Average Error: 0.0 → 0.0
Time: 5.1s
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 r4003491 = a;
        double r4003492 = b;
        double r4003493 = r4003491 + r4003492;
        double r4003494 = r4003493 * r4003493;
        return r4003494;
}
↓
double f(double a, double b) {
        double r4003495 = b;
        double r4003496 = r4003495 * r4003495;
        double r4003497 = a;
        double r4003498 = r4003497 * r4003497;
        double r4003499 = 2.0;
        double r4003500 = r4003497 * r4003499;
        double r4003501 = r4003500 * r4003495;
        double r4003502 = r4003498 + r4003501;
        double r4003503 = r4003496 + r4003502;
        return r4003503;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 
(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)))