Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{\frac{1}{x - y}}{\frac{1}{x + y}}\]
\frac{x + y}{x - y}
↓
\frac{\frac{1}{x - y}}{\frac{1}{x + y}}
double f(double x, double y) {
        double r625549 = x;
        double r625550 = y;
        double r625551 = r625549 + r625550;
        double r625552 = r625549 - r625550;
        double r625553 = r625551 / r625552;
        return r625553;
}
↓
double f(double x, double y) {
        double r625554 = 1.0;
        double r625555 = x;
        double r625556 = y;
        double r625557 = r625555 - r625556;
        double r625558 = r625554 / r625557;
        double r625559 = r625555 + r625556;
        double r625560 = r625554 / r625559;
        double r625561 = r625558 / r625560;
        return r625561;
}

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-inv0.2

    \[\leadsto \frac{1}{\color{blue}{\left(x - y\right) \cdot \frac{1}{x + y}}}\]

  6. Applied associate-/r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(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)))