Average Error: 0.0 → 0.0
Time: 37.8s
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 r23677505 = x;
        double r23677506 = y;
        double r23677507 = r23677505 + r23677506;
        double r23677508 = r23677505 - r23677506;
        double r23677509 = r23677507 / r23677508;
        return r23677509;
}
↓
double f(double x, double y) {
        double r23677510 = 1.0;
        double r23677511 = x;
        double r23677512 = y;
        double r23677513 = r23677511 + r23677512;
        double r23677514 = r23677511 / r23677513;
        double r23677515 = r23677512 / r23677513;
        double r23677516 = r23677514 - r23677515;
        double r23677517 = r23677510 / r23677516;
        return r23677517;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{1.0}{\frac{x}{x + y} - \frac{y}{x + y}}\]

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 2019165 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (+ x y) (- x y)))