Average Error: 0.1 → 0.1
Time: 6.6s
Precision: binary64
\[\left(x \cdot y + z\right) \cdot y + t \]
↓
\[\mathsf{fma}\left(1, y \cdot \left(y \cdot x\right), \mathsf{fma}\left(y, z, t\right)\right) \]
(FPCore (x y z t) :precision binary64 (+ (* (+ (* x y) z) y) t))
↓
(FPCore (x y z t) :precision binary64 (fma 1.0 (* y (* y x)) (fma y z t)))
double code(double x, double y, double z, double t) {
	return (((x * y) + z) * y) + t;
}
↓
double code(double x, double y, double z, double t) {
	return fma(1.0, (y * (y * x)), fma(y, z, t));
}

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * y) + z) * y) + t)
end
↓
function code(x, y, z, t)
	return fma(1.0, Float64(y * Float64(y * x)), fma(y, z, t))
end

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(1.0 * N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(y * z + t), $MachinePrecision]), $MachinePrecision]

\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(1, y \cdot \left(y \cdot x\right), \mathsf{fma}\left(y, z, t\right)\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.1

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

  2. Applied egg-rr0.1

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

  3. Applied egg-rr0.1

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

  4. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(1, y \cdot \left(y \cdot x\right), \mathsf{fma}\left(y, z, t\right)\right) \]

Reproduce

herbie shell --seed 2022133 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))