Average Error: 0.0 → 0.0
Time: 33.1s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[b \cdot \left(b + a \cdot 2\right) + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
b \cdot \left(b + a \cdot 2\right) + a \cdot a
double f(double a, double b) {
        double r14988246 = a;
        double r14988247 = b;
        double r14988248 = r14988246 + r14988247;
        double r14988249 = r14988248 * r14988248;
        return r14988249;
}
↓
double f(double a, double b) {
        double r14988250 = b;
        double r14988251 = a;
        double r14988252 = 2.0;
        double r14988253 = r14988251 * r14988252;
        double r14988254 = r14988250 + r14988253;
        double r14988255 = r14988250 * r14988254;
        double r14988256 = r14988251 * r14988251;
        double r14988257 = r14988255 + r14988256;
        return r14988257;
}

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 -inf 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019124 
(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)))