Average Error: 0.0 → 0.0
Time: 13.2s
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 r468402 = x;
        double r468403 = y;
        double r468404 = r468402 + r468403;
        double r468405 = r468402 - r468403;
        double r468406 = r468404 / r468405;
        return r468406;
}
↓
double f(double x, double y) {
        double r468407 = 1.0;
        double r468408 = x;
        double r468409 = y;
        double r468410 = r468408 + r468409;
        double r468411 = r468408 / r468410;
        double r468412 = r468410 / r468409;
        double r468413 = r468407 / r468412;
        double r468414 = r468411 - r468413;
        double r468415 = r468407 / r468414;
        return r468415;
}

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. Simplified0.0

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

  6. Applied div-sub0.0

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

  7. Simplified0.0

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

  8. Simplified0.0

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

  10. Applied clear-num0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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)))