Linear.V3:cross from linear-1.19.1.3

Average Error: 0.0 → 0.0

Time: 4.9s

Precision: binary64

Cost: 6784

Math

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

↓

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

FPCore

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

↓

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

C

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 1.3

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot y - z \cdot t}\right)}^{3}} \]

3. Applied egg-rr 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	22.8
Cost	1312

\[\begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{+203}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.662458923303652 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3731142334254816 \cdot 10^{+28}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.50844314280694 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5595230707726897 \cdot 10^{-76}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.0781007639073766 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	31.0
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2022318 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))