Average Error: 0.0 → 0.0
Time: 11.7s
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 r26793542 = x;
        double r26793543 = y;
        double r26793544 = r26793542 + r26793543;
        double r26793545 = r26793542 - r26793543;
        double r26793546 = r26793544 / r26793545;
        return r26793546;
}
↓
double f(double x, double y) {
        double r26793547 = y;
        double r26793548 = x;
        double r26793549 = r26793547 + r26793548;
        double r26793550 = r26793548 - r26793547;
        double r26793551 = r26793549 / r26793550;
        double r26793552 = exp(r26793551);
        double r26793553 = log(r26793552);
        return r26793553;
}

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 +o rules:numerics
(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)))