Linear.V3:cross from linear-1.19.1.3

Average Accuracy: 100.0% → 100.0%

Time: 3.1s

Precision: binary64

Cost: 6784

Math

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

↓

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

FPCore

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

↓

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

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Simplified 100.0%

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

   [Start] 100.0	\[ x \cdot y - z \cdot t \]
   fma-neg [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(x, y, -z \cdot t\right)} \]
   distribute-rgt-neg-in [=>] 100.0	\[ \mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-t\right)}\right) \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	66.4%
Cost	520

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-110}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Accuracy	100.0%
Cost	448

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

Alternative 3
Accuracy	51.8%
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2023150 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))