Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)}\]
\frac{x + y}{x - y}
↓
\frac{1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)}
double f(double x, double y) {
        double r483977 = x;
        double r483978 = y;
        double r483979 = r483977 + r483978;
        double r483980 = r483977 - r483978;
        double r483981 = r483979 / r483980;
        return r483981;
}
↓
double f(double x, double y) {
        double r483982 = 1.0;
        double r483983 = x;
        double r483984 = y;
        double r483985 = r483983 - r483984;
        double r483986 = r483983 + r483984;
        double r483987 = r483985 / r483986;
        double r483988 = expm1(r483987);
        double r483989 = log1p(r483988);
        double r483990 = r483982 / r483989;
        return r483990;
}

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 clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{x + y}}}\]
  4. Using strategy rm

  5. Applied log1p-expm1-u0.0

    \[\leadsto \frac{1}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)}}\]

  6. Final simplification0.0

    \[\leadsto \frac{1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)}\]

Reproduce

herbie shell --seed 2020036 +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)))