Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[b \cdot b + \left(a \cdot a + \left(a \cdot 2\right) \cdot b\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
b \cdot b + \left(a \cdot a + \left(a \cdot 2\right) \cdot b\right)
double f(double a, double b) {
        double r3789725 = a;
        double r3789726 = b;
        double r3789727 = r3789725 + r3789726;
        double r3789728 = r3789727 * r3789727;
        return r3789728;
}
↓
double f(double a, double b) {
        double r3789729 = b;
        double r3789730 = r3789729 * r3789729;
        double r3789731 = a;
        double r3789732 = r3789731 * r3789731;
        double r3789733 = 2.0;
        double r3789734 = r3789731 * r3789733;
        double r3789735 = r3789734 * r3789729;
        double r3789736 = r3789732 + r3789735;
        double r3789737 = r3789730 + r3789736;
        return r3789737;
}

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 -inf 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019138 
(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)))