Average Error: 0.0 → 0.0
Time: 26.3s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(b \cdot b + a \cdot a\right) + \left(a \cdot 2\right) \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(b \cdot b + a \cdot a\right) + \left(a \cdot 2\right) \cdot b
double f(double a, double b) {
        double r9269267 = a;
        double r9269268 = b;
        double r9269269 = r9269267 + r9269268;
        double r9269270 = r9269269 * r9269269;
        return r9269270;
}
↓
double f(double a, double b) {
        double r9269271 = b;
        double r9269272 = r9269271 * r9269271;
        double r9269273 = a;
        double r9269274 = r9269273 * r9269273;
        double r9269275 = r9269272 + r9269274;
        double r9269276 = 2.0;
        double r9269277 = r9269273 * r9269276;
        double r9269278 = r9269277 * r9269271;
        double r9269279 = r9269275 + r9269278;
        return r9269279;
}

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

    \[\leadsto \color{blue}{b \cdot \left(a \cdot 2 + b\right) + a \cdot a}\]
  4. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019104 
(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)))