Average Error: 0.0 → 0.0
Time: 13.7s
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 r22856058 = x;
        double r22856059 = y;
        double r22856060 = r22856058 + r22856059;
        double r22856061 = r22856058 - r22856059;
        double r22856062 = r22856060 / r22856061;
        return r22856062;
}
↓
double f(double x, double y) {
        double r22856063 = 1.0;
        double r22856064 = x;
        double r22856065 = y;
        double r22856066 = r22856064 + r22856065;
        double r22856067 = r22856064 / r22856066;
        double r22856068 = r22856065 / r22856066;
        double r22856069 = r22856067 - r22856068;
        double r22856070 = r22856063 / r22856069;
        return r22856070;
}

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

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 2019170 +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)))