Data.Colour.RGB:hslsv from colour-2.3.3, B

Average Error: 0.4 → 0.1

Time: 5.1s

Precision: 64

Math

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

↓

\[\mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r970674 = 60.0;
        double r970675 = x;
        double r970676 = y;
        double r970677 = r970675 - r970676;
        double r970678 = r970674 * r970677;
        double r970679 = z;
        double r970680 = t;
        double r970681 = r970679 - r970680;
        double r970682 = r970678 / r970681;
        double r970683 = a;
        double r970684 = 120.0;
        double r970685 = r970683 * r970684;
        double r970686 = r970682 + r970685;
        return r970686;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r970687 = 120.0;
        double r970688 = a;
        double r970689 = 60.0;
        double r970690 = z;
        double r970691 = t;
        double r970692 = r970690 - r970691;
        double r970693 = x;
        double r970694 = y;
        double r970695 = r970693 - r970694;
        double r970696 = r970692 / r970695;
        double r970697 = r970689 / r970696;
        double r970698 = fma(r970687, r970688, r970697);
        return r970698;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.4
Target	0.2
Herbie	0.1

\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

1. Initial program 0.4

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

2. Simplified 0.4

   \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
3. Using strategy rm

4. Applied associate-/l* 0.1

   \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right)\]

5. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(120, a, \frac{60}{\frac{z - t}{x - y}}\right)\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60 (/ (- z t) (- x y))) (* a 120))

  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))