Average Error: 0.0 → 0.0
Time: 6.1s
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 r4372 = x;
        double r4373 = y;
        double r4374 = r4372 - r4373;
        double r4375 = r4372 + r4373;
        double r4376 = r4374 / r4375;
        return r4376;
}
↓
double f(double x, double y) {
        double r4377 = x;
        double r4378 = y;
        double r4379 = r4377 + r4378;
        double r4380 = r4377 / r4379;
        double r4381 = r4378 / r4379;
        double r4382 = r4380 - r4381;
        return r4382;
}

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 2020025 +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)))