Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)\]
\frac{x - y}{x + y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)
double f(double x, double y) {
        double r919339 = x;
        double r919340 = y;
        double r919341 = r919339 - r919340;
        double r919342 = r919339 + r919340;
        double r919343 = r919341 / r919342;
        return r919343;
}
↓
double f(double x, double y) {
        double r919344 = x;
        double r919345 = y;
        double r919346 = r919344 + r919345;
        double r919347 = r919344 / r919346;
        double r919348 = r919345 / r919346;
        double r919349 = exp(r919348);
        double r919350 = log(r919349);
        double r919351 = r919347 - r919350;
        double r919352 = expm1(r919351);
        double r919353 = log1p(r919352);
        return r919353;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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. Using strategy rm

  7. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)}\]

  8. Final simplification0.0

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{x + y} - \log \left(e^{\frac{y}{x + y}}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020060 +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)))