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

Average Error: 0.4 → 0.1

Time: 5.7s

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 r859038 = 60.0;
        double r859039 = x;
        double r859040 = y;
        double r859041 = r859039 - r859040;
        double r859042 = r859038 * r859041;
        double r859043 = z;
        double r859044 = t;
        double r859045 = r859043 - r859044;
        double r859046 = r859042 / r859045;
        double r859047 = a;
        double r859048 = 120.0;
        double r859049 = r859047 * r859048;
        double r859050 = r859046 + r859049;
        return r859050;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r859051 = 120.0;
        double r859052 = a;
        double r859053 = 60.0;
        double r859054 = z;
        double r859055 = t;
        double r859056 = r859054 - r859055;
        double r859057 = x;
        double r859058 = y;
        double r859059 = r859057 - r859058;
        double r859060 = r859056 / r859059;
        double r859061 = r859053 / r859060;
        double r859062 = fma(r859051, r859052, r859061);
        return r859062;
}

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 2020062 +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)))