Average Error: 0.0 → 0.0
Time: 3.1s
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 r466961 = x;
        double r466962 = y;
        double r466963 = r466961 + r466962;
        double r466964 = r466961 - r466962;
        double r466965 = r466963 / r466964;
        return r466965;
}
↓
double f(double x, double y) {
        double r466966 = 1.0;
        double r466967 = x;
        double r466968 = y;
        double r466969 = r466967 + r466968;
        double r466970 = r466967 / r466969;
        double r466971 = r466968 / r466969;
        double r466972 = r466970 - r466971;
        double r466973 = r466966 / r466972;
        return r466973;
}

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 2020089 +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)))