Average Error: 2.8 → 0.8
Time: 17.9s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -140933690204890492166891680825344:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{elif}\;z \le 1.663038927321811361009908848030056352037 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{z \cdot \frac{1}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -140933690204890492166891680825344:\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\mathbf{elif}\;z \le 1.663038927321811361009908848030056352037 \cdot 10^{-155}:\\
\;\;\;\;\frac{x}{z \cdot \frac{1}{\frac{\sin y}{y}}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r309236 = x;
        double r309237 = y;
        double r309238 = sin(r309237);
        double r309239 = r309238 / r309237;
        double r309240 = r309236 * r309239;
        double r309241 = z;
        double r309242 = r309240 / r309241;
        return r309242;
}
↓
double f(double x, double y, double z) {
        double r309243 = z;
        double r309244 = -1.409336902048905e+32;
        bool r309245 = r309243 <= r309244;
        double r309246 = x;
        double r309247 = y;
        double r309248 = sin(r309247);
        double r309249 = r309248 / r309247;
        double r309250 = r309246 * r309249;
        double r309251 = r309250 / r309243;
        double r309252 = 1.6630389273218114e-155;
        bool r309253 = r309243 <= r309252;
        double r309254 = 1.0;
        double r309255 = r309254 / r309249;
        double r309256 = r309243 * r309255;
        double r309257 = r309246 / r309256;
        double r309258 = r309246 / r309243;
        double r309259 = r309258 / r309255;
        double r309260 = r309253 ? r309257 : r309259;
        double r309261 = r309245 ? r309251 : r309260;
        return r309261;
}

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

Original2.8
Target0.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.409336902048905e+32

    1. Initial program 0.1

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

    if -1.409336902048905e+32 < z < 1.6630389273218114e-155

    1. Initial program 6.6

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

    3. Applied associate-/l*0.4

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

    4. Simplified0.4

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

    6. Applied clear-num0.4

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

    if 1.6630389273218114e-155 < z

    1. Initial program 1.2

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

    3. Applied associate-/l*3.8

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

    4. Simplified3.8

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

    6. Applied clear-num3.8

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

    8. Applied associate-/r*1.5

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -140933690204890492166891680825344:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{elif}\;z \le 1.663038927321811361009908848030056352037 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{z \cdot \frac{1}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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))