Average Error: 0.0 → 0.0
Time: 2.3s
Precision: binary64
Cost: 6784
\[x \cdot y - z \cdot t \]
↓
\[\mathsf{fma}\left(t, -z, y \cdot x\right) \]
(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))
↓
(FPCore (x y z t) :precision binary64 (fma t (- z) (* y x)))
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(t, -z, (y * x));
}

function code(x, y, z, t)
	return Float64(Float64(x * y) - Float64(z * t))
end
↓
function code(x, y, z, t)
	return fma(t, Float64(-z), Float64(y * x))
end

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

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

Error

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{-1 \cdot \left(t \cdot z\right) + y \cdot x} \]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error21.5
Cost520
\[\begin{array}{l} \mathbf{if}\;x \leq -13337.671259625457:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.536379374977104 \cdot 10^{-87}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[y \cdot x - t \cdot z \]
Alternative 3
Error30.5
Cost192
\[y \cdot x \]

Error

Reproduce

herbie shell --seed 2022228 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))