Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(b \cdot 2 + a\right) \cdot a + b \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(b \cdot 2 + a\right) \cdot a + b \cdot b
double f(double a, double b) {
        double r4430322 = a;
        double r4430323 = b;
        double r4430324 = r4430322 + r4430323;
        double r4430325 = r4430324 * r4430324;
        return r4430325;
}
↓
double f(double a, double b) {
        double r4430326 = b;
        double r4430327 = 2.0;
        double r4430328 = r4430326 * r4430327;
        double r4430329 = a;
        double r4430330 = r4430328 + r4430329;
        double r4430331 = r4430330 * r4430329;
        double r4430332 = r4430326 * r4430326;
        double r4430333 = r4430331 + r4430332;
        return r4430333;
}

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 0 0.0

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

  3. Simplified0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Applied associate-+r+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(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)))