?

Average Error: 0.0 → 0.0
Time: 3.2s
Precision: binary64
Cost: 6784

?

\[x \cdot y - z \cdot t \]
↓
\[\mathsf{fma}\left(y, x, z \cdot \left(-t\right)\right) \]
(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))
↓
(FPCore (x y z t) :precision binary64 (fma y x (* 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(y, x, (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(y, x, Float64(z * Float64(-t)))
end

code[x_, y_, z_, t_] := N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(y * x + N[(z * (-t)), $MachinePrecision]), $MachinePrecision]

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

Error?

Derivation?

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error23.0
Cost1315
\[\begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-160}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-157} \lor \neg \left(y \leq 1.25 \cdot 10^{-111}\right) \land \left(y \leq 2.05 \cdot 10^{-41} \lor \neg \left(y \leq 1.4 \cdot 10^{-11}\right) \land \left(y \leq 1600000000000 \lor \neg \left(y \leq 8.8 \cdot 10^{+24}\right) \land y \leq 8.5 \cdot 10^{+41}\right)\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[y \cdot x - z \cdot t \]
Alternative 3
Error30.7
Cost192
\[y \cdot x \]

Error

Reproduce?

herbie shell --seed 2023039 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))