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

Average Accuracy: 100.0% → 100.0%

Time: 2.9s

Precision: binary64

Cost: 6720

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(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 100.0%

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

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ x \cdot y + z \cdot t \]
   +-commutative [=>] 100.0	\[ \color{blue}{z \cdot t + x \cdot y} \]
   fma-def [=>] 100.0	\[ \color{blue}{\mathsf{fma}\left(z, t, x \cdot y\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	66.0%
Cost	721

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+261}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+249} \lor \neg \left(x \leq -9 \cdot 10^{-19}\right) \land x \leq 4 \cdot 10^{-95}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Accuracy	100.0%
Cost	448

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

Alternative 3
Accuracy	52.7%
Cost	192

\[z \cdot t \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))