Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{1}{\frac{x + y}{x}} - \frac{y}{x + y}\]
\frac{x - y}{x + y}
↓
\frac{1}{\frac{x + y}{x}} - \frac{y}{x + y}
double f(double x, double y) {
        double r621385 = x;
        double r621386 = y;
        double r621387 = r621385 - r621386;
        double r621388 = r621385 + r621386;
        double r621389 = r621387 / r621388;
        return r621389;
}
↓
double f(double x, double y) {
        double r621390 = 1.0;
        double r621391 = x;
        double r621392 = y;
        double r621393 = r621391 + r621392;
        double r621394 = r621393 / r621391;
        double r621395 = r621390 / r621394;
        double r621396 = r621392 / r621393;
        double r621397 = r621395 - r621396;
        return r621397;
}

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 clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x}}} - \frac{y}{x + y}\]

  6. Final simplification0.0

    \[\leadsto \frac{1}{\frac{x + y}{x}} - \frac{y}{x + y}\]

Reproduce

herbie shell --seed 2019303 +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)))