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

Average Error: 0.4 → 0.1

Time: 13.3s

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 r684003 = 60.0;
        double r684004 = x;
        double r684005 = y;
        double r684006 = r684004 - r684005;
        double r684007 = r684003 * r684006;
        double r684008 = z;
        double r684009 = t;
        double r684010 = r684008 - r684009;
        double r684011 = r684007 / r684010;
        double r684012 = a;
        double r684013 = 120.0;
        double r684014 = r684012 * r684013;
        double r684015 = r684011 + r684014;
        return r684015;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r684016 = 120.0;
        double r684017 = a;
        double r684018 = 60.0;
        double r684019 = z;
        double r684020 = t;
        double r684021 = r684019 - r684020;
        double r684022 = x;
        double r684023 = y;
        double r684024 = r684022 - r684023;
        double r684025 = r684021 / r684024;
        double r684026 = r684018 / r684025;
        double r684027 = fma(r684016, r684017, r684026);
        return r684027;
}

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)))