Average Error: 0.0 → 0.0
Time: 13.3s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)
double f(double x, double y) {
        double r559140 = x;
        double r559141 = y;
        double r559142 = r559140 - r559141;
        double r559143 = r559140 + r559141;
        double r559144 = r559142 / r559143;
        return r559144;
}
↓
double f(double x, double y) {
        double r559145 = x;
        double r559146 = y;
        double r559147 = r559145 + r559146;
        double r559148 = r559145 / r559147;
        double r559149 = r559146 / r559147;
        double r559150 = exp(r559149);
        double r559151 = log(r559150);
        double r559152 = r559148 - r559151;
        return r559152;
}

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 add-log-exp0.0

    \[\leadsto \frac{x}{x + y} - \color{blue}{\log \left(e^{\frac{y}{x + y}}\right)}\]

  6. Final simplification0.0

    \[\leadsto \frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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