Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[5.0 \le a \le 10.0 \land 0.0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(b \cdot a + b \cdot a\right) + \left(b \cdot b + a \cdot a\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(b \cdot a + b \cdot a\right) + \left(b \cdot b + a \cdot a\right)
double f(double a, double b) {
        double r5312539 = a;
        double r5312540 = b;
        double r5312541 = r5312539 + r5312540;
        double r5312542 = r5312541 * r5312541;
        return r5312542;
}
↓
double f(double a, double b) {
        double r5312543 = b;
        double r5312544 = a;
        double r5312545 = r5312543 * r5312544;
        double r5312546 = r5312545 + r5312545;
        double r5312547 = r5312543 * r5312543;
        double r5312548 = r5312544 * r5312544;
        double r5312549 = r5312547 + r5312548;
        double r5312550 = r5312546 + r5312549;
        return r5312550;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(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)))