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

Percentage Accurate: 99.3% → 99.6%

Time: 2.9s

Precision: binary64

Cost: 6720

• Unsound rule application detected in e-graph. Results may not be sound.

• 22.7% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

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 * 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 99.2%

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

2. Simplified 100.0%

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

   [Start] 99.2%	\[ x \cdot y + z \cdot t \]
   fma-def [=>] 100.0%	\[ \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	99.6%
Cost	6720

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

Alternative 2
Accuracy	68.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+30}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3
Accuracy	99.3%
Cost	448

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

Alternative 4
Accuracy	51.0%
Cost	192

\[z \cdot t \]

Reproduce

herbie shell --seed 2023272 
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))