Average Error: 38.9 → 0.0
Time: 4.2s
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 r10984 = x;
        double r10985 = 1.0;
        double r10986 = r10984 + r10985;
        double r10987 = r10986 * r10986;
        double r10988 = r10987 - r10985;
        return r10988;
}
↓
double f(double x) {
        double r10989 = x;
        double r10990 = 2.0;
        double r10991 = r10989 + r10990;
        double r10992 = r10989 * r10991;
        return r10992;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.9

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

  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 2019209 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))