Average Error: 38.8 → 0.0
Time: 16.0s
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 r9931 = x;
        double r9932 = 1.0;
        double r9933 = r9931 + r9932;
        double r9934 = r9933 * r9933;
        double r9935 = r9934 - r9932;
        return r9935;
}
↓
double f(double x) {
        double r9936 = x;
        double r9937 = 2.0;
        double r9938 = r9936 + r9937;
        double r9939 = r9936 * r9938;
        return r9939;
}

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 2019326 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))