Average Error: 0.0 → 0.0
Time: 2.6s
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 r635131 = x;
        double r635132 = y;
        double r635133 = r635131 + r635132;
        double r635134 = r635131 - r635132;
        double r635135 = r635133 / r635134;
        return r635135;
}
↓
double f(double x, double y) {
        double r635136 = 1.0;
        double r635137 = x;
        double r635138 = y;
        double r635139 = r635137 - r635138;
        double r635140 = r635137 + r635138;
        double r635141 = r635139 / r635140;
        double r635142 = expm1(r635141);
        double r635143 = log1p(r635142);
        double r635144 = r635136 / r635143;
        return r635144;
}

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 2019354 +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)))