Average Error: 0.0 → 0.0
Time: 8.7s
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 r598182 = x;
        double r598183 = y;
        double r598184 = r598182 - r598183;
        double r598185 = r598182 + r598183;
        double r598186 = r598184 / r598185;
        return r598186;
}
↓
double f(double x, double y) {
        double r598187 = x;
        double r598188 = y;
        double r598189 = r598187 - r598188;
        double r598190 = r598187 + r598188;
        double r598191 = r598189 / r598190;
        double r598192 = expm1(r598191);
        double r598193 = log1p(r598192);
        return r598193;
}

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 2019198 +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)))