Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\log \left(e^{\frac{x}{x + y}}\right) - \frac{y}{x + y}\]
\frac{x - y}{x + y}
↓
\log \left(e^{\frac{x}{x + y}}\right) - \frac{y}{x + y}
double f(double x, double y) {
        double r867837 = x;
        double r867838 = y;
        double r867839 = r867837 - r867838;
        double r867840 = r867837 + r867838;
        double r867841 = r867839 / r867840;
        return r867841;
}
↓
double f(double x, double y) {
        double r867842 = x;
        double r867843 = y;
        double r867844 = r867842 + r867843;
        double r867845 = r867842 / r867844;
        double r867846 = exp(r867845);
        double r867847 = log(r867846);
        double r867848 = r867843 / r867844;
        double r867849 = r867847 - r867848;
        return r867849;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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