Average Error: 0.0 → 0.0
Time: 4.6s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[b \cdot b + a \cdot \left(a + 2 \cdot b\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
b \cdot b + a \cdot \left(a + 2 \cdot b\right)
double f(double a, double b) {
        double r1790489 = a;
        double r1790490 = b;
        double r1790491 = r1790489 + r1790490;
        double r1790492 = r1790491 * r1790491;
        return r1790492;
}
↓
double f(double a, double b) {
        double r1790493 = b;
        double r1790494 = r1790493 * r1790493;
        double r1790495 = a;
        double r1790496 = 2.0;
        double r1790497 = r1790496 * r1790493;
        double r1790498 = r1790495 + r1790497;
        double r1790499 = r1790495 * r1790498;
        double r1790500 = r1790494 + r1790499;
        return r1790500;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(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)))