Average Error: 0.0 → 0.0
Time: 11.4s
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 r474909 = x;
        double r474910 = y;
        double r474911 = r474909 - r474910;
        double r474912 = r474909 + r474910;
        double r474913 = r474911 / r474912;
        return r474913;
}
↓
double f(double x, double y) {
        double r474914 = 1.0;
        double r474915 = x;
        double r474916 = y;
        double r474917 = r474915 + r474916;
        double r474918 = r474917 / r474915;
        double r474919 = r474914 / r474918;
        double r474920 = r474916 / r474917;
        double r474921 = r474919 - r474920;
        return r474921;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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 2019305 +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)))