Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)
double f(double x, double y) {
        double r984219 = x;
        double r984220 = y;
        double r984221 = r984219 - r984220;
        double r984222 = r984219 + r984220;
        double r984223 = r984221 / r984222;
        return r984223;
}
↓
double f(double x, double y) {
        double r984224 = x;
        double r984225 = y;
        double r984226 = r984224 + r984225;
        double r984227 = r984224 / r984226;
        double r984228 = r984225 / r984226;
        double r984229 = exp(r984228);
        double r984230 = log(r984229);
        double r984231 = r984227 - r984230;
        return r984231;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 +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)))