Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot a + \left(b \cdot b + \left(a \cdot b + a \cdot b\right)\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot a + \left(b \cdot b + \left(a \cdot b + a \cdot b\right)\right)
double f(double a, double b) {
        double r1654130 = a;
        double r1654131 = b;
        double r1654132 = r1654130 + r1654131;
        double r1654133 = r1654132 * r1654132;
        return r1654133;
}
↓
double f(double a, double b) {
        double r1654134 = a;
        double r1654135 = r1654134 * r1654134;
        double r1654136 = b;
        double r1654137 = r1654136 * r1654136;
        double r1654138 = r1654134 * r1654136;
        double r1654139 = r1654138 + r1654138;
        double r1654140 = r1654137 + r1654139;
        double r1654141 = r1654135 + r1654140;
        return r1654141;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 
(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)))