Average Error: 0.1 → 0.1
Time: 3.7s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(x, y, z\right) \cdot y + t\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(x, y, z\right) \cdot y + t
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (x * y)) + z)) * y)) + t));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) fma(x, y, z)) * y)) + t));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot y + z\right) \cdot y + t\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.1

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

  4. Applied associate-*r*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020122 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))