Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A

Average Error: 0.0 → 0.0

Time: 5.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\left(x + y\right) - x \cdot y\]

↓

\[\mathsf{fma}\left(y, 1 - x, x\right)\]

C

double f(double x, double y) {
        double r200560 = x;
        double r200561 = y;
        double r200562 = r200560 + r200561;
        double r200563 = r200560 * r200561;
        double r200564 = r200562 - r200563;
        return r200564;
}

↓

double f(double x, double y) {
        double r200565 = y;
        double r200566 = 1.0;
        double r200567 = x;
        double r200568 = r200566 - r200567;
        double r200569 = fma(r200565, r200568, r200567);
        return r200569;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.0

   \[\left(x + y\right) - x \cdot y\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 1 - x, x\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(y, 1 - x, x\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))