Average Error: 14.7 → 0.4
Time: 4.2s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.8379060927151348 \cdot 10^{37} \lor \neg \left(y \le 2.53558016914647718 \cdot 10^{-106}\right):\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.8379060927151348 \cdot 10^{37} \lor \neg \left(y \le 2.53558016914647718 \cdot 10^{-106}\right):\\
\;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\

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

\end{array}
double f(double x, double y) {
        double r519957 = x;
        double r519958 = 2.0;
        double r519959 = r519957 * r519958;
        double r519960 = y;
        double r519961 = r519959 * r519960;
        double r519962 = r519957 - r519960;
        double r519963 = r519961 / r519962;
        return r519963;
}
↓
double f(double x, double y) {
        double r519964 = y;
        double r519965 = -1.8379060927151348e+37;
        bool r519966 = r519964 <= r519965;
        double r519967 = 2.535580169146477e-106;
        bool r519968 = r519964 <= r519967;
        double r519969 = !r519968;
        bool r519970 = r519966 || r519969;
        double r519971 = x;
        double r519972 = 2.0;
        double r519973 = r519971 * r519972;
        double r519974 = r519971 - r519964;
        double r519975 = r519964 / r519974;
        double r519976 = r519973 * r519975;
        double r519977 = r519973 / r519974;
        double r519978 = r519977 * r519964;
        double r519979 = r519970 ? r519976 : r519978;
        return r519979;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.7
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.8379060927151348e+37 or 2.535580169146477e-106 < y

    1. Initial program 14.6

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

    3. Applied *-un-lft-identity14.6

      \[\leadsto \frac{\left(x \cdot 2\right) \cdot y}{\color{blue}{1 \cdot \left(x - y\right)}}\]

    4. Applied times-frac0.6

      \[\leadsto \color{blue}{\frac{x \cdot 2}{1} \cdot \frac{y}{x - y}}\]

    5. Simplified0.6

      \[\leadsto \color{blue}{\left(x \cdot 2\right)} \cdot \frac{y}{x - y}\]

    if -1.8379060927151348e+37 < y < 2.535580169146477e-106

    1. Initial program 15.0

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

    3. Applied associate-/l*15.6

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

    5. Applied associate-/r/0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.8379060927151348 \cdot 10^{37} \lor \neg \left(y \le 2.53558016914647718 \cdot 10^{-106}\right):\\ \;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 +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)))