Average Error: 0.0 → 0.0
Time: 9.3s
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 r926203 = x;
        double r926204 = y;
        double r926205 = r926203 - r926204;
        double r926206 = r926203 + r926204;
        double r926207 = r926205 / r926206;
        return r926207;
}
↓
double f(double x, double y) {
        double r926208 = x;
        double r926209 = y;
        double r926210 = r926208 + r926209;
        double r926211 = r926208 / r926210;
        double r926212 = r926209 / r926210;
        double r926213 = exp(r926212);
        double r926214 = log(r926213);
        double r926215 = r926211 - r926214;
        return r926215;
}

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 2019350 +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)))