Average Error: 0.2 → 0.2
Time: 3.1s
Precision: binary64
\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
↓
\[\left(\left(\left(x - \frac{16}{116}\right) \cdot \left({\left(\sqrt[3]{3}\right)}^{2} \cdot \sqrt[3]{{\left(\sqrt[3]{3}\right)}^{2}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot y\]
\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]{{\left(\sqrt[3]{3}\right)}^{2}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot y
double code(double x, double y) {
	return ((double) (((double) (((double) (x - ((double) (16.0 / 116.0)))) * 3.0)) * y));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) (x - ((double) (16.0 / 116.0)))) * ((double) (((double) pow(((double) cbrt(3.0)), 2.0)) * ((double) cbrt(((double) pow(((double) cbrt(3.0)), 2.0)))))))) * ((double) cbrt(((double) cbrt(3.0)))))) * y));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.2
\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

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-cbrt0.2

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

  4. Applied associate-*r*0.7

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

  6. Applied add-cube-cbrt0.7

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

  7. Applied cbrt-prod0.7

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

  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. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020184 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))