Average Error: 12.7 → 2.2
Time: 9.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.853087044714604902283876436567930648232 \cdot 10^{69} \lor \neg \left(x \le -1.963551869374391924457823240719085408452 \cdot 10^{-268}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.853087044714604902283876436567930648232 \cdot 10^{69} \lor \neg \left(x \le -1.963551869374391924457823240719085408452 \cdot 10^{-268}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r685875 = x;
        double r685876 = y;
        double r685877 = z;
        double r685878 = r685876 - r685877;
        double r685879 = r685875 * r685878;
        double r685880 = r685879 / r685876;
        return r685880;
}
↓
double f(double x, double y, double z) {
        double r685881 = x;
        double r685882 = -2.853087044714605e+69;
        bool r685883 = r685881 <= r685882;
        double r685884 = -1.963551869374392e-268;
        bool r685885 = r685881 <= r685884;
        double r685886 = !r685885;
        bool r685887 = r685883 || r685886;
        double r685888 = y;
        double r685889 = z;
        double r685890 = r685888 - r685889;
        double r685891 = r685888 / r685890;
        double r685892 = r685881 / r685891;
        double r685893 = r685881 / r685888;
        double r685894 = r685889 * r685893;
        double r685895 = r685881 - r685894;
        double r685896 = r685887 ? r685892 : r685895;
        return r685896;
}

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

Original12.7
Target2.9
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.853087044714605e+69 or -1.963551869374392e-268 < x

    1. Initial program 16.3

      \[\frac{x \cdot \left(y - z\right)}{y}\]
    2. Using strategy rm

    3. Applied associate-/l*2.5

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

    if -2.853087044714605e+69 < x < -1.963551869374392e-268

    1. Initial program 4.0

      \[\frac{x \cdot \left(y - z\right)}{y}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity4.0

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

    4. Applied times-frac4.5

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

    5. Simplified4.5

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

    6. Taylor expanded around 0 1.8

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

    7. Simplified1.6

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.853087044714604902283876436567930648232 \cdot 10^{69} \lor \neg \left(x \le -1.963551869374391924457823240719085408452 \cdot 10^{-268}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))