Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)
double f(double a, double b) {
        double r80785 = a;
        double r80786 = b;
        double r80787 = r80785 + r80786;
        double r80788 = r80787 * r80787;
        return r80788;
}
↓
double f(double a, double b) {
        double r80789 = a;
        double r80790 = 2.0;
        double r80791 = pow(r80789, r80790);
        double r80792 = b;
        double r80793 = r80789 * r80792;
        double r80794 = r80790 * r80793;
        double r80795 = pow(r80792, r80790);
        double r80796 = r80794 + r80795;
        double r80797 = r80791 + r80796;
        return r80797;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a\]

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)}\]

  3. Final simplification0.0

    \[\leadsto {a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)\]

Reproduce

herbie shell --seed 2019304 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5 a 10) (<= 0.0 b 1e-3))

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

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