Average Error: 14.5 → 0.3
Time: 8.4s
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 r26433376 = x;
        double r26433377 = 2.0;
        double r26433378 = r26433376 * r26433377;
        double r26433379 = y;
        double r26433380 = r26433378 * r26433379;
        double r26433381 = r26433376 - r26433379;
        double r26433382 = r26433380 / r26433381;
        return r26433382;
}
↓
double f(double x, double y) {
        double r26433383 = x;
        double r26433384 = -1.435942788027777e+60;
        bool r26433385 = r26433383 <= r26433384;
        double r26433386 = 2.0;
        double r26433387 = r26433386 * r26433383;
        double r26433388 = y;
        double r26433389 = r26433383 - r26433388;
        double r26433390 = r26433387 / r26433389;
        double r26433391 = r26433390 * r26433388;
        double r26433392 = 1.5452684980844889e+57;
        bool r26433393 = r26433383 <= r26433392;
        double r26433394 = r26433383 / r26433388;
        double r26433395 = 1.0;
        double r26433396 = r26433394 - r26433395;
        double r26433397 = r26433387 / r26433396;
        double r26433398 = r26433393 ? r26433397 : r26433391;
        double r26433399 = r26433385 ? r26433391 : r26433398;
        return r26433399;
}

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 
(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)))