Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\log \left(e^{\frac{x}{x + y} - \frac{y}{x + y}}\right)\]
\frac{x - y}{x + y}
↓
\log \left(e^{\frac{x}{x + y} - \frac{y}{x + y}}\right)
double f(double x, double y) {
        double r887101 = x;
        double r887102 = y;
        double r887103 = r887101 - r887102;
        double r887104 = r887101 + r887102;
        double r887105 = r887103 / r887104;
        return r887105;
}
↓
double f(double x, double y) {
        double r887106 = x;
        double r887107 = y;
        double r887108 = r887106 + r887107;
        double r887109 = r887106 / r887108;
        double r887110 = r887107 / r887108;
        double r887111 = r887109 - r887110;
        double r887112 = exp(r887111);
        double r887113 = log(r887112);
        return r887113;
}

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
\[\frac{x}{x + y} - \frac{y}{x + y}\]

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

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

  6. Applied add-log-exp0.0

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

  7. Applied diff-log0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +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)))