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

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. Using strategy rm

  3. Applied fma-neg_binary640.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021211 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))