?

Average Error: 0.0 → 0.0
Time: 12.8s
Precision: binary64
Cost: 6720

?

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

Derivation?

  1. Initial program 0.0

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

  2. Simplified0.0

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

Alternatives

Alternative 1
Error17.6
Cost1112
\[\begin{array}{l} t_0 := -4 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -9 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[x - \left(y \cdot 4\right) \cdot z \]
Alternative 3
Error27.4
Cost64
\[x \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))