Average Error: 0.0 → 0.0
Time: 3.5s
Precision: binary64
Cost: 7296
\[x \cdot y - z \cdot t \]
↓
\[\left(\mathsf{fma}\left(-z, t, z \cdot t\right) + x \cdot y\right) - z \cdot t \]
(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))
↓
(FPCore (x y z t)
 :precision binary64
 (- (+ (fma (- z) t (* z t)) (* 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(-z, t, (z * t)) + (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 Float64(Float64(fma(Float64(-z), t, Float64(z * t)) + Float64(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[(N[(N[((-z) * t + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]

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

Error

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost6784
\[\mathsf{fma}\left(y, x, z \cdot \left(-t\right)\right) \]
Alternative 2
Error0.0
Cost6784
\[\mathsf{fma}\left(z, -t, x \cdot y\right) \]
Alternative 3
Error21.4
Cost786
\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-9} \lor \neg \left(z \leq -1.55 \cdot 10^{-28}\right) \land \left(z \leq -3.3 \cdot 10^{-83} \lor \neg \left(z \leq 1.45 \cdot 10^{-80}\right)\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 4
Error0.0
Cost448
\[x \cdot y - z \cdot t \]
Alternative 5
Error31.1
Cost192
\[x \cdot y \]

Error

Reproduce

herbie shell --seed 2023011 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))