Data.Colour.CIE:cieLAB from colour-2.3.3, A

Average Error: 0.2 → 0.2

Time: 2.2s

Precision: 64

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

↓

\[\left(\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot y\]

C

double code(double x, double y) {
	return (((x - (16.0 / 116.0)) * 3.0) * y);
}

↓

double code(double x, double y) {
	return ((((x - (16.0 / 116.0)) * (pow(cbrt(3.0), 2.0) * cbrt((cbrt(3.0) * cbrt(3.0))))) * cbrt(cbrt(3.0))) * y);
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

1. Initial program 0.2

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
2. Using strategy rm

3. Applied add-cube-cbrt 0.2

   \[\leadsto \left(\left(x - \frac{16}{116}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)}\right) \cdot y\]

4. Applied associate-*r* 0.8

   \[\leadsto \color{blue}{\left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{3}\right)} \cdot y\]
5. Using strategy rm

6. Applied add-cube-cbrt 0.8

   \[\leadsto \left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}}\right) \cdot y\]

7. Applied cbrt-prod 0.8

   \[\leadsto \left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right)}\right) \cdot y\]

8. Applied associate-*r* 0.7

   \[\leadsto \color{blue}{\left(\left(\left(\left(x - \frac{16}{116}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right)} \cdot y\]

9. Simplified 0.2

   \[\leadsto \left(\color{blue}{\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right)} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot y\]

10. Final simplification 0.2

    \[\leadsto \left(\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{\sqrt[3]{3} \cdot \sqrt[3]{3}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot y\]

Reproduce

herbie shell --seed 2020105 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))