Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(b \cdot b + a \cdot a\right) + \left(a \cdot 2\right) \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(b \cdot b + a \cdot a\right) + \left(a \cdot 2\right) \cdot b
double f(double a, double b) {
        double r3117724 = a;
        double r3117725 = b;
        double r3117726 = r3117724 + r3117725;
        double r3117727 = r3117726 * r3117726;
        return r3117727;
}
↓
double f(double a, double b) {
        double r3117728 = b;
        double r3117729 = r3117728 * r3117728;
        double r3117730 = a;
        double r3117731 = r3117730 * r3117730;
        double r3117732 = r3117729 + r3117731;
        double r3117733 = 2.0;
        double r3117734 = r3117730 * r3117733;
        double r3117735 = r3117734 * r3117728;
        double r3117736 = r3117732 + r3117735;
        return r3117736;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019143 
(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)))