Average Error: 0.0 → 0.0
Time: 12.8s
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 r546412 = x;
        double r546413 = y;
        double r546414 = r546412 - r546413;
        double r546415 = r546412 + r546413;
        double r546416 = r546414 / r546415;
        return r546416;
}
↓
double f(double x, double y) {
        double r546417 = x;
        double r546418 = y;
        double r546419 = r546417 + r546418;
        double r546420 = r546417 / r546419;
        double r546421 = r546418 / r546419;
        double r546422 = r546420 - r546421;
        double r546423 = exp(r546422);
        double r546424 = log(r546423);
        return r546424;
}

Error

Bits error versus x

Bits error versus y

Try it out

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Results

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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 2019303 
(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)))