Linear.V3:cross from linear-1.19.1.3

Average Error: 0.03% → 0.01%

Time: 3.0s

Precision: binary64

Cost: 6784

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (fma y x (* 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(y, x, (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(y, x, 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[(y * x + N[(z * (-t)), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.03

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

2. Applied egg-rr 0.01

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

3. Final simplification 0.01

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

Alternatives

Alternative 1
Error	36.07%
Cost	1050

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-114}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-198} \lor \neg \left(y \leq 2.6 \cdot 10^{-161}\right) \land \left(y \leq 1.8 \cdot 10^{+23} \lor \neg \left(y \leq 6.5 \cdot 10^{+56}\right) \land y \leq 8.5 \cdot 10^{+92}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	0.03%
Cost	448

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

Alternative 3
Error	48.39%
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))