Average Error: 0.4 → 0.2
Time: 4.6s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
↓
\[y \cdot \left(4 - z \cdot 6\right) + x \cdot \left(z \cdot 6 + -3\right) \]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
y \cdot \left(4 - z \cdot 6\right) + x \cdot \left(z \cdot 6 + -3\right)

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))
↓
(FPCore (x y z)
 :precision binary64
 (+ (* y (- 4.0 (* z 6.0))) (* x (+ (* z 6.0) -3.0))))
double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}
↓
double code(double x, double y, double z) {
	return (y * (4.0 - (z * 6.0))) + (x * ((z * 6.0) + -3.0));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]

  2. Simplified0.4

    \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

  3. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(4 \cdot y + 6 \cdot \left(z \cdot x\right)\right) - \left(6 \cdot \left(y \cdot z\right) + 3 \cdot x\right)} \]

  4. Simplified0.2

    \[\leadsto \color{blue}{4 \cdot y + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + x \cdot -3\right)} \]
  5. Using strategy rm

  6. Applied sub-neg_binary640.2

    \[\leadsto 4 \cdot y + \left(-6 \cdot \left(z \cdot \color{blue}{\left(y + \left(-x\right)\right)}\right) + x \cdot -3\right) \]

  7. Applied distribute-rgt-in_binary640.2

    \[\leadsto 4 \cdot y + \left(-6 \cdot \color{blue}{\left(y \cdot z + \left(-x\right) \cdot z\right)} + x \cdot -3\right) \]

  8. Applied distribute-rgt-in_binary640.2

    \[\leadsto 4 \cdot y + \left(\color{blue}{\left(\left(y \cdot z\right) \cdot -6 + \left(\left(-x\right) \cdot z\right) \cdot -6\right)} + x \cdot -3\right) \]

  9. Applied associate-+l+_binary640.2

    \[\leadsto 4 \cdot y + \color{blue}{\left(\left(y \cdot z\right) \cdot -6 + \left(\left(\left(-x\right) \cdot z\right) \cdot -6 + x \cdot -3\right)\right)} \]

  10. Simplified0.2

    \[\leadsto 4 \cdot y + \left(\left(y \cdot z\right) \cdot -6 + \color{blue}{x \cdot \left(-3 + 6 \cdot z\right)}\right) \]
  11. Using strategy rm

  12. Applied associate-+r+_binary640.2

    \[\leadsto \color{blue}{\left(4 \cdot y + \left(y \cdot z\right) \cdot -6\right) + x \cdot \left(-3 + 6 \cdot z\right)} \]

  13. Simplified0.2

    \[\leadsto \color{blue}{y \cdot \left(4 - z \cdot 6\right)} + x \cdot \left(-3 + 6 \cdot z\right) \]

  14. Final simplification0.2

    \[\leadsto y \cdot \left(4 - z \cdot 6\right) + x \cdot \left(z \cdot 6 + -3\right) \]

Reproduce

herbie shell --seed 2021207 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))