Linear.V3:cross from linear-1.19.1.3

Average Error: 0.0 → 0.0

Time: 36.9s

Precision: binary64

Cost: 6784

Math

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

↓

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

FPCore

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

↓

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

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, (-t * z));
}

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(Float64(-t) * z))
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[((-t) * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

Alternatives

Alternative 1
Error	21.8
Cost	1048

\[\begin{array}{l} t_1 := -t \cdot z\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-149}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	30.7
Cost	192

\[y \cdot x \]

Reproduce

herbie shell --seed 2023033 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))