(+ (* a c) (* c b))

Average Error: 0.0 → 0.0

Time: 1.0s

Precision: binary64

Math

\[a \cdot c + c \cdot b\]

↓

\[c \cdot \left(b + a\right)\]

C

double code(double a, double c, double b) {
	return ((double) (((double) (a * c)) + ((double) (c * b))));
}

↓

double code(double a, double c, double b) {
	return ((double) (c * ((double) (b + a))));
}

Error

Bits error versus a

Bits error versus c

Bits error versus b

Derivation

1. Initial program 0.0

   \[a \cdot c + c \cdot b\]

2. Simplified 0.0

   \[\leadsto \color{blue}{c \cdot \left(b + a\right)}\]

3. Final simplification 0.0

   \[\leadsto c \cdot \left(b + a\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a c b)
  :name "(+ (* a c) (* c b))"
  :precision binary64
  (+ (* a c) (* c b)))