Average Error: 0.0 → 0.0
Time: 11.4s
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 r637289 = x;
        double r637290 = y;
        double r637291 = r637289 + r637290;
        double r637292 = r637289 - r637290;
        double r637293 = r637291 / r637292;
        return r637293;
}
↓
double f(double x, double y) {
        double r637294 = x;
        double r637295 = y;
        double r637296 = r637294 + r637295;
        double r637297 = r637294 - r637295;
        double r637298 = r637296 / r637297;
        double r637299 = exp(r637298);
        double r637300 = log(r637299);
        return r637300;
}

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 +o rules:numerics
(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)))