Average Error: 12.7 → 2.2
Time: 9.2s
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 r669597 = x;
        double r669598 = y;
        double r669599 = z;
        double r669600 = r669598 - r669599;
        double r669601 = r669597 * r669600;
        double r669602 = r669601 / r669598;
        return r669602;
}
↓
double f(double x, double y, double z) {
        double r669603 = x;
        double r669604 = -2.853087044714605e+69;
        bool r669605 = r669603 <= r669604;
        double r669606 = -1.963551869374392e-268;
        bool r669607 = r669603 <= r669606;
        double r669608 = !r669607;
        bool r669609 = r669605 || r669608;
        double r669610 = y;
        double r669611 = z;
        double r669612 = r669610 - r669611;
        double r669613 = r669610 / r669612;
        double r669614 = r669603 / r669613;
        double r669615 = r669603 / r669610;
        double r669616 = r669611 * r669615;
        double r669617 = r669603 - r669616;
        double r669618 = r669609 ? r669614 : r669617;
        return r669618;
}

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))