Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]
\frac{x + y}{x - y}
↓
\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}
double f(double x, double y) {
        double r572643 = x;
        double r572644 = y;
        double r572645 = r572643 + r572644;
        double r572646 = r572643 - r572644;
        double r572647 = r572645 / r572646;
        return r572647;
}
↓
double f(double x, double y) {
        double r572648 = 1.0;
        double r572649 = x;
        double r572650 = y;
        double r572651 = r572649 + r572650;
        double r572652 = r572649 / r572651;
        double r572653 = r572650 / r572651;
        double r572654 = r572652 - r572653;
        double r572655 = r572648 / r572654;
        return r572655;
}

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

Derivation

  1. Initial program 0.0

    \[\frac{x + y}{x - y}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{x + y}}}\]
  4. Using strategy rm

  5. Applied div-sub0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1 (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (+ x y) (- x y)))