Average Error: 0.0 → 0.0
Time: 3.6s
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 r765845 = x;
        double r765846 = y;
        double r765847 = r765845 - r765846;
        double r765848 = 2.0;
        double r765849 = r765845 + r765846;
        double r765850 = r765848 - r765849;
        double r765851 = r765847 / r765850;
        return r765851;
}
↓
double f(double x, double y) {
        double r765852 = x;
        double r765853 = y;
        double r765854 = r765852 - r765853;
        double r765855 = 2.0;
        double r765856 = r765852 + r765853;
        double r765857 = r765855 - r765856;
        double r765858 = r765854 / r765857;
        double r765859 = expm1(r765858);
        double r765860 = log1p(r765859);
        return r765860;
}

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 2020035 +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))))