Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
Cost: 6784
\[x \cdot y - z \cdot t \]
↓
\[\mathsf{fma}\left(-z, t, x \cdot y\right) \]
(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(Float64(-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-rr36.8

    \[\leadsto \color{blue}{\sqrt[3]{{\left(x \cdot y - z \cdot t\right)}^{3}}} \]

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error21.6
Cost520
\[\begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -3.5591429229600293 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4206611900428636 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[x \cdot y - z \cdot t \]
Alternative 3
Error30.8
Cost192
\[x \cdot y \]

Error

Reproduce

herbie shell --seed 2022308 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))