Average Error: 0.0 → 0.0
Time: 3.1s
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 r916469 = x;
        double r916470 = y;
        double r916471 = r916469 - r916470;
        double r916472 = r916469 + r916470;
        double r916473 = r916471 / r916472;
        return r916473;
}
↓
double f(double x, double y) {
        double r916474 = x;
        double r916475 = y;
        double r916476 = r916474 + r916475;
        double r916477 = r916474 / r916476;
        double r916478 = r916475 / r916476;
        double r916479 = r916477 - r916478;
        return r916479;
}

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 2020021 
(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)))