Expression 4, p15

Average Error: 0.0 → 0.0

Time: 7.5s

Precision: 64

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

Math

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

↓

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

C

double f(double a, double b) {
        double r4451862 = a;
        double r4451863 = b;
        double r4451864 = r4451862 + r4451863;
        double r4451865 = r4451864 * r4451864;
        return r4451865;
}

↓

double f(double a, double b) {
        double r4451866 = a;
        double r4451867 = r4451866 * r4451866;
        double r4451868 = b;
        double r4451869 = r4451866 + r4451868;
        double r4451870 = r4451869 + r4451866;
        double r4451871 = r4451870 * r4451868;
        double r4451872 = r4451867 + r4451871;
        return r4451872;
}

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. Using strategy rm

3. Applied distribute-rgt-in 0.0

   \[\leadsto \color{blue}{a \cdot \left(a + b\right) + b \cdot \left(a + b\right)}\]
4. Using strategy rm

5. Applied distribute-rgt-in 0.0

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

6. Applied associate-+l+ 0.0

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

7. Simplified 0.0

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

8. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019129 
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5 a 10) (<= 0 b 0.001))

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

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