Average Error: 15.4 → 0.2
Time: 1.7s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -95380968.4142476171 \lor \neg \left(x \le 1.64772115240192995 \cdot 10^{69}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -95380968.4142476171 \lor \neg \left(x \le 1.64772115240192995 \cdot 10^{69}\right):\\
\;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\

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

\end{array}
double f(double x, double y) {
        double r499229 = x;
        double r499230 = 2.0;
        double r499231 = r499229 * r499230;
        double r499232 = y;
        double r499233 = r499231 * r499232;
        double r499234 = r499229 - r499232;
        double r499235 = r499233 / r499234;
        return r499235;
}
↓
double f(double x, double y) {
        double r499236 = x;
        double r499237 = -95380968.41424762;
        bool r499238 = r499236 <= r499237;
        double r499239 = 1.64772115240193e+69;
        bool r499240 = r499236 <= r499239;
        double r499241 = !r499240;
        bool r499242 = r499238 || r499241;
        double r499243 = y;
        double r499244 = r499236 - r499243;
        double r499245 = r499236 / r499244;
        double r499246 = 2.0;
        double r499247 = r499243 * r499246;
        double r499248 = r499245 * r499247;
        double r499249 = r499236 * r499246;
        double r499250 = r499244 / r499243;
        double r499251 = r499249 / r499250;
        double r499252 = r499242 ? r499248 : r499251;
        return r499252;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.4
Target0.3
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 < -95380968.41424762 or 1.64772115240193e+69 < x

    1. Initial program 18.4

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

    3. Applied associate-/l*16.2

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

    5. Applied div-inv16.4

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

    6. Applied times-frac0.2

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

    7. Simplified0.1

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

    if -95380968.41424762 < x < 1.64772115240193e+69

    1. Initial program 13.0

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

    3. Applied associate-/l*0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -95380968.4142476171 \lor \neg \left(x \le 1.64772115240192995 \cdot 10^{69}\right):\\ \;\;\;\;\frac{x}{x - y} \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 +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)))