Average Error: 15.3 → 0.3
Time: 1.8s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.93403941868859091 \cdot 10^{-36} \lor \neg \left(y \le 1.19064852231214522 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.93403941868859091 \cdot 10^{-36} \lor \neg \left(y \le 1.19064852231214522 \cdot 10^{-72}\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 r562611 = x;
        double r562612 = 2.0;
        double r562613 = r562611 * r562612;
        double r562614 = y;
        double r562615 = r562613 * r562614;
        double r562616 = r562611 - r562614;
        double r562617 = r562615 / r562616;
        return r562617;
}
↓
double f(double x, double y) {
        double r562618 = y;
        double r562619 = -1.934039418688591e-36;
        bool r562620 = r562618 <= r562619;
        double r562621 = 1.1906485223121452e-72;
        bool r562622 = r562618 <= r562621;
        double r562623 = !r562622;
        bool r562624 = r562620 || r562623;
        double r562625 = x;
        double r562626 = 2.0;
        double r562627 = r562625 * r562626;
        double r562628 = r562625 - r562618;
        double r562629 = r562628 / r562618;
        double r562630 = r562627 / r562629;
        double r562631 = r562627 / r562628;
        double r562632 = r562631 * r562618;
        double r562633 = r562624 ? r562630 : r562632;
        return r562633;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.3
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.934039418688591e-36 or 1.1906485223121452e-72 < y

    1. Initial program 14.4

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

    3. Applied associate-/l*0.4

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

    if -1.934039418688591e-36 < y < 1.1906485223121452e-72

    1. Initial program 16.6

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

    3. Applied associate-/l*17.8

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

    5. Applied associate-/r/0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.93403941868859091 \cdot 10^{-36} \lor \neg \left(y \le 1.19064852231214522 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +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)))