Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Average Error: 3.0 → 0.1

Time: 11.9s

Precision: 64

Math

\[x \cdot \left(1.0 - y \cdot z\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot z = -\infty:\\ \;\;\;\;1.0 \cdot x - y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \cdot z \le 3.6070881227494406 \cdot 10^{+301}:\\ \;\;\;\;1.0 \cdot x - x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;1.0 \cdot x - y \cdot \left(x \cdot z\right)\\ \end{array}\]

C

double f(double x, double y, double z) {
        double r12826610 = x;
        double r12826611 = 1.0;
        double r12826612 = y;
        double r12826613 = z;
        double r12826614 = r12826612 * r12826613;
        double r12826615 = r12826611 - r12826614;
        double r12826616 = r12826610 * r12826615;
        return r12826616;
}

↓

double f(double x, double y, double z) {
        double r12826617 = y;
        double r12826618 = z;
        double r12826619 = r12826617 * r12826618;
        double r12826620 = -inf.0;
        bool r12826621 = r12826619 <= r12826620;
        double r12826622 = 1.0;
        double r12826623 = x;
        double r12826624 = r12826622 * r12826623;
        double r12826625 = r12826623 * r12826618;
        double r12826626 = r12826617 * r12826625;
        double r12826627 = r12826624 - r12826626;
        double r12826628 = 3.6070881227494406e+301;
        bool r12826629 = r12826619 <= r12826628;
        double r12826630 = r12826623 * r12826619;
        double r12826631 = r12826624 - r12826630;
        double r12826632 = r12826629 ? r12826631 : r12826627;
        double r12826633 = r12826621 ? r12826627 : r12826632;
        return r12826633;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Split input into 2 regimes

2. if (* y z) < -inf.0 or 3.6070881227494406e+301 < (* y z)

   1. Initial program 58.1

      \[x \cdot \left(1.0 - y \cdot z\right)\]
   2. Using strategy rm

   3. Applied sub-neg 58.1

      \[\leadsto x \cdot \color{blue}{\left(1.0 + \left(-y \cdot z\right)\right)}\]

   4. Applied distribute-rgt-in 58.1

      \[\leadsto \color{blue}{1.0 \cdot x + \left(-y \cdot z\right) \cdot x}\]
   5. Using strategy rm

   6. Applied distribute-lft-neg-out 58.1

      \[\leadsto 1.0 \cdot x + \color{blue}{\left(-\left(y \cdot z\right) \cdot x\right)}\]

   7. Applied unsub-neg 58.1

      \[\leadsto \color{blue}{1.0 \cdot x - \left(y \cdot z\right) \cdot x}\]
   8. Using strategy rm

   9. Applied associate-*l* 0.3

      \[\leadsto 1.0 \cdot x - \color{blue}{y \cdot \left(z \cdot x\right)}\]

   if -inf.0 < (* y z) < 3.6070881227494406e+301

   1. Initial program 0.1

      \[x \cdot \left(1.0 - y \cdot z\right)\]
   2. Using strategy rm

   3. Applied sub-neg 0.1

      \[\leadsto x \cdot \color{blue}{\left(1.0 + \left(-y \cdot z\right)\right)}\]

   4. Applied distribute-rgt-in 0.1

      \[\leadsto \color{blue}{1.0 \cdot x + \left(-y \cdot z\right) \cdot x}\]
   5. Using strategy rm

   6. Applied distribute-lft-neg-out 0.1

      \[\leadsto 1.0 \cdot x + \color{blue}{\left(-\left(y \cdot z\right) \cdot x\right)}\]

   7. Applied unsub-neg 0.1

      \[\leadsto \color{blue}{1.0 \cdot x - \left(y \cdot z\right) \cdot x}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z = -\infty:\\ \;\;\;\;1.0 \cdot x - y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \cdot z \le 3.6070881227494406 \cdot 10^{+301}:\\ \;\;\;\;1.0 \cdot x - x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;1.0 \cdot x - y \cdot \left(x \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  (* x (- 1.0 (* y z))))