Average Error: 38.7 → 0.0
Time: 2.1s
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 r10843 = x;
        double r10844 = 1.0;
        double r10845 = r10843 + r10844;
        double r10846 = r10845 * r10845;
        double r10847 = r10846 - r10844;
        return r10847;
}
↓
double f(double x) {
        double r10848 = x;
        double r10849 = 2.0;
        double r10850 = r10848 + r10849;
        double r10851 = r10848 * r10850;
        return r10851;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.7

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(2 + x\right)}\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))