Expression 4, p15

Average Error: 0.0 → 0.0

Time: 1.4s

Precision: binary64

\[5 \leq a \land a \leq 10 \land 0 \leq b \land b \leq 0.001\]

Math

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

↓

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

C

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

↓

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

Error

Bits error versus a

Bits error versus b

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020196 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5.0 a 10.0) (<= 0.0 b 0.001))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

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