Average Error: 12.4 → 3.0
Time: 2.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1071459700543.7744 \lor \neg \left(y \le -4.37709134363842535 \cdot 10^{-213}\right):\\ \;\;\;\;\frac{x}{{\left(\frac{y}{y - z}\right)}^{1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1071459700543.7744 \lor \neg \left(y \le -4.37709134363842535 \cdot 10^{-213}\right):\\
\;\;\;\;\frac{x}{{\left(\frac{y}{y - z}\right)}^{1}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r726835 = x;
        double r726836 = y;
        double r726837 = z;
        double r726838 = r726836 - r726837;
        double r726839 = r726835 * r726838;
        double r726840 = r726839 / r726836;
        return r726840;
}
↓
double f(double x, double y, double z) {
        double r726841 = y;
        double r726842 = -1071459700543.7744;
        bool r726843 = r726841 <= r726842;
        double r726844 = -4.3770913436384254e-213;
        bool r726845 = r726841 <= r726844;
        double r726846 = !r726845;
        bool r726847 = r726843 || r726846;
        double r726848 = x;
        double r726849 = z;
        double r726850 = r726841 - r726849;
        double r726851 = r726841 / r726850;
        double r726852 = 1.0;
        double r726853 = pow(r726851, r726852);
        double r726854 = r726848 / r726853;
        double r726855 = r726848 / r726841;
        double r726856 = r726855 * r726850;
        double r726857 = r726847 ? r726854 : r726856;
        return r726857;
}

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
Target3.0
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 2 regimes

  2. if y < -1071459700543.7744 or -4.3770913436384254e-213 < y

    1. Initial program 14.2

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

    3. Applied associate-/l*2.6

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

    5. Applied pow12.6

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

    if -1071459700543.7744 < y < -4.3770913436384254e-213

    1. Initial program 3.5

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

    3. Applied associate-/l*5.9

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

    5. Applied associate-/r/5.0

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

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1071459700543.7744 \lor \neg \left(y \le -4.37709134363842535 \cdot 10^{-213}\right):\\ \;\;\;\;\frac{x}{{\left(\frac{y}{y - z}\right)}^{1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +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))