Average Error: 0.3 → 0.2
Time: 6.5s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[x + \left(-6 \cdot \left(x \cdot z\right) + 6 \cdot \left(z \cdot y\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
x + \left(-6 \cdot \left(x \cdot z\right) + 6 \cdot \left(z \cdot y\right)\right)
(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))
↓
(FPCore (x y z) :precision binary64 (+ x (+ (* -6.0 (* x z)) (* 6.0 (* z y)))))
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 * (x * z)) + (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

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

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_239410.2

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

  6. Applied distribute-rgt-in_binary64_238980.2

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

  7. Applied distribute-rgt-in_binary64_238980.2

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

  8. Simplified0.2

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

  9. Simplified0.2

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

  11. Applied *-un-lft-identity_binary64_239480.2

    \[\leadsto \color{blue}{1 \cdot \left(x + \left(-6 \cdot \left(x \cdot z\right) + 6 \cdot \left(y \cdot z\right)\right)\right)}\]

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2021076 
(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)))