Average Error: 12.8 → 3.0
Time: 2.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.02408268665799122 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le -1.59358918894430206 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.02408268665799122 \cdot 10^{-160}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;y \le -1.59358918894430206 \cdot 10^{-289}:\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r746098 = x;
        double r746099 = y;
        double r746100 = z;
        double r746101 = r746099 - r746100;
        double r746102 = r746098 * r746101;
        double r746103 = r746102 / r746099;
        return r746103;
}
↓
double f(double x, double y, double z) {
        double r746104 = y;
        double r746105 = -2.0240826866579912e-160;
        bool r746106 = r746104 <= r746105;
        double r746107 = x;
        double r746108 = z;
        double r746109 = r746104 - r746108;
        double r746110 = r746109 / r746104;
        double r746111 = r746107 * r746110;
        double r746112 = -1.593589188944302e-289;
        bool r746113 = r746104 <= r746112;
        double r746114 = r746107 / r746104;
        double r746115 = r746114 * r746109;
        double r746116 = r746104 / r746109;
        double r746117 = r746107 / r746116;
        double r746118 = r746113 ? r746115 : r746117;
        double r746119 = r746106 ? r746111 : r746118;
        return r746119;
}

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
Target3.4
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -2.0240826866579912e-160

    1. Initial program 12.8

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

    3. Applied *-un-lft-identity12.8

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

    4. Applied times-frac1.3

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

    5. Simplified1.3

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

    if -2.0240826866579912e-160 < y < -1.593589188944302e-289

    1. Initial program 10.8

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

    3. Applied associate-/l*11.7

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

    5. Applied associate-/r/10.2

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

    if -1.593589188944302e-289 < y

    1. Initial program 13.1

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

    3. Applied associate-/l*3.3

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.02408268665799122 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;y \le -1.59358918894430206 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :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))