Average Error: 38.8 → 0.0
Time: 14.9s
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 r9924 = x;
        double r9925 = 1.0;
        double r9926 = r9924 + r9925;
        double r9927 = r9926 * r9926;
        double r9928 = r9927 - r9925;
        return r9928;
}
↓
double f(double x) {
        double r9929 = x;
        double r9930 = 2.0;
        double r9931 = r9929 + r9930;
        double r9932 = r9929 * r9931;
        return r9932;
}

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))