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-rr36.9

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

  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
Error21.2
Cost784
\[\begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4.090502700905202 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.115324874491051 \cdot 10^{-147}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 7.724444194856738 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.0383989643036576 \cdot 10^{-93}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[x \cdot y - z \cdot t \]
Alternative 3
Error30.8
Cost192
\[x \cdot y \]

Error

Reproduce

herbie shell --seed 2022295 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))