Average Error: 14.5 → 0.3
Time: 7.9s
Precision: 64
\[\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.435942788027777 \cdot 10^{+60}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \le 1.5452684980844889 \cdot 10^{+57}:\\ \;\;\;\;\frac{2.0 \cdot x}{\frac{x}{y} - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \end{array}\]
\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.435942788027777 \cdot 10^{+60}:\\
\;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\

\mathbf{elif}\;x \le 1.5452684980844889 \cdot 10^{+57}:\\
\;\;\;\;\frac{2.0 \cdot x}{\frac{x}{y} - 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\

\end{array}
double f(double x, double y) {
        double r22766332 = x;
        double r22766333 = 2.0;
        double r22766334 = r22766332 * r22766333;
        double r22766335 = y;
        double r22766336 = r22766334 * r22766335;
        double r22766337 = r22766332 - r22766335;
        double r22766338 = r22766336 / r22766337;
        return r22766338;
}
↓
double f(double x, double y) {
        double r22766339 = x;
        double r22766340 = -1.435942788027777e+60;
        bool r22766341 = r22766339 <= r22766340;
        double r22766342 = 2.0;
        double r22766343 = r22766342 * r22766339;
        double r22766344 = y;
        double r22766345 = r22766339 - r22766344;
        double r22766346 = r22766343 / r22766345;
        double r22766347 = r22766346 * r22766344;
        double r22766348 = 1.5452684980844889e+57;
        bool r22766349 = r22766339 <= r22766348;
        double r22766350 = r22766339 / r22766344;
        double r22766351 = 1.0;
        double r22766352 = r22766350 - r22766351;
        double r22766353 = r22766343 / r22766352;
        double r22766354 = r22766349 ? r22766353 : r22766347;
        double r22766355 = r22766341 ? r22766347 : r22766354;
        return r22766355;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.5
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 8.364504563556443 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot 2.0}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.435942788027777e+60 or 1.5452684980844889e+57 < x

    1. Initial program 18.6

      \[\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}\]
    2. Using strategy rm

    3. Applied associate-/l*17.3

      \[\leadsto \color{blue}{\frac{x \cdot 2.0}{\frac{x - y}{y}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.0

      \[\leadsto \color{blue}{\frac{x \cdot 2.0}{x - y} \cdot y}\]

    if -1.435942788027777e+60 < x < 1.5452684980844889e+57

    1. Initial program 11.8

      \[\frac{\left(x \cdot 2.0\right) \cdot y}{x - y}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

      \[\leadsto \color{blue}{\frac{x \cdot 2.0}{\frac{x - y}{y}}}\]
    4. Using strategy rm

    5. Applied div-sub0.6

      \[\leadsto \frac{x \cdot 2.0}{\color{blue}{\frac{x}{y} - \frac{y}{y}}}\]

    6. Simplified0.6

      \[\leadsto \frac{x \cdot 2.0}{\frac{x}{y} - \color{blue}{1}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.435942788027777 \cdot 10^{+60}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \le 1.5452684980844889 \cdot 10^{+57}:\\ \;\;\;\;\frac{2.0 \cdot x}{\frac{x}{y} - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2.0 \cdot x}{x - y} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 8.364504563556443e+16) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))