Average Error: 0.0 → 0.0
Time: 14.7s
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 r565726 = x;
        double r565727 = y;
        double r565728 = r565726 - r565727;
        double r565729 = r565726 + r565727;
        double r565730 = r565728 / r565729;
        return r565730;
}
↓
double f(double x, double y) {
        double r565731 = x;
        double r565732 = y;
        double r565733 = r565731 + r565732;
        double r565734 = r565731 / r565733;
        double r565735 = r565732 / r565733;
        double r565736 = r565734 - r565735;
        double r565737 = exp(r565736);
        double r565738 = log(r565737);
        return r565738;
}

Error

Bits error versus x

Bits error versus y

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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)))