Average Error: 0.4 → 0.2
Time: 15.3s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(6 \cdot \left(x \cdot z\right) + 4 \cdot y\right) - \left(x \cdot 3 + 6 \cdot \left(z \cdot y\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(6 \cdot \left(x \cdot z\right) + 4 \cdot y\right) - \left(x \cdot 3 + 6 \cdot \left(z \cdot y\right)\right)
(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))
↓
(FPCore (x y z)
 :precision binary64
 (- (+ (* 6.0 (* x z)) (* 4.0 y)) (+ (* x 3.0) (* 6.0 (* z y)))))
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 ((6.0 * (x * z)) + (4.0 * y)) - ((x * 3.0) + (6.0 * (z * y)));
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2021014 
(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))))