Average Error: 2.9 → 0.2
Time: 5.4s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.579176583523817341408656991031950031801 \cdot 10^{-58} \lor \neg \left(z \le 14047118970.9252910614013671875\right):\\ \;\;\;\;\frac{x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.579176583523817341408656991031950031801 \cdot 10^{-58} \lor \neg \left(z \le 14047118970.9252910614013671875\right):\\
\;\;\;\;\frac{x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r587254 = x;
        double r587255 = y;
        double r587256 = sin(r587255);
        double r587257 = r587256 / r587255;
        double r587258 = r587254 * r587257;
        double r587259 = z;
        double r587260 = r587258 / r587259;
        return r587260;
}
↓
double f(double x, double y, double z) {
        double r587261 = z;
        double r587262 = -1.5791765835238173e-58;
        bool r587263 = r587261 <= r587262;
        double r587264 = 14047118970.925291;
        bool r587265 = r587261 <= r587264;
        double r587266 = !r587265;
        bool r587267 = r587263 || r587266;
        double r587268 = x;
        double r587269 = 1.0;
        double r587270 = y;
        double r587271 = r587269 / r587270;
        double r587272 = sin(r587270);
        double r587273 = r587269 / r587272;
        double r587274 = r587271 / r587273;
        double r587275 = r587268 * r587274;
        double r587276 = r587275 / r587261;
        double r587277 = r587272 / r587270;
        double r587278 = r587261 / r587277;
        double r587279 = r587268 / r587278;
        double r587280 = r587267 ? r587276 : r587279;
        return r587280;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -1.5791765835238173e-58 or 14047118970.925291 < z

    1. Initial program 0.2

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

    3. Applied clear-num0.2

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

    5. Applied div-inv0.3

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

    6. Applied associate-/r*0.2

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

    if -1.5791765835238173e-58 < z < 14047118970.925291

    1. Initial program 6.6

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

    3. Applied associate-/l*0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.579176583523817341408656991031950031801 \cdot 10^{-58} \lor \neg \left(z \le 14047118970.9252910614013671875\right):\\ \;\;\;\;\frac{x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))