Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
{a}^{2} + \left(2 \cdot \left(a \cdot b\right) + {b}^{2}\right)
double f(double a, double b) {
        double r92585 = a;
        double r92586 = b;
        double r92587 = r92585 + r92586;
        double r92588 = r92587 * r92587;
        return r92588;
}
↓
double f(double a, double b) {
        double r92589 = a;
        double r92590 = 2.0;
        double r92591 = pow(r92589, r92590);
        double r92592 = b;
        double r92593 = r92589 * r92592;
        double r92594 = r92590 * r92593;
        double r92595 = pow(r92592, r92590);
        double r92596 = r92594 + r92595;
        double r92597 = r92591 + r92596;
        return r92597;
}

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. Using strategy rm

  3. Applied flip-+0.0

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

  4. Applied associate-*r/0.1

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

  5. Simplified0.1

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

  6. Taylor expanded around 0 0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5 a 10) (<= 0.0 b 1e-3))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))