Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\log \left(e^{\frac{x + y}{x - y}}\right)\]
\frac{x + y}{x - y}
↓
\log \left(e^{\frac{x + y}{x - y}}\right)
double f(double x, double y) {
        double r334633 = x;
        double r334634 = y;
        double r334635 = r334633 + r334634;
        double r334636 = r334633 - r334634;
        double r334637 = r334635 / r334636;
        return r334637;
}
↓
double f(double x, double y) {
        double r334638 = x;
        double r334639 = y;
        double r334640 = r334638 + r334639;
        double r334641 = r334638 - r334639;
        double r334642 = r334640 / r334641;
        double r334643 = exp(r334642);
        double r334644 = log(r334643);
        return r334644;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

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