Average Error: 0.0 → 0.0
Time: 8.1s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(a \cdot a + b \cdot b\right) + \left(a \cdot b + a \cdot b\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(a \cdot a + b \cdot b\right) + \left(a \cdot b + a \cdot b\right)
double f(double a, double b) {
        double r11566638 = a;
        double r11566639 = b;
        double r11566640 = r11566638 + r11566639;
        double r11566641 = r11566640 * r11566640;
        return r11566641;
}
↓
double f(double a, double b) {
        double r11566642 = a;
        double r11566643 = r11566642 * r11566642;
        double r11566644 = b;
        double r11566645 = r11566644 * r11566644;
        double r11566646 = r11566643 + r11566645;
        double r11566647 = r11566642 * r11566644;
        double r11566648 = r11566647 + r11566647;
        double r11566649 = r11566646 + r11566648;
        return r11566649;
}

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

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(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)))