Average Error: 2.6 → 0.3
Time: 48.7s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.9751805342320895 \cdot 10^{-52} \lor \neg \left(z \le 60113221.3286090866\right):\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{\frac{\sin y}{y}}}{x}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.9751805342320895 \cdot 10^{-52} \lor \neg \left(z \le 60113221.3286090866\right):\\
\;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r288163 = x;
        double r288164 = y;
        double r288165 = sin(r288164);
        double r288166 = r288165 / r288164;
        double r288167 = r288163 * r288166;
        double r288168 = z;
        double r288169 = r288167 / r288168;
        return r288169;
}
↓
double f(double x, double y, double z) {
        double r288170 = z;
        double r288171 = -2.9751805342320895e-52;
        bool r288172 = r288170 <= r288171;
        double r288173 = 60113221.32860909;
        bool r288174 = r288170 <= r288173;
        double r288175 = !r288174;
        bool r288176 = r288172 || r288175;
        double r288177 = y;
        double r288178 = sin(r288177);
        double r288179 = r288178 / r288177;
        double r288180 = x;
        double r288181 = r288179 * r288180;
        double r288182 = r288181 / r288170;
        double r288183 = 1.0;
        double r288184 = r288170 / r288179;
        double r288185 = r288184 / r288180;
        double r288186 = r288183 / r288185;
        double r288187 = r288176 ? r288182 : r288186;
        return r288187;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -2.9751805342320895e-52 or 60113221.32860909 < z

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    5. Applied *-un-lft-identity0.2

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

    6. Applied associate-*l*0.2

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

    7. Simplified0.1

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

    if -2.9751805342320895e-52 < z < 60113221.32860909

    1. Initial program 6.0

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

    3. Applied div-inv6.1

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

    5. Applied clear-num6.2

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

    6. Simplified0.5

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.9751805342320895 \cdot 10^{-52} \lor \neg \left(z \le 60113221.3286090866\right):\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{\frac{\sin y}{y}}}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 +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))