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

Average Error: 0.5 → 0.1

Time: 8.0s

Precision: 64

Math

\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

↓

\[\mathsf{fma}\left(120, a, 60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right)\right)\]

C

double code(double x, double y, double z, double t, double a) {
	return (((60.0 * (x - y)) / (z - t)) + (a * 120.0));
}

↓

double code(double x, double y, double z, double t, double a) {
	return fma(120.0, a, (60.0 * ((x / (z - t)) - (y / (z - t)))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.5
Target	0.2
Herbie	0.1

\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

1. Initial program 0.5

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

2. Simplified 0.5

   \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
3. Using strategy rm

4. Applied *-un-lft-identity 0.5

   \[\leadsto \mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{\color{blue}{1 \cdot \left(z - t\right)}}\right)\]

5. Applied times-frac 0.1

   \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{60}{1} \cdot \frac{x - y}{z - t}}\right)\]

6. Simplified 0.1

   \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{60} \cdot \frac{x - y}{z - t}\right)\]
7. Using strategy rm

8. Applied div-sub 0.1

   \[\leadsto \mathsf{fma}\left(120, a, 60 \cdot \color{blue}{\left(\frac{x}{z - t} - \frac{y}{z - t}\right)}\right)\]

9. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(120, a, 60 \cdot \left(\frac{x}{z - t} - \frac{y}{z - t}\right)\right)\]

Reproduce

herbie shell --seed 2020102 +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)))