Expression 4, p15

Average Error: 0.0 → 0.0

Time: 8.2s

Precision: 64

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

Math

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

↓

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

C

double f(double a, double b) {
        double r4449733 = a;
        double r4449734 = b;
        double r4449735 = r4449733 + r4449734;
        double r4449736 = r4449735 * r4449735;
        return r4449736;
}

↓

double f(double a, double b) {
        double r4449737 = a;
        double r4449738 = b;
        double r4449739 = r4449738 + r4449737;
        double r4449740 = r4449737 * r4449739;
        double r4449741 = r4449739 * r4449738;
        double r4449742 = r4449740 + r4449741;
        return r4449742;
}

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-lft-in 0.0

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

4. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019158 
(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)))