Average Error: 13.0 → 3.5
Time: 2.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.666543304720725 \cdot 10^{104} \lor \neg \left(z \le 2.45560343256893582 \cdot 10^{-35}\right):\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.666543304720725 \cdot 10^{104} \lor \neg \left(z \le 2.45560343256893582 \cdot 10^{-35}\right):\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r738781 = x;
        double r738782 = y;
        double r738783 = z;
        double r738784 = r738782 - r738783;
        double r738785 = r738781 * r738784;
        double r738786 = r738785 / r738782;
        return r738786;
}
↓
double f(double x, double y, double z) {
        double r738787 = z;
        double r738788 = -2.666543304720725e+104;
        bool r738789 = r738787 <= r738788;
        double r738790 = 2.455603432568936e-35;
        bool r738791 = r738787 <= r738790;
        double r738792 = !r738791;
        bool r738793 = r738789 || r738792;
        double r738794 = x;
        double r738795 = r738794 * r738787;
        double r738796 = y;
        double r738797 = r738795 / r738796;
        double r738798 = r738794 - r738797;
        double r738799 = r738787 / r738796;
        double r738800 = r738794 * r738799;
        double r738801 = r738794 - r738800;
        double r738802 = r738793 ? r738798 : r738801;
        return r738802;
}

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

Original13.0
Target3.5
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.666543304720725e+104 or 2.455603432568936e-35 < z

    1. Initial program 12.1

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

    3. Applied associate-/l*8.0

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

    4. Taylor expanded around 0 8.7

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

    if -2.666543304720725e+104 < z < 2.455603432568936e-35

    1. Initial program 13.5

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

    3. Applied associate-/l*0.4

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

    4. Taylor expanded around 0 2.9

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

    6. Applied *-un-lft-identity2.9

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

    7. Applied times-frac0.4

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

    8. Simplified0.4

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.666543304720725 \cdot 10^{104} \lor \neg \left(z \le 2.45560343256893582 \cdot 10^{-35}\right):\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 +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))