Expression 4, p15

Average Error: 0.0 → 0.0

Time: 16.6s

Precision: 64

\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]

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 r4042233 = a;
        double r4042234 = b;
        double r4042235 = r4042233 + r4042234;
        double r4042236 = r4042235 * r4042235;
        return r4042236;
}

↓

double f(double a, double b) {
        double r4042237 = a;
        double r4042238 = b;
        double r4042239 = r4042237 + r4042238;
        double r4042240 = r4042239 * r4042239;
        return r4042240;
}

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 2019200 +o rules:numerics
(FPCore (a b)
  :name "Expression 4, p15"
  :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)))