Average Error: 0.4 → 0.2
Time: 12.3s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[4 \cdot y + \left(\left(y \cdot z\right) \cdot -6 + x \cdot \left(z \cdot 6 - 3\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
4 \cdot y + \left(\left(y \cdot z\right) \cdot -6 + x \cdot \left(z \cdot 6 - 3\right)\right)
(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))
↓
(FPCore (x y z)
 :precision binary64
 (+ (* 4.0 y) (+ (* (* y 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 (4.0 * y) + (((y * 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

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

  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_binary64_96190.2

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

  7. Applied distribute-rgt-in_binary64_95760.2

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

  8. Applied distribute-rgt-in_binary64_95760.2

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

  9. Applied associate-+l+_binary64_95590.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2021015 
(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))))