Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot a + b \cdot \left(2 \cdot a + b\right)\]
\left(a + b\right) \cdot \left(a + b\right)
↓
a \cdot a + b \cdot \left(2 \cdot a + b\right)
double f(double a, double b) {
        double r59930 = a;
        double r59931 = b;
        double r59932 = r59930 + r59931;
        double r59933 = r59932 * r59932;
        return r59933;
}
↓
double f(double a, double b) {
        double r59934 = a;
        double r59935 = r59934 * r59934;
        double r59936 = b;
        double r59937 = 2.0;
        double r59938 = r59937 * r59934;
        double r59939 = r59938 + r59936;
        double r59940 = r59936 * r59939;
        double r59941 = r59935 + r59940;
        return r59941;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5.0 a 10.0) (<= 0.0 b 0.001))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))