Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \frac{1}{\frac{x + y}{y}}\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \frac{1}{\frac{x + y}{y}}
double f(double x, double y) {
        double r856302 = x;
        double r856303 = y;
        double r856304 = r856302 - r856303;
        double r856305 = r856302 + r856303;
        double r856306 = r856304 / r856305;
        return r856306;
}
↓
double f(double x, double y) {
        double r856307 = x;
        double r856308 = y;
        double r856309 = r856307 + r856308;
        double r856310 = r856307 / r856309;
        double r856311 = 1.0;
        double r856312 = r856309 / r856308;
        double r856313 = r856311 / r856312;
        double r856314 = r856310 - r856313;
        return r856314;
}

Error

Bits error versus x

Bits error versus y

Try it out

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

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 +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)))