Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[x \cdot y - z \cdot t \]
↓
\[\mathsf{fma}\left(t, -z, x \cdot y\right) \]
x \cdot y - z \cdot t
↓
\mathsf{fma}\left(t, -z, x \cdot y\right)

(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))
↓
(FPCore (x y z t) :precision binary64 (fma t (- z) (* 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(t, -z, (x * y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr32.2

    \[\leadsto \color{blue}{{\left(\sqrt{x \cdot y - z \cdot t}\right)}^{2}} \]

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022130 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))