Expression 4, p15

Average Error: 0.0 → 0.0

Time: 2.9s

Precision: 64

\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]

Math

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

↓

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

C

double f(double a, double b) {
        double r100454 = a;
        double r100455 = b;
        double r100456 = r100454 + r100455;
        double r100457 = r100456 * r100456;
        return r100457;
}

↓

double f(double a, double b) {
        double r100458 = a;
        double r100459 = b;
        double r100460 = r100458 + r100459;
        double r100461 = r100460 * r100460;
        return r100461;
}

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 2020035 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5 a 10) (<= 0.0 b 0.001))

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

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