Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot a + b \cdot \left(b + 2 \cdot a\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot a + b \cdot \left(b + 2 \cdot a\right)
double f(double a, double b) {
        double r3373678 = a;
        double r3373679 = b;
        double r3373680 = r3373678 + r3373679;
        double r3373681 = r3373680 * r3373680;
        return r3373681;
}
↓
double f(double a, double b) {
        double r3373682 = a;
        double r3373683 = r3373682 * r3373682;
        double r3373684 = b;
        double r3373685 = 2.0;
        double r3373686 = r3373685 * r3373682;
        double r3373687 = r3373684 + r3373686;
        double r3373688 = r3373684 * r3373687;
        double r3373689 = r3373683 + r3373688;
        return r3373689;
}

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. Taylor expanded around -inf 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019135 
(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)))