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

Average Error: 0.5 → 0.1

Time: 2.5s

Precision: 64

Math

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

↓

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

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, ((x - y) / ((z / 60.0) - (t / 60.0))));
}

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 *-commutative 0.5

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

5. Applied associate-/l* 0.1

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

7. Applied div-sub 0.1

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

8. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020078 +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)))