Average Error: 0.0 → 0.0
Time: 10.6s
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 r1024317 = x;
        double r1024318 = y;
        double r1024319 = r1024317 - r1024318;
        double r1024320 = r1024317 + r1024318;
        double r1024321 = r1024319 / r1024320;
        return r1024321;
}
↓
double f(double x, double y) {
        double r1024322 = x;
        double r1024323 = y;
        double r1024324 = r1024322 + r1024323;
        double r1024325 = r1024322 / r1024324;
        double r1024326 = r1024323 / r1024324;
        double r1024327 = r1024325 - r1024326;
        double r1024328 = exp(r1024327);
        double r1024329 = log(r1024328);
        return r1024329;
}

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)))