Average Error: 0.0 → 0.0
Time: 3.0s
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 r564860 = x;
        double r564861 = y;
        double r564862 = r564860 + r564861;
        double r564863 = r564860 - r564861;
        double r564864 = r564862 / r564863;
        return r564864;
}
↓
double f(double x, double y) {
        double r564865 = 1.0;
        double r564866 = x;
        double r564867 = y;
        double r564868 = r564866 + r564867;
        double r564869 = r564866 / r564868;
        double r564870 = r564867 / r564868;
        double r564871 = r564869 - r564870;
        double r564872 = r564865 / r564871;
        return r564872;
}

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 +o rules:numerics
(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)))