Average Error: 0.0 → 0.0
Time: 33.1s
Precision: 64
\[5 \le a \le 10 \land 0 \le b \le 0.001\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot a + \left(b \cdot b + \left(a \cdot b + a \cdot b\right)\right)\]
\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 r2222348 = a;
        double r2222349 = b;
        double r2222350 = r2222348 + r2222349;
        double r2222351 = r2222350 * r2222350;
        return r2222351;
}
↓
double f(double a, double b) {
        double r2222352 = a;
        double r2222353 = r2222352 * r2222352;
        double r2222354 = b;
        double r2222355 = r2222354 * r2222354;
        double r2222356 = r2222352 * r2222354;
        double r2222357 = r2222356 + r2222356;
        double r2222358 = r2222355 + r2222357;
        double r2222359 = r2222353 + r2222358;
        return r2222359;
}

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

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

  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 2019151 
(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)))