Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right)\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right)
double f(double x, double y) {
        double r565424 = x;
        double r565425 = y;
        double r565426 = r565424 - r565425;
        double r565427 = r565424 + r565425;
        double r565428 = r565426 / r565427;
        return r565428;
}
↓
double f(double x, double y) {
        double r565429 = x;
        double r565430 = y;
        double r565431 = r565429 + r565430;
        double r565432 = r565429 / r565431;
        double r565433 = r565430 / r565431;
        double r565434 = log1p(r565433);
        double r565435 = expm1(r565434);
        double r565436 = r565432 - r565435;
        return r565436;
}

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 expm1-log1p-u0.0

    \[\leadsto \frac{x}{x + y} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right)}\]

  6. Final simplification0.0

    \[\leadsto \frac{x}{x + y} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right)\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(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)))