Average Error: 0.0 → 0.0
Time: 2.4s
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 r457023 = x;
        double r457024 = y;
        double r457025 = r457023 + r457024;
        double r457026 = r457023 - r457024;
        double r457027 = r457025 / r457026;
        return r457027;
}
↓
double f(double x, double y) {
        double r457028 = x;
        double r457029 = y;
        double r457030 = r457028 + r457029;
        double r457031 = r457028 - r457029;
        double r457032 = r457030 / r457031;
        double r457033 = exp(r457032);
        double r457034 = log(r457033);
        return r457034;
}

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

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

Reproduce

herbie shell --seed 2020003 
(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)))