Average Error: 38.8 → 0.0
Time: 17.9s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(x + 2\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(x + 2\right)
double f(double x) {
        double r3643 = x;
        double r3644 = 1.0;
        double r3645 = r3643 + r3644;
        double r3646 = r3645 * r3645;
        double r3647 = r3646 - r3644;
        return r3647;
}
↓
double f(double x) {
        double r3648 = x;
        double r3649 = 2.0;
        double r3650 = r3648 + r3649;
        double r3651 = r3648 * r3650;
        return r3651;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} + 2 \cdot x}\]

  3. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto x \cdot \left(x + 2\right)\]

Reproduce

herbie shell --seed 2019351 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))