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

Average Error: 0.4 → 0.2

Time: 15.2s

Precision: 64

Math

\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]

↓

\[\left(x + \left(6 \cdot \frac{2}{3}\right) \cdot \left(y - x\right)\right) + \left(-\left(z \cdot 6\right) \cdot \left(y - x\right)\right)\]

C

double f(double x, double y, double z) {
        double r242209 = x;
        double r242210 = y;
        double r242211 = r242210 - r242209;
        double r242212 = 6.0;
        double r242213 = r242211 * r242212;
        double r242214 = 2.0;
        double r242215 = 3.0;
        double r242216 = r242214 / r242215;
        double r242217 = z;
        double r242218 = r242216 - r242217;
        double r242219 = r242213 * r242218;
        double r242220 = r242209 + r242219;
        return r242220;
}

↓

double f(double x, double y, double z) {
        double r242221 = x;
        double r242222 = 6.0;
        double r242223 = 2.0;
        double r242224 = 3.0;
        double r242225 = r242223 / r242224;
        double r242226 = r242222 * r242225;
        double r242227 = y;
        double r242228 = r242227 - r242221;
        double r242229 = r242226 * r242228;
        double r242230 = r242221 + r242229;
        double r242231 = z;
        double r242232 = r242231 * r242222;
        double r242233 = r242232 * r242228;
        double r242234 = -r242233;
        double r242235 = r242230 + r242234;
        return r242235;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.4

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
2. Using strategy rm

3. Applied sub-neg 0.4

   \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}\]

4. Applied distribute-lft-in 0.4

   \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\right)}\]

5. Applied associate-+r+ 0.4

   \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)}\]

6. Simplified 0.2

   \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + x\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]
7. Using strategy rm

8. Applied pow1 0.2

   \[\leadsto \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + x\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{{\left(-z\right)}^{1}}\]

9. Applied pow1 0.2

   \[\leadsto \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + x\right) + \left(\left(y - x\right) \cdot \color{blue}{{6}^{1}}\right) \cdot {\left(-z\right)}^{1}\]

10. Applied pow1 0.2

    \[\leadsto \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + x\right) + \left(\color{blue}{{\left(y - x\right)}^{1}} \cdot {6}^{1}\right) \cdot {\left(-z\right)}^{1}\]

11. Applied pow-prod-down 0.2

    \[\leadsto \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + x\right) + \color{blue}{{\left(\left(y - x\right) \cdot 6\right)}^{1}} \cdot {\left(-z\right)}^{1}\]

12. Applied pow-prod-down 0.2

    \[\leadsto \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + x\right) + \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\right)}^{1}}\]

13. Simplified 0.2

    \[\leadsto \left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + x\right) + {\color{blue}{\left(\left(-6 \cdot z\right) \cdot \left(y - x\right)\right)}}^{1}\]

14. Final simplification 0.2

    \[\leadsto \left(x + \left(6 \cdot \frac{2}{3}\right) \cdot \left(y - x\right)\right) + \left(-\left(z \cdot 6\right) \cdot \left(y - x\right)\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))