Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[x \cdot y + z \cdot t \]
↓
\[\mathsf{fma}\left(t, z, y \cdot x\right) \]
(FPCore (x y z t) :precision binary64 (+ (* x y) (* z t)))
↓
(FPCore (x y z t) :precision binary64 (fma t z (* y x)))
double code(double x, double y, double z, double t) {
	return (x * y) + (z * t);
}
↓
double code(double x, double y, double z, double t) {
	return fma(t, z, (y * x));
}

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

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

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot t \]

  2. Simplified0.0

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

  3. Taylor expanded in x around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022150 
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))