Average Error: 15.2 → 7.2
Time: 5.2s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\frac{x}{x - y} \cdot \left(y \cdot 2\right)\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\frac{x}{x - y} \cdot \left(y \cdot 2\right)
double f(double x, double y) {
        double r363301 = x;
        double r363302 = 2.0;
        double r363303 = r363301 * r363302;
        double r363304 = y;
        double r363305 = r363303 * r363304;
        double r363306 = r363301 - r363304;
        double r363307 = r363305 / r363306;
        return r363307;
}
↓
double f(double x, double y) {
        double r363308 = x;
        double r363309 = y;
        double r363310 = r363308 - r363309;
        double r363311 = r363308 / r363310;
        double r363312 = 2.0;
        double r363313 = r363309 * r363312;
        double r363314 = r363311 * r363313;
        return r363314;
}

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
Target0.3
Herbie7.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.721044263414944729490876394165887012892 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -9.984365809073704e+82 or 6.6178108635873146e-52 < y

    1. Initial program 16.4

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

    3. Applied associate-/l*0.5

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

    5. Applied div-sub0.5

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

    6. Simplified0.5

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

    if -9.984365809073704e+82 < y < 6.6178108635873146e-52

    1. Initial program 14.1

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

    3. Applied associate-/l*13.1

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

    5. Applied div-inv13.3

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

    6. Applied times-frac0.5

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

    7. Simplified0.3

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

  4. Final simplification7.2

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

  (/ (* (* x 2) y) (- x y)))