Average Error: 0.0 → 0.0
Time: 6.3s
Precision: binary64
Cost: 7296
\[x \cdot y - z \cdot t \]
↓
\[\left(\mathsf{fma}\left(-t, z, t \cdot z\right) + x \cdot y\right) - t \cdot z \]
(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))
↓
(FPCore (x y z t)
 :precision binary64
 (- (+ (fma (- t) z (* t z)) (* x y)) (* t z)))
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, (t * z)) + (x * y)) - (t * z);
}

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(-t), z, Float64(t * z)) + Float64(x * y)) - Float64(t * z))
end

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

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

Error

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.3

    \[\leadsto \color{blue}{\frac{1}{\frac{1}{x \cdot y - z \cdot t}}} \]

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost6784
\[\mathsf{fma}\left(y, x, t \cdot \left(-z\right)\right) \]
Alternative 2
Error0.0
Cost960
\[t \cdot z + \left(\left(x \cdot y - t \cdot z\right) - t \cdot z\right) \]
Alternative 3
Error21.8
Cost521
\[\begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-114} \lor \neg \left(t \leq 1.45 \cdot 10^{+20}\right):\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
Alternative 4
Error0.0
Cost448
\[x \cdot y - t \cdot z \]
Alternative 5
Error30.6
Cost192
\[x \cdot y \]

Error

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))