Average Error: 15.1 → 0.3
Time: 4.1s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.73735157607842638 \cdot 10^{-55} \lor \neg \left(x \le 2.31015467420133914 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.73735157607842638 \cdot 10^{-55} \lor \neg \left(x \le 2.31015467420133914 \cdot 10^{-42}\right):\\
\;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\

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

\end{array}
double f(double x, double y) {
        double r696046 = x;
        double r696047 = 2.0;
        double r696048 = r696046 * r696047;
        double r696049 = y;
        double r696050 = r696048 * r696049;
        double r696051 = r696046 - r696049;
        double r696052 = r696050 / r696051;
        return r696052;
}
↓
double f(double x, double y) {
        double r696053 = x;
        double r696054 = -1.7373515760784264e-55;
        bool r696055 = r696053 <= r696054;
        double r696056 = 2.310154674201339e-42;
        bool r696057 = r696053 <= r696056;
        double r696058 = !r696057;
        bool r696059 = r696055 || r696058;
        double r696060 = 2.0;
        double r696061 = r696053 * r696060;
        double r696062 = y;
        double r696063 = r696053 - r696062;
        double r696064 = r696061 / r696063;
        double r696065 = r696064 * r696062;
        double r696066 = r696063 / r696062;
        double r696067 = r696061 / r696066;
        double r696068 = r696059 ? r696065 : r696067;
        return r696068;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.1
Target0.4
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 x < -1.7373515760784264e-55 or 2.310154674201339e-42 < x

    1. Initial program 13.7

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

    3. Applied associate-/l*13.3

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

    5. Applied associate-/r/0.4

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

    if -1.7373515760784264e-55 < x < 2.310154674201339e-42

    1. Initial program 17.0

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

    3. Applied associate-/l*0.0

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.73735157607842638 \cdot 10^{-55} \lor \neg \left(x \le 2.31015467420133914 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{x \cdot 2}{x - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))