Average Error: 0.0 → 0.0
Time: 13.7s
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 r555211 = x;
        double r555212 = y;
        double r555213 = r555211 - r555212;
        double r555214 = r555211 + r555212;
        double r555215 = r555213 / r555214;
        return r555215;
}
↓
double f(double x, double y) {
        double r555216 = x;
        double r555217 = y;
        double r555218 = r555216 + r555217;
        double r555219 = r555216 / r555218;
        double r555220 = r555217 / r555218;
        double r555221 = exp(r555220);
        double r555222 = log(r555221);
        double r555223 = r555219 - r555222;
        return r555223;
}

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 2019325 +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)))