Average Error: 0.0 → 0.0
Time: 6.3s
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 r3655384 = a;
        double r3655385 = b;
        double r3655386 = r3655384 + r3655385;
        double r3655387 = r3655386 * r3655386;
        return r3655387;
}
↓
double f(double a, double b) {
        double r3655388 = b;
        double r3655389 = r3655388 * r3655388;
        double r3655390 = a;
        double r3655391 = 2.0;
        double r3655392 = r3655391 * r3655388;
        double r3655393 = r3655390 + r3655392;
        double r3655394 = r3655390 * r3655393;
        double r3655395 = r3655389 + r3655394;
        return r3655395;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019132 
(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)))