Linear.V2:$cdot from linear-1.19.1.3, A

Average Error: 0.0 → 0.0

Time: 1.9s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6720

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

Alternative 2
Error	21.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+97}:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;z \leq -1.3341255195551827 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -1455.9242130524867:\\ \;\;\;\;t \cdot z\\ \mathbf{elif}\;z \leq 1.5099846677011274 \cdot 10^{-93}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot z\\ \end{array} \]

Alternative 3
Error	0.0
Cost	448

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

Alternative 4
Error	31.3
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))