Average Error: 12.5 → 2.9
Time: 13.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7.987697433686588590285611969201440389173 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;x \le 1.318326588609397900170163534445278958933 \cdot 10^{-303}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -7.987697433686588590285611969201440389173 \cdot 10^{-172}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;x \le 1.318326588609397900170163534445278958933 \cdot 10^{-303}:\\
\;\;\;\;x - \frac{z \cdot x}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r37454689 = x;
        double r37454690 = y;
        double r37454691 = z;
        double r37454692 = r37454690 - r37454691;
        double r37454693 = r37454689 * r37454692;
        double r37454694 = r37454693 / r37454690;
        return r37454694;
}
↓
double f(double x, double y, double z) {
        double r37454695 = x;
        double r37454696 = -7.987697433686589e-172;
        bool r37454697 = r37454695 <= r37454696;
        double r37454698 = y;
        double r37454699 = z;
        double r37454700 = r37454698 - r37454699;
        double r37454701 = r37454700 / r37454698;
        double r37454702 = r37454695 * r37454701;
        double r37454703 = 1.3183265886093979e-303;
        bool r37454704 = r37454695 <= r37454703;
        double r37454705 = r37454699 * r37454695;
        double r37454706 = r37454705 / r37454698;
        double r37454707 = r37454695 - r37454706;
        double r37454708 = r37454698 / r37454700;
        double r37454709 = r37454695 / r37454708;
        double r37454710 = r37454704 ? r37454707 : r37454709;
        double r37454711 = r37454697 ? r37454702 : r37454710;
        return r37454711;
}

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

Original12.5
Target2.9
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -7.987697433686589e-172

    1. Initial program 14.3

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

    3. Applied *-un-lft-identity14.3

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

    4. Applied times-frac1.8

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

    5. Simplified1.8

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

    if -7.987697433686589e-172 < x < 1.3183265886093979e-303

    1. Initial program 8.3

      \[\frac{x \cdot \left(y - z\right)}{y}\]

    2. Taylor expanded around 0 4.9

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

    if 1.3183265886093979e-303 < x

    1. Initial program 12.3

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

    3. Applied associate-/l*3.1

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7.987697433686588590285611969201440389173 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;x \le 1.318326588609397900170163534445278958933 \cdot 10^{-303}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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))