Expression 4, p15

Average Error: 0.0 → 0.0

Time: 8.1s

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 r3348190 = a;
        double r3348191 = b;
        double r3348192 = r3348190 + r3348191;
        double r3348193 = r3348192 * r3348192;
        return r3348193;
}

↓

double f(double a, double b) {
        double r3348194 = a;
        double r3348195 = b;
        double r3348196 = r3348195 + r3348194;
        double r3348197 = r3348194 * r3348196;
        double r3348198 = r3348196 * r3348195;
        double r3348199 = r3348197 + r3348198;
        return r3348199;
}

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. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019144 
(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)))