Average Error: 0.0 → 0.0
Time: 6.5s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(\left(b \cdot a + b \cdot a\right) + a \cdot a\right) + b \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(\left(b \cdot a + b \cdot a\right) + a \cdot a\right) + b \cdot b
double f(double a, double b) {
        double r4762931 = a;
        double r4762932 = b;
        double r4762933 = r4762931 + r4762932;
        double r4762934 = r4762933 * r4762933;
        return r4762934;
}
↓
double f(double a, double b) {
        double r4762935 = b;
        double r4762936 = a;
        double r4762937 = r4762935 * r4762936;
        double r4762938 = r4762937 + r4762937;
        double r4762939 = r4762936 * r4762936;
        double r4762940 = r4762938 + r4762939;
        double r4762941 = r4762935 * r4762935;
        double r4762942 = r4762940 + r4762941;
        return r4762942;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(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)))