Expression 4, p15

Average Error: 0.0 → 0.0

Time: 2.3s

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 r105122 = a;
        double r105123 = b;
        double r105124 = r105122 + r105123;
        double r105125 = r105124 * r105124;
        return r105125;
}

↓

double f(double a, double b) {
        double r105126 = a;
        double r105127 = b;
        double r105128 = r105126 + r105127;
        double r105129 = r105128 * r105128;
        return r105129;
}

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 2020083 
(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)))