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

Average Error: 0.4 → 0.2

Time: 16.6s

Precision: 64

Math

\[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]

↓

\[\mathsf{fma}\left(\frac{60.0}{z - t}, x - y, 120.0 \cdot a\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r38491906 = 60.0;
        double r38491907 = x;
        double r38491908 = y;
        double r38491909 = r38491907 - r38491908;
        double r38491910 = r38491906 * r38491909;
        double r38491911 = z;
        double r38491912 = t;
        double r38491913 = r38491911 - r38491912;
        double r38491914 = r38491910 / r38491913;
        double r38491915 = a;
        double r38491916 = 120.0;
        double r38491917 = r38491915 * r38491916;
        double r38491918 = r38491914 + r38491917;
        return r38491918;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r38491919 = 60.0;
        double r38491920 = z;
        double r38491921 = t;
        double r38491922 = r38491920 - r38491921;
        double r38491923 = r38491919 / r38491922;
        double r38491924 = x;
        double r38491925 = y;
        double r38491926 = r38491924 - r38491925;
        double r38491927 = 120.0;
        double r38491928 = a;
        double r38491929 = r38491927 * r38491928;
        double r38491930 = fma(r38491923, r38491926, r38491929);
        return r38491930;
}

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	0.2

\[\frac{60.0}{\frac{z - t}{x - y}} + a \cdot 120.0\]

Derivation

1. Initial program 0.4

   \[\frac{60.0 \cdot \left(x - y\right)}{z - t} + a \cdot 120.0\]

2. Simplified 0.2

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{60.0}{z - t}, x - y, a \cdot 120.0\right)}\]

3. Final simplification 0.2

   \[\leadsto \mathsf{fma}\left(\frac{60.0}{z - t}, x - y, 120.0 \cdot a\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))