Average Error: 0.0 → 0.0
Time: 9.1s
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 r812164 = x;
        double r812165 = y;
        double r812166 = r812164 + r812165;
        double r812167 = r812164 - r812165;
        double r812168 = r812166 / r812167;
        return r812168;
}
↓
double f(double x, double y) {
        double r812169 = x;
        double r812170 = y;
        double r812171 = r812169 + r812170;
        double r812172 = r812169 - r812170;
        double r812173 = r812171 / r812172;
        double r812174 = exp(r812173);
        double r812175 = log(r812174);
        return r812175;
}

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 2020047 
(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)))