Average Error: 0.0 → 0.0
Time: 6.0s
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 r104329 = a;
        double r104330 = b;
        double r104331 = r104329 + r104330;
        double r104332 = r104331 * r104331;
        return r104332;
}
↓
double f(double a, double b) {
        double r104333 = b;
        double r104334 = 2.0;
        double r104335 = a;
        double r104336 = r104334 * r104335;
        double r104337 = r104336 + r104333;
        double r104338 = r104333 * r104337;
        double r104339 = r104335 * r104335;
        double r104340 = r104338 + r104339;
        return r104340;
}

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 2020045 
(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)))