Average Error: 0.0 → 0.0
Time: 11.7s
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 r399867 = x;
        double r399868 = y;
        double r399869 = r399867 + r399868;
        double r399870 = r399867 - r399868;
        double r399871 = r399869 / r399870;
        return r399871;
}
↓
double f(double x, double y) {
        double r399872 = x;
        double r399873 = y;
        double r399874 = r399872 + r399873;
        double r399875 = r399872 - r399873;
        double r399876 = r399874 / r399875;
        double r399877 = expm1(r399876);
        double r399878 = log1p(r399877);
        return r399878;
}

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
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

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 2019212 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1 (- (/ x (+ x y)) (/ y (+ x y))))

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