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

Average Error: 0.3 → 0.2

Time: 7.5s

Precision: 64

Math

\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot z\]

↓

\[\mathsf{fma}\left(6.0 \cdot z, y - x, x\right)\]

C

double f(double x, double y, double z) {
        double r15247317 = x;
        double r15247318 = y;
        double r15247319 = r15247318 - r15247317;
        double r15247320 = 6.0;
        double r15247321 = r15247319 * r15247320;
        double r15247322 = z;
        double r15247323 = r15247321 * r15247322;
        double r15247324 = r15247317 + r15247323;
        return r15247324;
}

↓

double f(double x, double y, double z) {
        double r15247325 = 6.0;
        double r15247326 = z;
        double r15247327 = r15247325 * r15247326;
        double r15247328 = y;
        double r15247329 = x;
        double r15247330 = r15247328 - r15247329;
        double r15247331 = fma(r15247327, r15247330, r15247329);
        return r15247331;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.3
Target	0.2
Herbie	0.2

\[x - \left(6.0 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

1. Initial program 0.3

   \[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot z\]

2. Simplified 0.2

   \[\leadsto \color{blue}{\mathsf{fma}\left(6.0 \cdot z, y - x, x\right)}\]

3. Final simplification 0.2

   \[\leadsto \mathsf{fma}\left(6.0 \cdot z, y - x, x\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))