Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{1}{\frac{x}{x + y} - \frac{1}{\frac{x + y}{y}}}\]
\frac{x + y}{x - y}
↓
\frac{1}{\frac{x}{x + y} - \frac{1}{\frac{x + y}{y}}}
double f(double x, double y) {
        double r381542 = x;
        double r381543 = y;
        double r381544 = r381542 + r381543;
        double r381545 = r381542 - r381543;
        double r381546 = r381544 / r381545;
        return r381546;
}
↓
double f(double x, double y) {
        double r381547 = 1.0;
        double r381548 = x;
        double r381549 = y;
        double r381550 = r381548 + r381549;
        double r381551 = r381548 / r381550;
        double r381552 = r381550 / r381549;
        double r381553 = r381547 / r381552;
        double r381554 = r381551 - r381553;
        double r381555 = r381547 / r381554;
        return r381555;
}

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. Using strategy rm

  7. Applied clear-num0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +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)))