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

Average Error: 0.0 → 0.0

Time: 3.5s

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 r209487 = x;
        double r209488 = y;
        double r209489 = r209487 + r209488;
        double r209490 = r209487 * r209488;
        double r209491 = r209489 - r209490;
        return r209491;
}

↓

double f(double x, double y) {
        double r209492 = y;
        double r209493 = 1.0;
        double r209494 = x;
        double r209495 = r209493 - r209494;
        double r209496 = fma(r209492, r209495, r209494);
        return r209496;
}

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 2020045 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))