Average Error: 39.6 → 0.0
Time: 4.4s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + 2 \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + 2 \cdot x
double f(double x) {
        double r10977 = x;
        double r10978 = 1.0;
        double r10979 = r10977 + r10978;
        double r10980 = r10979 * r10979;
        double r10981 = r10980 - r10978;
        return r10981;
}
↓
double f(double x) {
        double r10982 = x;
        double r10983 = r10982 * r10982;
        double r10984 = 2.0;
        double r10985 = r10984 * r10982;
        double r10986 = r10983 + r10985;
        return r10986;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.6

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

  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. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

    \[\leadsto x \cdot x + 2 \cdot x\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))