Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
\[\left(x + y\right) \cdot z \]
↓
\[\mathsf{fma}\left(x, z, z \cdot y\right) \]
(FPCore (x y z) :precision binary64 (* (+ x y) z))
↓
(FPCore (x y z) :precision binary64 (fma x z (* z y)))
double code(double x, double y, double z) {
	return (x + y) * z;
}
↓
double code(double x, double y, double z) {
	return fma(x, z, (z * y));
}

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{y \cdot z + z \cdot x} \]

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022150 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))