Average Error: 0.0 → 0.0
Time: 2.3s
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 r124469 = a;
        double r124470 = b;
        double r124471 = r124469 + r124470;
        double r124472 = r124471 * r124471;
        return r124472;
}
↓
double f(double a, double b) {
        double r124473 = a;
        double r124474 = 2.0;
        double r124475 = pow(r124473, r124474);
        double r124476 = b;
        double r124477 = r124473 * r124476;
        double r124478 = r124474 * r124477;
        double r124479 = pow(r124476, r124474);
        double r124480 = r124478 + r124479;
        double r124481 = r124475 + r124480;
        return r124481;
}

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 distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  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 2020001 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5 a 10) (<= 0.0 b 0.001))

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

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