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

Average Error: 0.3 → 0.2

Time: 15.6s

Precision: 64

Math

\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

↓

\[\mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]

C

double f(double x, double y, double z) {
        double r42762639 = x;
        double r42762640 = y;
        double r42762641 = r42762640 - r42762639;
        double r42762642 = 6.0;
        double r42762643 = r42762641 * r42762642;
        double r42762644 = z;
        double r42762645 = r42762643 * r42762644;
        double r42762646 = r42762639 + r42762645;
        return r42762646;
}

↓

double f(double x, double y, double z) {
        double r42762647 = y;
        double r42762648 = x;
        double r42762649 = r42762647 - r42762648;
        double r42762650 = 6.0;
        double r42762651 = z;
        double r42762652 = r42762650 * r42762651;
        double r42762653 = fma(r42762649, r42762652, r42762648);
        return r42762653;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.3
Target	0.2
Herbie	0.2

\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

1. Initial program 0.3

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

2. Simplified 0.2

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)}\]

3. Final simplification 0.2

   \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]

Reproduce

herbie shell --seed 2019174 +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)))