Average Error: 0.0 → 0.0
Time: 7.5s
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 r617566 = x;
        double r617567 = y;
        double r617568 = r617566 - r617567;
        double r617569 = r617566 + r617567;
        double r617570 = r617568 / r617569;
        return r617570;
}
↓
double f(double x, double y) {
        double r617571 = x;
        double r617572 = y;
        double r617573 = r617571 + r617572;
        double r617574 = r617571 / r617573;
        double r617575 = r617572 / r617573;
        double r617576 = r617574 - r617575;
        return r617576;
}

Error

Bits error versus x

Bits error versus y

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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 2019208 
(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)))