Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[x - \left(y \cdot 4\right) \cdot z \]
↓
\[\mathsf{fma}\left(y, z \cdot -4, x\right) \]
(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))
↓
(FPCore (x y z) :precision binary64 (fma y (* z -4.0) x))
double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}
↓
double code(double x, double y, double z) {
	return fma(y, (z * -4.0), x);
}

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end
↓
function code(x, y, z)
	return fma(y, Float64(z * -4.0), x)
end

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_] := N[(y * N[(z * -4.0), $MachinePrecision] + x), $MachinePrecision]

x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(y, z \cdot -4, x\right)

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x - \left(y \cdot 4\right) \cdot z \]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot -4, x\right)} \]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, z \cdot -4, x\right) \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))