Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{1}{\frac{x}{x + y} \cdot \frac{x}{x + y} - \frac{y}{x + y} \cdot \frac{y}{x + y}} \cdot \left(\frac{x}{x + y} + \frac{y}{x + y}\right)\]
\frac{x + y}{x - y}
↓
\frac{1}{\frac{x}{x + y} \cdot \frac{x}{x + y} - \frac{y}{x + y} \cdot \frac{y}{x + y}} \cdot \left(\frac{x}{x + y} + \frac{y}{x + y}\right)
double f(double x, double y) {
        double r632005 = x;
        double r632006 = y;
        double r632007 = r632005 + r632006;
        double r632008 = r632005 - r632006;
        double r632009 = r632007 / r632008;
        return r632009;
}
↓
double f(double x, double y) {
        double r632010 = 1.0;
        double r632011 = x;
        double r632012 = y;
        double r632013 = r632011 + r632012;
        double r632014 = r632011 / r632013;
        double r632015 = r632014 * r632014;
        double r632016 = r632012 / r632013;
        double r632017 = r632016 * r632016;
        double r632018 = r632015 - r632017;
        double r632019 = r632010 / r632018;
        double r632020 = r632014 + r632016;
        double r632021 = r632019 * r632020;
        return r632021;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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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 flip--0.0

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

  8. Applied associate-/r/0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 +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)))