Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[b \cdot \left(2 \cdot a + b\right) + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
b \cdot \left(2 \cdot a + b\right) + a \cdot a
double f(double a, double b) {
        double r69737 = a;
        double r69738 = b;
        double r69739 = r69737 + r69738;
        double r69740 = r69739 * r69739;
        return r69740;
}
↓
double f(double a, double b) {
        double r69741 = b;
        double r69742 = 2.0;
        double r69743 = a;
        double r69744 = r69742 * r69743;
        double r69745 = r69744 + r69741;
        double r69746 = r69741 * r69745;
        double r69747 = r69743 * r69743;
        double r69748 = r69746 + r69747;
        return r69748;
}

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

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5 a 10) (<= 0.0 b 0.001))

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

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