Average Error: 0.0 → 0.0
Time: 2.6s
Precision: binary64
Cost: 6720
\[x \cdot y + z \cdot t \]
↓
\[\mathsf{fma}\left(x, y, z \cdot t\right) \]
(FPCore (x y z t) :precision binary64 (+ (* x y) (* z t)))
↓
(FPCore (x y z t) :precision binary64 (fma x y (* z t)))
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));
}

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

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]

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

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} \]
    Proof
    (fma.f64 x y (*.f64 z t)): 0 points increase in error, 0 points decrease in error
    (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x y) (*.f64 z t))): 0 points increase in error, 0 points decrease in error

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error24.0
Cost1251
\[\begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-133}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-102} \lor \neg \left(t \leq 1.55 \cdot 10^{-27}\right) \land \left(t \leq 900000000000 \lor \neg \left(t \leq 2.5 \cdot 10^{+61}\right) \land \left(t \leq 2.5 \cdot 10^{+94} \lor \neg \left(t \leq 1.1 \cdot 10^{+209}\right) \land t \leq 1.08 \cdot 10^{+247}\right)\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[z \cdot t + x \cdot y \]
Alternative 3
Error31.0
Cost192
\[z \cdot t \]

Error

Reproduce

herbie shell --seed 2022340 
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))