Average Error: 0.0 → 0.0
Time: 8.2s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(\left(b \cdot a + b \cdot a\right) + a \cdot a\right) + b \cdot b\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(\left(b \cdot a + b \cdot a\right) + a \cdot a\right) + b \cdot b
double f(double a, double b) {
        double r4188957 = a;
        double r4188958 = b;
        double r4188959 = r4188957 + r4188958;
        double r4188960 = r4188959 * r4188959;
        return r4188960;
}
↓
double f(double a, double b) {
        double r4188961 = b;
        double r4188962 = a;
        double r4188963 = r4188961 * r4188962;
        double r4188964 = r4188963 + r4188963;
        double r4188965 = r4188962 * r4188962;
        double r4188966 = r4188964 + r4188965;
        double r4188967 = r4188961 * r4188961;
        double r4188968 = r4188966 + r4188967;
        return r4188968;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(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)))