Average Error: 15.3 → 0.2
Time: 6.2s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -29856493142547368 \lor \neg \left(y \le 2.1640309147455017 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -29856493142547368 \lor \neg \left(y \le 2.1640309147455017 \cdot 10^{-67}\right):\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\

\end{array}
double f(double x, double y) {
        double r575394 = x;
        double r575395 = 2.0;
        double r575396 = r575394 * r575395;
        double r575397 = y;
        double r575398 = r575396 * r575397;
        double r575399 = r575394 - r575397;
        double r575400 = r575398 / r575399;
        return r575400;
}
↓
double f(double x, double y) {
        double r575401 = y;
        double r575402 = -2.985649314254737e+16;
        bool r575403 = r575401 <= r575402;
        double r575404 = 2.1640309147455017e-67;
        bool r575405 = r575401 <= r575404;
        double r575406 = !r575405;
        bool r575407 = r575403 || r575406;
        double r575408 = x;
        double r575409 = 2.0;
        double r575410 = r575408 * r575409;
        double r575411 = r575408 - r575401;
        double r575412 = r575411 / r575401;
        double r575413 = r575410 / r575412;
        double r575414 = r575408 / r575411;
        double r575415 = r575401 * r575409;
        double r575416 = r575414 * r575415;
        double r575417 = r575407 ? r575413 : r575416;
        return r575417;
}

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
Target0.2
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 < -2.985649314254737e+16 or 2.1640309147455017e-67 < y

    1. Initial program 15.3

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

    3. Applied associate-/l*0.4

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

    if -2.985649314254737e+16 < y < 2.1640309147455017e-67

    1. Initial program 15.3

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

    3. Applied associate-/l*16.1

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

    5. Applied div-inv16.2

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

    6. Applied times-frac0.2

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

    7. Simplified0.0

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -29856493142547368 \lor \neg \left(y \le 2.1640309147455017 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +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)))