Average Error: 0.0 → 0.0
Time: 19.7s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[b \cdot \left(b + a \cdot 2\right) + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
b \cdot \left(b + a \cdot 2\right) + a \cdot a
double f(double a, double b) {
        double r16008367 = a;
        double r16008368 = b;
        double r16008369 = r16008367 + r16008368;
        double r16008370 = r16008369 * r16008369;
        return r16008370;
}
↓
double f(double a, double b) {
        double r16008371 = b;
        double r16008372 = a;
        double r16008373 = 2.0;
        double r16008374 = r16008372 * r16008373;
        double r16008375 = r16008371 + r16008374;
        double r16008376 = r16008371 * r16008375;
        double r16008377 = r16008372 * r16008372;
        double r16008378 = r16008376 + r16008377;
        return r16008378;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 
(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)))