Average Error: 0.0 → 0.0
Time: 11.2s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\log \left(e^{\frac{y + x}{x - y}}\right)\]
\frac{x + y}{x - y}
↓
\log \left(e^{\frac{y + x}{x - y}}\right)
double f(double x, double y) {
        double r27050645 = x;
        double r27050646 = y;
        double r27050647 = r27050645 + r27050646;
        double r27050648 = r27050645 - r27050646;
        double r27050649 = r27050647 / r27050648;
        return r27050649;
}
↓
double f(double x, double y) {
        double r27050650 = y;
        double r27050651 = x;
        double r27050652 = r27050650 + r27050651;
        double r27050653 = r27050651 - r27050650;
        double r27050654 = r27050652 / r27050653;
        double r27050655 = exp(r27050654);
        double r27050656 = log(r27050655);
        return r27050656;
}

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 add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x + y}{x - y}}\right)}\]

  4. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{y + x}{x - y}}\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"

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

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