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

Average Error: 0.4 → 0.1

Time: 14.5s

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 r428903 = 60.0;
        double r428904 = x;
        double r428905 = y;
        double r428906 = r428904 - r428905;
        double r428907 = r428903 * r428906;
        double r428908 = z;
        double r428909 = t;
        double r428910 = r428908 - r428909;
        double r428911 = r428907 / r428910;
        double r428912 = a;
        double r428913 = 120.0;
        double r428914 = r428912 * r428913;
        double r428915 = r428911 + r428914;
        return r428915;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r428916 = 120.0;
        double r428917 = a;
        double r428918 = 60.0;
        double r428919 = z;
        double r428920 = t;
        double r428921 = r428919 - r428920;
        double r428922 = x;
        double r428923 = y;
        double r428924 = r428922 - r428923;
        double r428925 = r428921 / r428924;
        double r428926 = r428918 / r428925;
        double r428927 = fma(r428916, r428917, r428926);
        return r428927;
}

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 2019326 +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)))