(+ (* x z) (* y z))

Average Error: 0.0 → 0.0

Time: 1.0s

Precision: binary64

Math

\[x \cdot z + y \cdot z\]

↓

\[z \cdot \left(x + y\right)\]

C

double code(double x, double z, double y) {
	return ((double) (((double) (x * z)) + ((double) (y * z))));
}

↓

double code(double x, double z, double y) {
	return ((double) (z * ((double) (x + y))));
}

Error

Bits error versus x

Bits error versus z

Bits error versus y

Derivation

1. Initial program 0.0

   \[x \cdot z + y \cdot z\]

2. Simplified 0.0

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

3. Final simplification 0.0

   \[\leadsto z \cdot \left(x + y\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x z y)
  :name "(+ (* x z) (* y z))"
  :precision binary64
  (+ (* x z) (* y z)))