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

Average Error: 0.5 → 0.4

Time: 5.6s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r934889 = 60.0;
        double r934890 = x;
        double r934891 = y;
        double r934892 = r934890 - r934891;
        double r934893 = r934889 * r934892;
        double r934894 = z;
        double r934895 = t;
        double r934896 = r934894 - r934895;
        double r934897 = r934893 / r934896;
        double r934898 = a;
        double r934899 = 120.0;
        double r934900 = r934898 * r934899;
        double r934901 = r934897 + r934900;
        return r934901;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r934902 = 120.0;
        double r934903 = a;
        double r934904 = 60.0;
        double r934905 = x;
        double r934906 = y;
        double r934907 = r934905 - r934906;
        double r934908 = r934904 * r934907;
        double r934909 = z;
        double r934910 = t;
        double r934911 = r934909 - r934910;
        double r934912 = r934908 / r934911;
        double r934913 = fma(r934902, r934903, r934912);
        return r934913;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.5
Target	0.2
Herbie	0.4

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

Derivation

1. Initial program 0.5

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

2. Simplified 0.4

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

3. Final simplification 0.4

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

Reproduce

herbie shell --seed 2020027 +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)))