Average Error: 0.3 → 0.3
Time: 4.5s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[x + \left(6 \cdot y - x \cdot 6\right) \cdot z\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
x + \left(6 \cdot y - x \cdot 6\right) \cdot z
(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))
↓
(FPCore (x y z) :precision binary64 (+ x (* (- (* 6.0 y) (* x 6.0)) z)))
double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}
↓
double code(double x, double y, double z) {
	return x + (((6.0 * y) - (x * 6.0)) * z);
}

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

Target

Original0.3
Target0.1
Herbie0.3
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

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

  2. Taylor expanded around 0 0.2

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

  3. Simplified0.2

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

  5. Applied sub-neg_binary64_215540.2

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

  6. Applied distribute-rgt-in_binary64_215110.2

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

  7. Simplified0.2

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

  8. Taylor expanded around 0 0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2021043 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))