cdot \left(\sin y \cdot \frac{1}{y}\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\sin y}{y} \cdot x \le -9.952501648391637084358678946699592551584 \cdot 10^{-273}:\\
\;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\

\mathbf{elif}\;\frac{\sin y}{y} \cdot x \le -0.0:\\
\;\;\;\;\left(\frac{1}{z} \cdot \left(\sin y \cdot \frac{1}{y}\right)\right) \cdot x\\

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

\end{array}
double f(double x, double y, double z) {
        double r19366922 = x;
        double r19366923 = y;
        double r19366924 = sin(r19366923);
        double r19366925 = r19366924 / r19366923;
        double r19366926 = r19366922 * r19366925;
        double r19366927 = z;
        double r19366928 = r19366926 / r19366927;
        return r19366928;
}
↓
double f(double x, double y, double z) {
        double r19366929 = y;
        double r19366930 = sin(r19366929);
        double r19366931 = r19366930 / r19366929;
        double r19366932 = x;
        double r19366933 = r19366931 * r19366932;
        double r19366934 = -9.952501648391637e-273;
        bool r19366935 = r19366933 <= r19366934;
        double r19366936 = z;
        double r19366937 = r19366933 / r19366936;
        double r19366938 = -0.0;
        bool r19366939 = r19366933 <= r19366938;
        double r19366940 = 1.0;
        double r19366941 = r19366940 / r19366936;
        double r19366942 = r19366940 / r19366929;
        double r19366943 = r19366930 * r19366942;
        double r19366944 = r19366941 * r19366943;
        double r19366945 = r19366944 * r19366932;
        double r19366946 = r19366939 ? r19366945 : r19366937;
        double r19366947 = r19366935 ? r19366937 : r19366946;
        return r19366947;
}

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

Original2.6
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -9.952501648391637e-273 or -0.0 < (* x (/ (sin y) y))

    1. Initial program 0.3

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

    if -9.952501648391637e-273 < (* x (/ (sin y) y)) < -0.0

    1. Initial program 14.9

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

    3. Applied *-un-lft-identity14.9

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    7. Applied div-inv0.3

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

    9. Applied div-inv0.3

      \[\leadsto x \cdot \left(\color{blue}{\left(\sin y \cdot \frac{1}{y}\right)} \cdot \frac{1}{z}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \cdot x \le -9.952501648391637084358678946699592551584 \cdot 10^{-273}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{elif}\;\frac{\sin y}{y} \cdot x \le -0.0:\\ \;\;\;\;\left(\frac{1}{z} \cdot \left(\sin y \cdot \frac{1}{y}\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :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))