Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\frac{x - y}{x + y}}\right)\right)\]
\frac{x + y}{x - y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\frac{x - y}{x + y}}\right)\right)
double f(double x, double y) {
        double r543979 = x;
        double r543980 = y;
        double r543981 = r543979 + r543980;
        double r543982 = r543979 - r543980;
        double r543983 = r543981 / r543982;
        return r543983;
}
↓
double f(double x, double y) {
        double r543984 = 1.0;
        double r543985 = x;
        double r543986 = y;
        double r543987 = r543985 - r543986;
        double r543988 = r543985 + r543986;
        double r543989 = r543987 / r543988;
        double r543990 = r543984 / r543989;
        double r543991 = expm1(r543990);
        double r543992 = log1p(r543991);
        return r543992;
}

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. Using strategy rm

  5. Applied clear-num0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 +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)))