Average Error: 0.4 → 0.2
Time: 3.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[4 \cdot \left(y - x\right) + \left(x + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
4 \cdot \left(y - x\right) + \left(x + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\right)
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * 6.0)) * ((double) (((double) (2.0 / 3.0)) - z))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (4.0 * ((double) (y - x)))) + ((double) (x + ((double) (((double) -(z)) * ((double) (((double) (y - x)) * 6.0))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Using strategy rm

  3. Applied sub-neg0.4

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

  4. Applied distribute-rgt-in0.4

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

  5. Applied associate-+r+0.4

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

  7. Applied +-commutative0.4

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

  8. Applied associate-+l+0.4

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

  9. Taylor expanded around 0 0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020113 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))