Average Error: 0.0 → 0.0
Time: 14.7s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{\frac{1}{x - y}}{\frac{1}{x + y}}\]
\frac{x + y}{x - y}
↓
\frac{\frac{1}{x - y}}{\frac{1}{x + y}}
double f(double x, double y) {
        double r30778114 = x;
        double r30778115 = y;
        double r30778116 = r30778114 + r30778115;
        double r30778117 = r30778114 - r30778115;
        double r30778118 = r30778116 / r30778117;
        return r30778118;
}
↓
double f(double x, double y) {
        double r30778119 = 1.0;
        double r30778120 = x;
        double r30778121 = y;
        double r30778122 = r30778120 - r30778121;
        double r30778123 = r30778119 / r30778122;
        double r30778124 = r30778120 + r30778121;
        double r30778125 = r30778119 / r30778124;
        double r30778126 = r30778123 / r30778125;
        return r30778126;
}

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-inv0.2

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

  6. Applied associate-/r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +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)))