Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
Cost: 6720
\[x \cdot y + z \cdot t \]
↓
\[\mathsf{fma}\left(z, t, x \cdot y\right) \]
(FPCore (x y z t) :precision binary64 (+ (* x y) (* z t)))
↓
(FPCore (x y z t) :precision binary64 (fma z t (* x y)))
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));
}

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

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]

x \cdot y + z \cdot t
↓
\mathsf{fma}\left(z, t, x \cdot y\right)

Error

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error23.0
Cost984
\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-152}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-69}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-42}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+78}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[x \cdot y + z \cdot t \]
Alternative 3
Error30.3
Cost192
\[z \cdot t \]

Error

Reproduce

herbie shell --seed 2022332 
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))