Average Error: 0.0 → 0.0
Time: 13.3s
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 r20909242 = x;
        double r20909243 = y;
        double r20909244 = r20909242 + r20909243;
        double r20909245 = r20909242 - r20909243;
        double r20909246 = r20909244 / r20909245;
        return r20909246;
}
↓
double f(double x, double y) {
        double r20909247 = y;
        double r20909248 = x;
        double r20909249 = r20909247 + r20909248;
        double r20909250 = r20909248 - r20909247;
        double r20909251 = r20909249 / r20909250;
        double r20909252 = exp(r20909251);
        double r20909253 = log(r20909252);
        return r20909253;
}

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 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)))