Average Error: 0.4 → 0.2
Time: 3.3s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right)\right) + z \cdot \left(6 \cdot \left(x - y\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right)\right) + z \cdot \left(6 \cdot \left(x - 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
 (+ (+ x (* (- y x) (* 6.0 (/ 2.0 3.0)))) (* z (* 6.0 (- x y)))))
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * 6.0)) * ((double) ((2.0 / 3.0) - z))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (x + ((double) (((double) (y - x)) * ((double) (6.0 * (2.0 / 3.0))))))) + ((double) (z * ((double) (6.0 * ((double) (x - 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 Error: 0.4 bits

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

  2. SimplifiedError: 0.2 bits

    \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\]
  3. Using strategy rm

  4. Applied sub-negError: 0.2 bits

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

  5. Applied distribute-lft-inError: 0.2 bits

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

  6. Applied distribute-lft-inError: 0.2 bits

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

  7. Applied associate-+r+Error: 0.2 bits

    \[\leadsto \color{blue}{\left(x + \left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right)\right) + \left(y - x\right) \cdot \left(6 \cdot \left(-z\right)\right)}\]
  8. Using strategy rm

  9. Applied associate-*r*Error: 0.2 bits

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

  10. Final simplificationError: 0.2 bits

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

Reproduce

herbie shell --seed 2020204 
(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))))