Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(2 \cdot a + b\right) \cdot b + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(2 \cdot a + b\right) \cdot b + a \cdot a
double f(double a, double b) {
        double r14457435 = a;
        double r14457436 = b;
        double r14457437 = r14457435 + r14457436;
        double r14457438 = r14457437 * r14457437;
        return r14457438;
}
↓
double f(double a, double b) {
        double r14457439 = 2.0;
        double r14457440 = a;
        double r14457441 = r14457439 * r14457440;
        double r14457442 = b;
        double r14457443 = r14457441 + r14457442;
        double r14457444 = r14457443 * r14457442;
        double r14457445 = r14457440 * r14457440;
        double r14457446 = r14457444 + r14457445;
        return r14457446;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(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)))