Average Error: 0.0 → 0.0
Time: 7.4s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{\frac{x}{x + y} \cdot \frac{x}{x + y} - \frac{y}{x + y} \cdot \frac{y}{x + y}}{\frac{x}{x + y} + \frac{y}{x + y}}\]
\frac{x - y}{x + y}
↓
\frac{\frac{x}{x + y} \cdot \frac{x}{x + y} - \frac{y}{x + y} \cdot \frac{y}{x + y}}{\frac{x}{x + y} + \frac{y}{x + y}}
double f(double x, double y) {
        double r55778758 = x;
        double r55778759 = y;
        double r55778760 = r55778758 - r55778759;
        double r55778761 = r55778758 + r55778759;
        double r55778762 = r55778760 / r55778761;
        return r55778762;
}
↓
double f(double x, double y) {
        double r55778763 = x;
        double r55778764 = y;
        double r55778765 = r55778763 + r55778764;
        double r55778766 = r55778763 / r55778765;
        double r55778767 = r55778766 * r55778766;
        double r55778768 = r55778764 / r55778765;
        double r55778769 = r55778768 * r55778768;
        double r55778770 = r55778767 - r55778769;
        double r55778771 = r55778766 + r55778768;
        double r55778772 = r55778770 / r55778771;
        return r55778772;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

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

  5. Applied flip--0.0

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

  6. Final simplification0.0

    \[\leadsto \frac{\frac{x}{x + y} \cdot \frac{x}{x + y} - \frac{y}{x + y} \cdot \frac{y}{x + y}}{\frac{x}{x + y} + \frac{y}{x + y}}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))