Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{\frac{x}{y + x} \cdot \frac{x}{y + x} - \frac{y}{y + x} \cdot \frac{y}{y + x}}{\frac{x}{y + x} + \frac{y}{y + x}}\]
\frac{x - y}{x + y}
↓
\frac{\frac{x}{y + x} \cdot \frac{x}{y + x} - \frac{y}{y + x} \cdot \frac{y}{y + x}}{\frac{x}{y + x} + \frac{y}{y + x}}
double f(double x, double y) {
        double r37159891 = x;
        double r37159892 = y;
        double r37159893 = r37159891 - r37159892;
        double r37159894 = r37159891 + r37159892;
        double r37159895 = r37159893 / r37159894;
        return r37159895;
}
↓
double f(double x, double y) {
        double r37159896 = x;
        double r37159897 = y;
        double r37159898 = r37159897 + r37159896;
        double r37159899 = r37159896 / r37159898;
        double r37159900 = r37159899 * r37159899;
        double r37159901 = r37159897 / r37159898;
        double r37159902 = r37159901 * r37159901;
        double r37159903 = r37159900 - r37159902;
        double r37159904 = r37159899 + r37159901;
        double r37159905 = r37159903 / r37159904;
        return r37159905;
}

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

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

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

  5. Applied flip--0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"

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

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