Average Error: 0.0 → 0.0
Time: 14.2s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)\]
\frac{x - y}{x + y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)
double f(double x, double y) {
        double r554764 = x;
        double r554765 = y;
        double r554766 = r554764 - r554765;
        double r554767 = r554764 + r554765;
        double r554768 = r554766 / r554767;
        return r554768;
}
↓
double f(double x, double y) {
        double r554769 = x;
        double r554770 = y;
        double r554771 = r554769 - r554770;
        double r554772 = r554769 + r554770;
        double r554773 = r554771 / r554772;
        double r554774 = expm1(r554773);
        double r554775 = log1p(r554774);
        return r554775;
}

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 log1p-expm1-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +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)))