Average Error: 0.0 → 0.0
Time: 2.6s
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 r498963 = x;
        double r498964 = y;
        double r498965 = r498963 + r498964;
        double r498966 = r498963 - r498964;
        double r498967 = r498965 / r498966;
        return r498967;
}
↓
double f(double x, double y) {
        double r498968 = x;
        double r498969 = y;
        double r498970 = r498968 + r498969;
        double r498971 = r498968 - r498969;
        double r498972 = r498970 / r498971;
        double r498973 = expm1(r498972);
        double r498974 = log1p(r498973);
        return r498974;
}

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 2020033 +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)))