Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot a + \left(b \cdot b + \left(a \cdot b + a \cdot b\right)\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot a + \left(b \cdot b + \left(a \cdot b + a \cdot b\right)\right)
double f(double a, double b) {
        double r1797489 = a;
        double r1797490 = b;
        double r1797491 = r1797489 + r1797490;
        double r1797492 = r1797491 * r1797491;
        return r1797492;
}
↓
double f(double a, double b) {
        double r1797493 = a;
        double r1797494 = r1797493 * r1797493;
        double r1797495 = b;
        double r1797496 = r1797495 * r1797495;
        double r1797497 = r1797493 * r1797495;
        double r1797498 = r1797497 + r1797497;
        double r1797499 = r1797496 + r1797498;
        double r1797500 = r1797494 + r1797499;
        return r1797500;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(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)))