Average Error: 0.3 → 0.2
Time: 2.1s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\mathsf{fma}\left(\left(y - x\right) \cdot 6, z, x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\mathsf{fma}\left(\left(y - x\right) \cdot 6, z, x\right)
double code(double x, double y, double z) {
	return (x + (((y - x) * 6.0) * z));
}
↓
double code(double x, double y, double z) {
	return fma(((y - x) * 6.0), z, x);
}

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. Using strategy rm

  3. Applied *-commutative0.3

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

  4. Applied associate-*l*0.2

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

  5. Taylor expanded around 0 0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(\left(y - x\right) \cdot 6, z, x\right)\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))