Average Error: 0.0 → 0.0
Time: 10.9s
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 r4196316 = a;
        double r4196317 = b;
        double r4196318 = r4196316 + r4196317;
        double r4196319 = r4196318 * r4196318;
        return r4196319;
}
↓
double f(double a, double b) {
        double r4196320 = b;
        double r4196321 = r4196320 * r4196320;
        double r4196322 = a;
        double r4196323 = r4196322 * r4196322;
        double r4196324 = 2.0;
        double r4196325 = r4196322 * r4196324;
        double r4196326 = r4196325 * r4196320;
        double r4196327 = r4196323 + r4196326;
        double r4196328 = r4196321 + r4196327;
        return r4196328;
}

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 2019146 
(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)))