Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} + \left(-\frac{y}{x + y}\right)\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} + \left(-\frac{y}{x + y}\right)
double f(double x, double y) {
        double r736707 = x;
        double r736708 = y;
        double r736709 = r736707 - r736708;
        double r736710 = r736707 + r736708;
        double r736711 = r736709 / r736710;
        return r736711;
}
↓
double f(double x, double y) {
        double r736712 = x;
        double r736713 = y;
        double r736714 = r736712 + r736713;
        double r736715 = r736712 / r736714;
        double r736716 = r736713 / r736714;
        double r736717 = -r736716;
        double r736718 = r736715 + r736717;
        return r736718;
}

Error

Bits error versus x

Bits error versus y

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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. Using strategy rm

  5. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x}{x + y}}\right)} - \frac{y}{x + y}\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(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)))