Average Error: 0.0 → 0.0
Time: 17.1s
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 r497137 = x;
        double r497138 = y;
        double r497139 = r497137 - r497138;
        double r497140 = r497137 + r497138;
        double r497141 = r497139 / r497140;
        return r497141;
}
↓
double f(double x, double y) {
        double r497142 = x;
        double r497143 = y;
        double r497144 = r497142 + r497143;
        double r497145 = r497142 / r497144;
        double r497146 = r497143 / r497144;
        double r497147 = r497145 - r497146;
        return r497147;
}

Error

Bits error versus x

Bits error versus y

Try it out

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Results

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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 2019323 +o rules:numerics
(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)))