Average Error: 12.8 → 3.0
Time: 9.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.903569732992712809241890778232907235744 \cdot 10^{-201} \lor \neg \left(y \le 1.727845853063427358970787003444816519654 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.903569732992712809241890778232907235744 \cdot 10^{-201} \lor \neg \left(y \le 1.727845853063427358970787003444816519654 \cdot 10^{-151}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\end{array}
double f(double x, double y, double z) {
        double r539895 = x;
        double r539896 = y;
        double r539897 = z;
        double r539898 = r539896 - r539897;
        double r539899 = r539895 * r539898;
        double r539900 = r539899 / r539896;
        return r539900;
}
↓
double f(double x, double y, double z) {
        double r539901 = y;
        double r539902 = -4.903569732992713e-201;
        bool r539903 = r539901 <= r539902;
        double r539904 = 1.7278458530634274e-151;
        bool r539905 = r539901 <= r539904;
        double r539906 = !r539905;
        bool r539907 = r539903 || r539906;
        double r539908 = x;
        double r539909 = z;
        double r539910 = r539901 - r539909;
        double r539911 = r539901 / r539910;
        double r539912 = r539908 / r539911;
        double r539913 = r539908 * r539910;
        double r539914 = r539913 / r539901;
        double r539915 = r539907 ? r539912 : r539914;
        return r539915;
}

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

Original12.8
Target3.2
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.903569732992713e-201 or 1.7278458530634274e-151 < y

    1. Initial program 13.0

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

    3. Applied associate-/l*1.4

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

    if -4.903569732992713e-201 < y < 1.7278458530634274e-151

    1. Initial program 11.9

      \[\frac{x \cdot \left(y - z\right)}{y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.903569732992712809241890778232907235744 \cdot 10^{-201} \lor \neg \left(y \le 1.727845853063427358970787003444816519654 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(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))