Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)\]
\frac{x - y}{2 - \left(x + y\right)}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)
double f(double x, double y) {
        double r885303 = x;
        double r885304 = y;
        double r885305 = r885303 - r885304;
        double r885306 = 2.0;
        double r885307 = r885303 + r885304;
        double r885308 = r885306 - r885307;
        double r885309 = r885305 / r885308;
        return r885309;
}
↓
double f(double x, double y) {
        double r885310 = x;
        double r885311 = y;
        double r885312 = r885310 - r885311;
        double r885313 = 2.0;
        double r885314 = r885310 + r885311;
        double r885315 = r885313 - r885314;
        double r885316 = r885312 / r885315;
        double r885317 = expm1(r885316);
        double r885318 = log1p(r885317);
        return r885318;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)}\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y))))

  (/ (- x y) (- 2 (+ x y))))