Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[x \cdot y - z \cdot t \]
↓
\[\mathsf{fma}\left(x, y, -t \cdot z\right) + \mathsf{fma}\left(-t, z, t \cdot z\right) \]
x \cdot y - z \cdot t
↓
\mathsf{fma}\left(x, y, -t \cdot z\right) + \mathsf{fma}\left(-t, z, t \cdot z\right)

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

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 prod-diff_binary640.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021275 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))