Average Error: 0.0 → 0.0
Time: 12.7s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[b \cdot \left(a + b\right) + \left(a \cdot a + a \cdot b\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
b \cdot \left(a + b\right) + \left(a \cdot a + a \cdot b\right)
double f(double a, double b) {
        double r4151458 = a;
        double r4151459 = b;
        double r4151460 = r4151458 + r4151459;
        double r4151461 = r4151460 * r4151460;
        return r4151461;
}
↓
double f(double a, double b) {
        double r4151462 = b;
        double r4151463 = a;
        double r4151464 = r4151463 + r4151462;
        double r4151465 = r4151462 * r4151464;
        double r4151466 = r4151463 * r4151463;
        double r4151467 = r4151463 * r4151462;
        double r4151468 = r4151466 + r4151467;
        double r4151469 = r4151465 + r4151468;
        return r4151469;
}

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-rgt-in0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019139 
(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)))