Average Error: 12.4 → 3.1
Time: 2.4s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.2863222767697794 \cdot 10^{-106} \lor \neg \left(y \le 1.74861345841040224 \cdot 10^{-274}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.2863222767697794 \cdot 10^{-106} \lor \neg \left(y \le 1.74861345841040224 \cdot 10^{-274}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r787925 = x;
        double r787926 = y;
        double r787927 = z;
        double r787928 = r787926 - r787927;
        double r787929 = r787925 * r787928;
        double r787930 = r787929 / r787926;
        return r787930;
}
↓
double f(double x, double y, double z) {
        double r787931 = y;
        double r787932 = -1.2863222767697794e-106;
        bool r787933 = r787931 <= r787932;
        double r787934 = 1.7486134584104022e-274;
        bool r787935 = r787931 <= r787934;
        double r787936 = !r787935;
        bool r787937 = r787933 || r787936;
        double r787938 = x;
        double r787939 = z;
        double r787940 = r787931 - r787939;
        double r787941 = r787931 / r787940;
        double r787942 = r787938 / r787941;
        double r787943 = r787938 / r787931;
        double r787944 = r787943 * r787940;
        double r787945 = r787937 ? r787942 : r787944;
        return r787945;
}

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

Original12.4
Target3.2
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.2863222767697794e-106 or 1.7486134584104022e-274 < y

    1. Initial program 12.9

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

    3. Applied associate-/l*1.8

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

    if -1.2863222767697794e-106 < y < 1.7486134584104022e-274

    1. Initial program 9.5

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

    3. Applied associate-/l*10.9

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

    5. Applied associate-/r/10.7

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.2863222767697794 \cdot 10^{-106} \lor \neg \left(y \le 1.74861345841040224 \cdot 10^{-274}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +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))