Average Error: 15.5 → 0.2
Time: 2.0s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.5251409834127483 \cdot 10^{52} \lor \neg \left(y \le 1.226684745187438 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.5251409834127483 \cdot 10^{52} \lor \neg \left(y \le 1.226684745187438 \cdot 10^{-25}\right):\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\

\end{array}
double f(double x, double y) {
        double r479355 = x;
        double r479356 = 2.0;
        double r479357 = r479355 * r479356;
        double r479358 = y;
        double r479359 = r479357 * r479358;
        double r479360 = r479355 - r479358;
        double r479361 = r479359 / r479360;
        return r479361;
}
↓
double f(double x, double y) {
        double r479362 = y;
        double r479363 = -2.5251409834127483e+52;
        bool r479364 = r479362 <= r479363;
        double r479365 = 1.226684745187438e-25;
        bool r479366 = r479362 <= r479365;
        double r479367 = !r479366;
        bool r479368 = r479364 || r479367;
        double r479369 = x;
        double r479370 = 2.0;
        double r479371 = r479369 * r479370;
        double r479372 = r479369 - r479362;
        double r479373 = r479372 / r479362;
        double r479374 = r479371 / r479373;
        double r479375 = r479371 / r479372;
        double r479376 = r479375 * r479362;
        double r479377 = r479368 ? r479374 : r479376;
        return r479377;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.5
Target0.4
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.5251409834127483e+52 or 1.226684745187438e-25 < y

    1. Initial program 17.4

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

    3. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]

    if -2.5251409834127483e+52 < y < 1.226684745187438e-25

    1. Initial program 13.7

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

    3. Applied associate-/l*14.3

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.5251409834127483 \cdot 10^{52} \lor \neg \left(y \le 1.226684745187438 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

  (/ (* (* x 2) y) (- x y)))