Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \frac{y}{x + y}\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \frac{y}{x + y}
double f(double x, double y) {
        double r777626 = x;
        double r777627 = y;
        double r777628 = r777626 - r777627;
        double r777629 = r777626 + r777627;
        double r777630 = r777628 / r777629;
        return r777630;
}
↓
double f(double x, double y) {
        double r777631 = x;
        double r777632 = y;
        double r777633 = r777631 + r777632;
        double r777634 = r777631 / r777633;
        double r777635 = r777632 / r777633;
        double r777636 = r777634 - r777635;
        return r777636;
}

Error

Bits error versus x

Bits error versus y

Try it out

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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