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

Average Error: 0.4 → 0.1

Time: 4.3s

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 r921908 = 60.0;
        double r921909 = x;
        double r921910 = y;
        double r921911 = r921909 - r921910;
        double r921912 = r921908 * r921911;
        double r921913 = z;
        double r921914 = t;
        double r921915 = r921913 - r921914;
        double r921916 = r921912 / r921915;
        double r921917 = a;
        double r921918 = 120.0;
        double r921919 = r921917 * r921918;
        double r921920 = r921916 + r921919;
        return r921920;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r921921 = 120.0;
        double r921922 = a;
        double r921923 = 60.0;
        double r921924 = z;
        double r921925 = t;
        double r921926 = r921924 - r921925;
        double r921927 = x;
        double r921928 = y;
        double r921929 = r921927 - r921928;
        double r921930 = r921926 / r921929;
        double r921931 = r921923 / r921930;
        double r921932 = fma(r921921, r921922, r921931);
        return r921932;
}

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	0.1
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 2020002 +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)))