Average Error: 15.2 → 0.2
Time: 1.8s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.7538803200316063 \cdot 10^{49} \lor \neg \left(x \le 2.59687826800368321 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{1 \cdot \left(\frac{x}{y} - 1\right)}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.7538803200316063 \cdot 10^{49} \lor \neg \left(x \le 2.59687826800368321 \cdot 10^{-23}\right):\\
\;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{1 \cdot \left(\frac{x}{y} - 1\right)}\\

\end{array}
double f(double x, double y) {
        double r455310 = x;
        double r455311 = 2.0;
        double r455312 = r455310 * r455311;
        double r455313 = y;
        double r455314 = r455312 * r455313;
        double r455315 = r455310 - r455313;
        double r455316 = r455314 / r455315;
        return r455316;
}
↓
double f(double x, double y) {
        double r455317 = x;
        double r455318 = -1.7538803200316063e+49;
        bool r455319 = r455317 <= r455318;
        double r455320 = 2.5968782680036832e-23;
        bool r455321 = r455317 <= r455320;
        double r455322 = !r455321;
        bool r455323 = r455319 || r455322;
        double r455324 = y;
        double r455325 = r455317 - r455324;
        double r455326 = r455317 / r455325;
        double r455327 = 2.0;
        double r455328 = r455324 * r455327;
        double r455329 = r455326 * r455328;
        double r455330 = r455317 * r455327;
        double r455331 = 1.0;
        double r455332 = r455317 / r455324;
        double r455333 = r455332 - r455331;
        double r455334 = r455331 * r455333;
        double r455335 = r455330 / r455334;
        double r455336 = r455323 ? r455329 : r455335;
        return r455336;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.2
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 x < -1.7538803200316063e+49 or 2.5968782680036832e-23 < x

    1. Initial program 16.5

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
    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 div-inv15.8

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

    6. Applied times-frac0.3

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

    7. Simplified0.1

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

    if -1.7538803200316063e+49 < x < 2.5968782680036832e-23

    1. Initial program 13.9

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

    3. Applied associate-/l*0.2

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

    5. Applied *-un-lft-identity0.2

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

    6. Applied *-un-lft-identity0.2

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

    7. Applied times-frac0.2

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

    8. Simplified0.2

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

    9. Simplified0.2

      \[\leadsto \frac{x \cdot 2}{1 \cdot \color{blue}{\left(\frac{x}{y} - 1\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.7538803200316063 \cdot 10^{49} \lor \neg \left(x \le 2.59687826800368321 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{1 \cdot \left(\frac{x}{y} - 1\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 +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)))