Average Error: 0.0 → 0.0

Time: 4.0s

Precision: binary64

Cost: 6784

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

↓

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

(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))

↓

(FPCore (x y z t) :precision binary64 (fma y x (- (* z t))))

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(y, x, -(z * t));
}

function code(x, y, z, t)
	return Float64(Float64(x * y) - Float64(z * t))
end

↓

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

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

↓

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

x \cdot y - z \cdot t

↓

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

Derivation

Initial program 0.0
\[x \cdot y - z \cdot t \]
Applied egg-rr0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -z \cdot t\right)} \]

Alternatives

Alternative 1
Error	14.9
Cost	776

\[\begin{array}{l} t_1 := -z \cdot t\\ \mathbf{if}\;z \cdot t \leq -2.6 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	30.5
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))