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

Average Error: 0.4 → 0.1

Time: 8.5s

Precision: binary64

Math

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

↓

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

C

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

↓

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.4
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. Using strategy rm

3. Applied associate-/l* 0.2

   \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120\]
4. Using strategy rm

5. Applied associate-/r/ 0.2

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

7. Applied clear-num 0.2

   \[\leadsto \color{blue}{\frac{1}{\frac{z - t}{60}}} \cdot \left(x - y\right) + a \cdot 120\]
8. Using strategy rm

9. Applied associate-*l/ 0.1

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

10. Simplified 0.1

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

11. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020147 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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