Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[5 \le a \le 10 \land 0.0 \le b \le 0.001000000000000000020816681711721685132943\]
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[\left(a \cdot 2 + b\right) \cdot b + a \cdot a\]
\left(a + b\right) \cdot \left(a + b\right)
↓
\left(a \cdot 2 + b\right) \cdot b + a \cdot a
double f(double a, double b) {
        double r66447 = a;
        double r66448 = b;
        double r66449 = r66447 + r66448;
        double r66450 = r66449 * r66449;
        return r66450;
}
↓
double f(double a, double b) {
        double r66451 = a;
        double r66452 = 2.0;
        double r66453 = r66451 * r66452;
        double r66454 = b;
        double r66455 = r66453 + r66454;
        double r66456 = r66455 * r66454;
        double r66457 = r66451 * r66451;
        double r66458 = r66456 + r66457;
        return r66458;
}

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. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))